spotbugs-exclude.xml
true
diff --git a/src/main/java/com/thealgorithms/datastructures/trees/SegmentTree2D.java b/src/main/java/com/thealgorithms/datastructures/trees/SegmentTree2D.java
new file mode 100644
index 000000000000..40b9e8a73533
--- /dev/null
+++ b/src/main/java/com/thealgorithms/datastructures/trees/SegmentTree2D.java
@@ -0,0 +1,201 @@
+package com.thealgorithms.datastructures.trees;
+
+/**
+ * 2D Segment Tree (Tree of Trees) implementation.
+ * This data structure supports point updates and submatrix sum queries
+ * in a 2D grid. It achieves this by nesting 1D Segment Trees within a 1D Segment Tree.
+ *
+ * Time Complexity:
+ * - Build/Initialization: O(N * M)
+ * - Point Update: O(log N * log M)
+ * - Submatrix Query: O(log N * log M)
+ *
+ * @see 2D Segment Tree
+ */
+public class SegmentTree2D {
+
+ /**
+ * Represents a 1D Segment Tree.
+ * This is equivalent to your 'Sagara' struct. It manages the columns (X-axis).
+ */
+ public static class SegmentTree1D {
+ private int n;
+ private final int[] tree;
+
+ /**
+ * Initializes the 1D Segment Tree with the nearest power of 2.
+ *
+ * @param size The expected number of elements (columns).
+ */
+ public SegmentTree1D(int size) {
+ n = 1;
+ while (n < size) {
+ n *= 2;
+ }
+ tree = new int[n * 2];
+ }
+
+ /**
+ * Recursively updates a point in the 1D tree.
+ */
+ private void update(int index, int val, int node, int lx, int rx) {
+ if (rx - lx == 1) {
+ tree[node] = val;
+ return;
+ }
+
+ int mid = lx + (rx - lx) / 2;
+ int leftChild = node * 2 + 1;
+ int rightChild = node * 2 + 2;
+
+ if (index < mid) {
+ update(index, val, leftChild, lx, mid);
+ } else {
+ update(index, val, rightChild, mid, rx);
+ }
+
+ tree[node] = tree[leftChild] + tree[rightChild];
+ }
+
+ /**
+ * Public wrapper to update a specific index.
+ *
+ * @param index The column index to update.
+ * @param val The new value.
+ */
+ public void update(int index, int val) {
+ update(index, val, 0, 0, n);
+ }
+
+ /**
+ * Retrieves the exact value at a specific leaf node.
+ *
+ * @param index The column index.
+ * @return The value at the given index.
+ */
+ public int get(int index) {
+ return query(index, index + 1, 0, 0, n);
+ }
+
+ /**
+ * Recursively queries the sum in a 1D range.
+ */
+ private int query(int l, int r, int node, int lx, int rx) {
+ if (lx >= r || rx <= l) {
+ return 0; // Out of bounds
+ }
+ if (lx >= l && rx <= r) {
+ return tree[node]; // Fully inside
+ }
+
+ int mid = lx + (rx - lx) / 2;
+ int leftSum = query(l, r, node * 2 + 1, lx, mid);
+ int rightSum = query(l, r, node * 2 + 2, mid, rx);
+
+ return leftSum + rightSum;
+ }
+
+ /**
+ * Public wrapper to query the sum in the range [l, r).
+ *
+ * @param l Left boundary (inclusive).
+ * @param r Right boundary (exclusive).
+ * @return The sum of the range.
+ */
+ public int query(int l, int r) {
+ return query(l, r, 0, 0, n);
+ }
+ }
+
+ // --- Start of 2D Segment Tree (equivalent to 'Sagara2D') ---
+
+ private int n;
+ private final SegmentTree1D[] tree;
+
+ /**
+ * Initializes the 2D Segment Tree.
+ *
+ * @param rows The number of rows in the matrix.
+ * @param cols The number of columns in the matrix.
+ */
+ public SegmentTree2D(int rows, int cols) {
+ n = 1;
+ while (n < rows) {
+ n *= 2;
+ }
+ tree = new SegmentTree1D[n * 2];
+ for (int i = 0; i < n * 2; i++) {
+ // Every node in the outer tree is a full 1D tree!
+ tree[i] = new SegmentTree1D(cols);
+ }
+ }
+
+ /**
+ * Recursively updates a point in the 2D grid.
+ */
+ private void update(int row, int col, int val, int node, int lx, int rx) {
+ if (rx - lx == 1) {
+ tree[node].update(col, val);
+ return;
+ }
+
+ int mid = lx + (rx - lx) / 2;
+ int leftChild = node * 2 + 1;
+ int rightChild = node * 2 + 2;
+
+ if (row < mid) {
+ update(row, col, val, leftChild, lx, mid);
+ } else {
+ update(row, col, val, rightChild, mid, rx);
+ }
+
+ // The value of the current node's column is the sum of its children's column values
+ int leftVal = tree[leftChild].get(col);
+ int rightVal = tree[rightChild].get(col);
+ tree[node].update(col, leftVal + rightVal);
+ }
+
+ /**
+ * Public wrapper to update a specific point (row, col).
+ *
+ * @param row The row index.
+ * @param col The column index.
+ * @param val The new value.
+ */
+ public void update(int row, int col, int val) {
+ update(row, col, val, 0, 0, n);
+ }
+
+ /**
+ * Recursively queries the sum in a submatrix.
+ */
+ private int query(int top, int bottom, int left, int right, int node, int lx, int rx) {
+ if (lx >= bottom || rx <= top) {
+ return 0; // Out of bounds
+ }
+ if (lx >= top && rx <= bottom) {
+ // Fully inside the row range, so delegate the column query to the 1D tree
+ return tree[node].query(left, right);
+ }
+
+ int mid = lx + (rx - lx) / 2;
+ int leftSum = query(top, bottom, left, right, node * 2 + 1, lx, mid);
+ int rightSum = query(top, bottom, left, right, node * 2 + 2, mid, rx);
+
+ return leftSum + rightSum;
+ }
+
+ /**
+ * Public wrapper to query the sum of a submatrix.
+ * Note: boundaries are [top, bottom) and [left, right).
+ *
+ * @param top Top row index (inclusive).
+ * @param bottom Bottom row index (exclusive).
+ * @param left Left column index (inclusive).
+ * @param right Right column index (exclusive).
+ * @return The sum of the submatrix.
+ */
+ public int query(int top, int bottom, int left, int right) {
+ return query(top, bottom, left, right, 0, 0, n);
+ }
+}
diff --git a/src/main/java/com/thealgorithms/dynamicprogramming/OptimalBinarySearchTree.java b/src/main/java/com/thealgorithms/dynamicprogramming/OptimalBinarySearchTree.java
new file mode 100644
index 000000000000..428176ea6c40
--- /dev/null
+++ b/src/main/java/com/thealgorithms/dynamicprogramming/OptimalBinarySearchTree.java
@@ -0,0 +1,130 @@
+package com.thealgorithms.dynamicprogramming;
+
+import java.util.Arrays;
+import java.util.Comparator;
+
+/**
+ * Computes the minimum search cost of an optimal binary search tree.
+ *
+ * The algorithm sorts the keys, preserves the corresponding search frequencies, and uses
+ * dynamic programming with Knuth's optimization to compute the minimum weighted search cost.
+ *
+ *
Example: if keys = [10, 12] and frequencies = [34, 50], the best tree puts 12 at the root
+ * and 10 as its left child. The total cost is 50 * 1 + 34 * 2 = 118.
+ *
+ *
Reference:
+ * https://en.wikipedia.org/wiki/Optimal_binary_search_tree
+ */
+public final class OptimalBinarySearchTree {
+ private OptimalBinarySearchTree() {
+ }
+
+ /**
+ * Computes the minimum weighted search cost for the given keys and search frequencies.
+ *
+ * @param keys the BST keys
+ * @param frequencies the search frequencies associated with the keys
+ * @return the minimum search cost
+ * @throws IllegalArgumentException if the input is invalid
+ */
+ public static long findOptimalCost(int[] keys, int[] frequencies) {
+ validateInput(keys, frequencies);
+ if (keys.length == 0) {
+ return 0L;
+ }
+
+ int[][] sortedNodes = sortNodes(keys, frequencies);
+ int nodeCount = sortedNodes.length;
+ long[] prefixSums = buildPrefixSums(sortedNodes);
+ long[][] optimalCost = new long[nodeCount][nodeCount];
+ int[][] root = new int[nodeCount][nodeCount];
+
+ // Small example:
+ // keys = [10, 12]
+ // frequencies = [34, 50]
+ // Choosing 12 as the root gives cost 50 * 1 + 34 * 2 = 118,
+ // which is better than choosing 10 as the root.
+
+ // Base case: a subtree containing one key has cost equal to its frequency,
+ // because that key becomes the root of the subtree and is searched at depth 1.
+ for (int index = 0; index < nodeCount; index++) {
+ optimalCost[index][index] = sortedNodes[index][1];
+ root[index][index] = index;
+ }
+
+ // Build solutions for longer and longer key ranges.
+ // optimalCost[start][end] stores the minimum search cost for keys in that range.
+ for (int length = 2; length <= nodeCount; length++) {
+ for (int start = 0; start <= nodeCount - length; start++) {
+ int end = start + length - 1;
+
+ // Every key in this range moves one level deeper when we choose a root,
+ // so the sum of frequencies is added once to the subtree cost.
+ long frequencySum = prefixSums[end + 1] - prefixSums[start];
+ optimalCost[start][end] = Long.MAX_VALUE;
+
+ // Knuth's optimization:
+ // the best root for [start, end] lies between the best roots of
+ // [start, end - 1] and [start + 1, end], so we search only this interval.
+ int leftBoundary = root[start][end - 1];
+ int rightBoundary = root[start + 1][end];
+ for (int currentRoot = leftBoundary; currentRoot <= rightBoundary; currentRoot++) {
+ long leftCost = currentRoot > start ? optimalCost[start][currentRoot - 1] : 0L;
+ long rightCost = currentRoot < end ? optimalCost[currentRoot + 1][end] : 0L;
+ long currentCost = frequencySum + leftCost + rightCost;
+
+ if (currentCost < optimalCost[start][end]) {
+ optimalCost[start][end] = currentCost;
+ root[start][end] = currentRoot;
+ }
+ }
+ }
+ }
+
+ return optimalCost[0][nodeCount - 1];
+ }
+
+ private static void validateInput(int[] keys, int[] frequencies) {
+ if (keys == null || frequencies == null) {
+ throw new IllegalArgumentException("Keys and frequencies cannot be null");
+ }
+ if (keys.length != frequencies.length) {
+ throw new IllegalArgumentException("Keys and frequencies must have the same length");
+ }
+
+ for (int frequency : frequencies) {
+ if (frequency < 0) {
+ throw new IllegalArgumentException("Frequencies cannot be negative");
+ }
+ }
+ }
+
+ private static int[][] sortNodes(int[] keys, int[] frequencies) {
+ int[][] sortedNodes = new int[keys.length][2];
+ for (int index = 0; index < keys.length; index++) {
+ sortedNodes[index][0] = keys[index];
+ sortedNodes[index][1] = frequencies[index];
+ }
+
+ // Sort by key so the nodes can be treated as an in-order BST sequence.
+ Arrays.sort(sortedNodes, Comparator.comparingInt(node -> node[0]));
+
+ for (int index = 1; index < sortedNodes.length; index++) {
+ if (sortedNodes[index - 1][0] == sortedNodes[index][0]) {
+ throw new IllegalArgumentException("Keys must be distinct");
+ }
+ }
+
+ return sortedNodes;
+ }
+
+ private static long[] buildPrefixSums(int[][] sortedNodes) {
+ long[] prefixSums = new long[sortedNodes.length + 1];
+ for (int index = 0; index < sortedNodes.length; index++) {
+ // prefixSums[i] holds the total frequency of the first i sorted keys.
+ // This lets us get the frequency sum of any range in O(1) time.
+ prefixSums[index + 1] = prefixSums[index] + sortedNodes[index][1];
+ }
+ return prefixSums;
+ }
+}
diff --git a/src/main/java/com/thealgorithms/geometry/LineIntersection.java b/src/main/java/com/thealgorithms/geometry/LineIntersection.java
new file mode 100644
index 000000000000..8d65833816b3
--- /dev/null
+++ b/src/main/java/com/thealgorithms/geometry/LineIntersection.java
@@ -0,0 +1,105 @@
+package com.thealgorithms.geometry;
+
+import java.awt.geom.Point2D;
+import java.util.Optional;
+
+/**
+ * Utility methods for checking and computing 2D line segment intersections.
+ */
+public final class LineIntersection {
+ private LineIntersection() {
+ }
+
+ /**
+ * Checks whether two line segments intersect.
+ *
+ * @param p1 first endpoint of segment 1
+ * @param p2 second endpoint of segment 1
+ * @param q1 first endpoint of segment 2
+ * @param q2 second endpoint of segment 2
+ * @return true when the segments intersect (including touching endpoints)
+ */
+ public static boolean intersects(Point p1, Point p2, Point q1, Point q2) {
+ int o1 = orientation(p1, p2, q1);
+ int o2 = orientation(p1, p2, q2);
+ int o3 = orientation(q1, q2, p1);
+ int o4 = orientation(q1, q2, p2);
+
+ if (o1 != o2 && o3 != o4) {
+ return true;
+ }
+
+ if (o1 == 0 && onSegment(p1, q1, p2)) {
+ return true;
+ }
+ if (o2 == 0 && onSegment(p1, q2, p2)) {
+ return true;
+ }
+ if (o3 == 0 && onSegment(q1, p1, q2)) {
+ return true;
+ }
+ if (o4 == 0 && onSegment(q1, p2, q2)) {
+ return true;
+ }
+
+ return false;
+ }
+
+ /**
+ * Computes the single geometric intersection point between two non-parallel
+ * segments when it exists.
+ *
+ *
For parallel/collinear overlap, this method returns {@code Optional.empty()}.
+ *
+ * @param p1 first endpoint of segment 1
+ * @param p2 second endpoint of segment 1
+ * @param q1 first endpoint of segment 2
+ * @param q2 second endpoint of segment 2
+ * @return the intersection point when uniquely defined and on both segments
+ */
+ public static Optional intersectionPoint(Point p1, Point p2, Point q1, Point q2) {
+ if (!intersects(p1, p2, q1, q2)) {
+ return Optional.empty();
+ }
+
+ long x1 = p1.x();
+ long y1 = p1.y();
+ long x2 = p2.x();
+ long y2 = p2.y();
+ long x3 = q1.x();
+ long y3 = q1.y();
+ long x4 = q2.x();
+ long y4 = q2.y();
+
+ long denominator = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4);
+ if (denominator == 0L) {
+ return sharedEndpoint(p1, p2, q1, q2);
+ }
+
+ long determinant1 = x1 * y2 - y1 * x2;
+ long determinant2 = x3 * y4 - y3 * x4;
+ long numeratorX = determinant1 * (x3 - x4) - (x1 - x2) * determinant2;
+ long numeratorY = determinant1 * (y3 - y4) - (y1 - y2) * determinant2;
+
+ return Optional.of(new Point2D.Double(numeratorX / (double) denominator, numeratorY / (double) denominator));
+ }
+
+ private static int orientation(Point a, Point b, Point c) {
+ long cross = ((long) b.x() - a.x()) * ((long) c.y() - a.y()) - ((long) b.y() - a.y()) * ((long) c.x() - a.x());
+ return Long.compare(cross, 0L);
+ }
+
+ private static Optional sharedEndpoint(Point p1, Point p2, Point q1, Point q2) {
+ if (p1.equals(q1) || p1.equals(q2)) {
+ return Optional.of(new Point2D.Double(p1.x(), p1.y()));
+ }
+ if (p2.equals(q1) || p2.equals(q2)) {
+ return Optional.of(new Point2D.Double(p2.x(), p2.y()));
+ }
+ return Optional.empty();
+ }
+
+ private static boolean onSegment(Point a, Point b, Point c) {
+ return b.x() >= Math.min(a.x(), c.x()) && b.x() <= Math.max(a.x(), c.x()) && b.y() >= Math.min(a.y(), c.y()) && b.y() <= Math.max(a.y(), c.y());
+ }
+}
diff --git a/src/main/java/com/thealgorithms/graph/AccountMerge.java b/src/main/java/com/thealgorithms/graph/AccountMerge.java
new file mode 100644
index 000000000000..cf934a72eb68
--- /dev/null
+++ b/src/main/java/com/thealgorithms/graph/AccountMerge.java
@@ -0,0 +1,112 @@
+package com.thealgorithms.graph;
+
+import java.util.ArrayList;
+import java.util.Collections;
+import java.util.HashMap;
+import java.util.LinkedHashMap;
+import java.util.List;
+import java.util.Map;
+
+/**
+ * Merges account records using Disjoint Set Union (Union-Find) on shared emails.
+ *
+ * Input format: each account is a list where the first element is the user name and the
+ * remaining elements are emails.
+ */
+public final class AccountMerge {
+ private AccountMerge() {
+ }
+
+ public static List> mergeAccounts(List> accounts) {
+ if (accounts == null || accounts.isEmpty()) {
+ return List.of();
+ }
+
+ UnionFind dsu = new UnionFind(accounts.size());
+ Map emailToAccount = new HashMap<>();
+
+ for (int i = 0; i < accounts.size(); i++) {
+ List account = accounts.get(i);
+ for (int j = 1; j < account.size(); j++) {
+ String email = account.get(j);
+ Integer previous = emailToAccount.putIfAbsent(email, i);
+ if (previous != null) {
+ dsu.union(i, previous);
+ }
+ }
+ }
+
+ Map> rootToEmails = new LinkedHashMap<>();
+ for (Map.Entry entry : emailToAccount.entrySet()) {
+ int root = dsu.find(entry.getValue());
+ rootToEmails.computeIfAbsent(root, ignored -> new ArrayList<>()).add(entry.getKey());
+ }
+ for (int i = 0; i < accounts.size(); i++) {
+ if (accounts.get(i).size() <= 1) {
+ int root = dsu.find(i);
+ rootToEmails.computeIfAbsent(root, ignored -> new ArrayList<>());
+ }
+ }
+
+ List> merged = new ArrayList<>();
+ for (Map.Entry> entry : rootToEmails.entrySet()) {
+ int root = entry.getKey();
+ List emails = entry.getValue();
+ Collections.sort(emails);
+
+ List mergedAccount = new ArrayList<>();
+ mergedAccount.add(accounts.get(root).getFirst());
+ mergedAccount.addAll(emails);
+ merged.add(mergedAccount);
+ }
+
+ merged.sort((a, b) -> {
+ int cmp = a.getFirst().compareTo(b.getFirst());
+ if (cmp != 0) {
+ return cmp;
+ }
+ if (a.size() == 1 || b.size() == 1) {
+ return Integer.compare(a.size(), b.size());
+ }
+ return a.get(1).compareTo(b.get(1));
+ });
+ return merged;
+ }
+
+ private static final class UnionFind {
+ private final int[] parent;
+ private final int[] rank;
+
+ private UnionFind(int size) {
+ this.parent = new int[size];
+ this.rank = new int[size];
+ for (int i = 0; i < size; i++) {
+ parent[i] = i;
+ }
+ }
+
+ private int find(int x) {
+ if (parent[x] != x) {
+ parent[x] = find(parent[x]);
+ }
+ return parent[x];
+ }
+
+ private void union(int x, int y) {
+ int rootX = find(x);
+ int rootY = find(y);
+ if (rootX == rootY) {
+ return;
+ }
+
+ if (rank[rootX] < rank[rootY]) {
+ parent[rootX] = rootY;
+ } else if (rank[rootX] > rank[rootY]) {
+ parent[rootY] = rootX;
+ } else {
+ parent[rootY] = rootX;
+ rank[rootX]++;
+ }
+ }
+ }
+}
diff --git a/src/main/java/com/thealgorithms/graph/TarjanBridges.java b/src/main/java/com/thealgorithms/graph/TarjanBridges.java
new file mode 100644
index 000000000000..dbe2e710429a
--- /dev/null
+++ b/src/main/java/com/thealgorithms/graph/TarjanBridges.java
@@ -0,0 +1,122 @@
+package com.thealgorithms.graph;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * Implementation of Tarjan's Bridge-Finding Algorithm for undirected graphs.
+ *
+ * A bridge (also called a cut-edge) is an edge in an undirected graph whose removal
+ * increases the number of connected components. Bridges represent critical links
+ * in a network — if any bridge is removed, part of the network becomes unreachable.
+ *
+ * The algorithm performs a single Depth-First Search (DFS) traversal, tracking two
+ * values for each vertex:
+ *
+ * - discoveryTime — the time step at which the vertex was first visited.
+ * - lowLink — the smallest discovery time reachable from the subtree rooted
+ * at that vertex (via back edges).
+ *
+ *
+ * An edge (u, v) is a bridge if and only if {@code lowLink[v] > discoveryTime[u]},
+ * meaning there is no back edge from the subtree of v that can reach u or any ancestor of u.
+ *
+ * Time Complexity: O(V + E), where V is the number of vertices and E is the number of edges.
+ * Space Complexity: O(V + E) for the adjacency list, discovery/low arrays, and recursion stack.
+ *
+ * @see Wikipedia: Bridge (graph theory)
+ */
+public final class TarjanBridges {
+
+ private TarjanBridges() {
+ throw new UnsupportedOperationException("Utility class");
+ }
+
+ /**
+ * Finds all bridge edges in an undirected graph.
+ *
+ * The graph is represented as an adjacency list where each vertex is identified by
+ * an integer in the range {@code [0, vertexCount)}. For each undirected edge (u, v),
+ * v must appear in {@code adjacencyList.get(u)} and u must appear in
+ * {@code adjacencyList.get(v)}.
+ *
+ * @param vertexCount the total number of vertices in the graph (must be non-negative)
+ * @param adjacencyList the adjacency list representation of the graph; must contain
+ * exactly {@code vertexCount} entries (one per vertex)
+ * @return a list of bridge edges, where each bridge is represented as an {@code int[]}
+ * of length 2 with {@code edge[0] < edge[1]}; returns an empty list if no bridges exist
+ * @throws IllegalArgumentException if {@code vertexCount} is negative, or if
+ * {@code adjacencyList} is null or its size does not match
+ * {@code vertexCount}
+ */
+ public static List findBridges(int vertexCount, List> adjacencyList) {
+ if (vertexCount < 0) {
+ throw new IllegalArgumentException("vertexCount must be non-negative");
+ }
+ if (adjacencyList == null || adjacencyList.size() != vertexCount) {
+ throw new IllegalArgumentException("adjacencyList size must equal vertexCount");
+ }
+
+ List bridges = new ArrayList<>();
+
+ if (vertexCount == 0) {
+ return bridges;
+ }
+
+ BridgeFinder finder = new BridgeFinder(vertexCount, adjacencyList, bridges);
+
+ // Run DFS from every unvisited vertex to handle disconnected graphs
+ for (int i = 0; i < vertexCount; i++) {
+ if (!finder.visited[i]) {
+ finder.dfs(i, -1);
+ }
+ }
+
+ return bridges;
+ }
+
+ private static class BridgeFinder {
+ private final List> adjacencyList;
+ private final List bridges;
+ private final int[] discoveryTime;
+ private final int[] lowLink;
+ boolean[] visited;
+ private int timer;
+
+ BridgeFinder(int vertexCount, List> adjacencyList, List bridges) {
+ this.adjacencyList = adjacencyList;
+ this.bridges = bridges;
+ this.discoveryTime = new int[vertexCount];
+ this.lowLink = new int[vertexCount];
+ this.visited = new boolean[vertexCount];
+ this.timer = 0;
+ }
+
+ /**
+ * Performs DFS from the given vertex, computing discovery times and low-link values,
+ * and collects any bridge edges found.
+ *
+ * @param u the current vertex being explored
+ * @param parent the parent of u in the DFS tree (-1 if u is a root)
+ */
+ void dfs(int u, int parent) {
+ visited[u] = true;
+ discoveryTime[u] = timer;
+ lowLink[u] = timer;
+ timer++;
+
+ for (int v : adjacencyList.get(u)) {
+ if (!visited[v]) {
+ dfs(v, u);
+ lowLink[u] = Math.min(lowLink[u], lowLink[v]);
+
+ if (lowLink[v] > discoveryTime[u]) {
+ bridges.add(new int[] {Math.min(u, v), Math.max(u, v)});
+ }
+ } else if (v != parent) {
+ lowLink[u] = Math.min(lowLink[u], discoveryTime[v]);
+ }
+ }
+ }
+ }
+}
diff --git a/src/main/java/com/thealgorithms/maths/Average.java b/src/main/java/com/thealgorithms/maths/Average.java
index a550a7f6504d..cf55af509ccc 100644
--- a/src/main/java/com/thealgorithms/maths/Average.java
+++ b/src/main/java/com/thealgorithms/maths/Average.java
@@ -1,9 +1,16 @@
package com.thealgorithms.maths;
+import java.util.Arrays;
+import java.util.OptionalDouble;
+
/**
* A utility class for computing the average of numeric arrays.
- * This class provides static methods to calculate the average of arrays
- * of both {@code double} and {@code int} values.
+ *
+ * This class provides static methods to calculate the arithmetic mean
+ * of arrays of both {@code double} and {@code int} values. It also offers
+ * a Stream-based alternative for modern, declarative usage.
+ *
+ *
All methods guard against {@code null} or empty inputs.
*/
public final class Average {
@@ -13,11 +20,14 @@ private Average() {
}
/**
- * Computes the average of a {@code double} array.
+ * Computes the arithmetic mean of a {@code double} array.
+ *
+ *
The average is calculated as the sum of all elements divided
+ * by the number of elements: {@code avg = Σ(numbers[i]) / n}.
*
- * @param numbers an array of {@code double} values
- * @return the average of the given numbers
- * @throws IllegalArgumentException if the input array is {@code null} or empty
+ * @param numbers a non-null, non-empty array of {@code double} values
+ * @return the arithmetic mean of the given numbers
+ * @throws IllegalArgumentException if {@code numbers} is {@code null} or empty
*/
public static double average(double[] numbers) {
if (numbers == null || numbers.length == 0) {
@@ -31,11 +41,14 @@ public static double average(double[] numbers) {
}
/**
- * Computes the average of an {@code int} array.
+ * Computes the arithmetic mean of an {@code int} array.
+ *
+ *
The sum is accumulated in a {@code long} to prevent integer overflow
+ * when processing large arrays or large values.
*
- * @param numbers an array of {@code int} values
- * @return the average of the given numbers
- * @throws IllegalArgumentException if the input array is {@code null} or empty
+ * @param numbers a non-null, non-empty array of {@code int} values
+ * @return the arithmetic mean as a {@code long} (truncated toward zero)
+ * @throws IllegalArgumentException if {@code numbers} is {@code null} or empty
*/
public static long average(int[] numbers) {
if (numbers == null || numbers.length == 0) {
@@ -47,4 +60,21 @@ public static long average(int[] numbers) {
}
return sum / numbers.length;
}
+
+ /**
+ * Computes the arithmetic mean of a {@code double} array using Java Streams.
+ *
+ *
This method is a declarative alternative to {@link #average(double[])}.
+ * Instead of throwing on empty input, it returns an empty {@link OptionalDouble},
+ * following the convention of the Stream API.
+ *
+ * @param numbers an array of {@code double} values, may be {@code null} or empty
+ * @return an {@link OptionalDouble} with the mean, or empty if input is null/empty
+ */
+ public static OptionalDouble averageStream(double[] numbers) {
+ if (numbers == null || numbers.length == 0) {
+ return OptionalDouble.empty();
+ }
+ return Arrays.stream(numbers).average();
+ }
}
diff --git a/src/main/java/com/thealgorithms/maths/Correlation.java b/src/main/java/com/thealgorithms/maths/Correlation.java
new file mode 100644
index 000000000000..a46445fb23b7
--- /dev/null
+++ b/src/main/java/com/thealgorithms/maths/Correlation.java
@@ -0,0 +1,51 @@
+package com.thealgorithms.maths;
+
+/**
+ * Class for correlation of two discrete variables
+ */
+
+public final class Correlation {
+ private Correlation() {
+ }
+
+ public static final double DELTA = 1e-9;
+
+ /**
+ * Discrete correlation function.
+ * Correlation between two discrete variables is calculated
+ * according to the formula: Cor(x, y)=Cov(x, y)/sqrt(Var(x)*Var(y)).
+ * Correlation with a constant variable is taken to be zero.
+ *
+ * @param x The first discrete variable
+ * @param y The second discrete variable
+ * @param n The number of values for each variable
+ * @return The result of the correlation of variables x,y.
+ */
+ public static double correlation(double[] x, double[] y, int n) {
+ double exy = 0; // E(XY)
+ double ex = 0; // E(X)
+ double exx = 0; // E(X^2)
+ double ey = 0; // E(Y)
+ double eyy = 0; // E(Y^2)
+ for (int i = 0; i < n; i++) {
+ exy += x[i] * y[i];
+ ex += x[i];
+ exx += x[i] * x[i];
+ ey += y[i];
+ eyy += y[i] * y[i];
+ }
+ exy /= n;
+ ex /= n;
+ exx /= n;
+ ey /= n;
+ eyy /= n;
+ double cov = exy - ex * ey; // Cov(X, Y) = E(XY)-E(X)E(Y)
+ double varx = Math.sqrt(exx - ex * ex); // Var(X) = sqrt(E(X^2)-E(X)^2)
+ double vary = Math.sqrt(eyy - ey * ey); // Var(Y) = sqrt(E(Y^2)-E(Y)^2)
+ if (varx * vary < DELTA) { // Var(X) = 0 means X = const, the same about Y
+ return 0;
+ } else {
+ return cov / Math.sqrt(varx * vary);
+ }
+ }
+}
diff --git a/src/main/java/com/thealgorithms/maths/Factorial.java b/src/main/java/com/thealgorithms/maths/Factorial.java
index 511cc1f84f05..8ad219a3066c 100644
--- a/src/main/java/com/thealgorithms/maths/Factorial.java
+++ b/src/main/java/com/thealgorithms/maths/Factorial.java
@@ -1,23 +1,19 @@
package com.thealgorithms.maths;
+import java.math.BigInteger;
+
public final class Factorial {
private Factorial() {
}
- /**
- * Calculate factorial N using iteration
- *
- * @param n the number
- * @return the factorial of {@code n}
- */
- public static long factorial(int n) {
+ public static BigInteger factorial(int n) {
if (n < 0) {
throw new IllegalArgumentException("Input number cannot be negative");
}
- long factorial = 1;
- for (int i = 1; i <= n; ++i) {
- factorial *= i;
+ BigInteger result = BigInteger.ONE;
+ for (int i = 1; i <= n; i++) {
+ result = result.multiply(BigInteger.valueOf(i));
}
- return factorial;
+ return result;
}
}
diff --git a/src/main/java/com/thealgorithms/maths/Volume.java b/src/main/java/com/thealgorithms/maths/Volume.java
index c0898c5424a0..488b921cae83 100644
--- a/src/main/java/com/thealgorithms/maths/Volume.java
+++ b/src/main/java/com/thealgorithms/maths/Volume.java
@@ -125,4 +125,16 @@ public static double volumeFrustumOfPyramid(double upperBaseArea, double lowerBa
public static double volumeTorus(double majorRadius, double minorRadius) {
return 2 * Math.PI * Math.PI * majorRadius * minorRadius * minorRadius;
}
+
+ /**
+ * Calculate the volume of an ellipsoid.
+ *
+ * @param a first semi-axis of an ellipsoid
+ * @param b second semi-axis of an ellipsoid
+ * @param c third semi-axis of an ellipsoid
+ * @return volume of the ellipsoid
+ */
+ public static double volumeEllipsoid(double a, double b, double c) {
+ return (4 * Math.PI * a * b * c) / 3;
+ }
}
diff --git a/src/main/java/com/thealgorithms/physics/Relativity.java b/src/main/java/com/thealgorithms/physics/Relativity.java
new file mode 100644
index 000000000000..ed823c2cc879
--- /dev/null
+++ b/src/main/java/com/thealgorithms/physics/Relativity.java
@@ -0,0 +1,81 @@
+package com.thealgorithms.physics;
+
+/**
+ * Implements relativity theory formulae.
+ * Provides simple static methods to calculate length contraction and time dilation
+ * in the laboratory frame with respect to the object's own frame, and velocity
+ * with respect to the moving frame.
+ *
+ * @see Wikipedia
+ */
+public final class Relativity {
+
+ /* Speed of light in m s^-1 */
+ public static final double SPEED_OF_LIGHT = 299792458.0;
+
+ /**
+ * Private constructor to prevent instantiation of this utility class.
+ */
+ private Relativity() {
+ }
+
+ /**
+ * Calculates the gamma parameter that is of paramount importance in relativity
+ * theory. It is a dimensionless parameter that is equal to 1 for zero velocity
+ * but tends to infinity when velocity approaches the speed of light.
+ *
+ * @param v The velocity (m/s).
+ * @return The value of gamma parameter.
+ */
+ public static double gamma(double v) {
+ if (Math.abs(v) >= SPEED_OF_LIGHT) {
+ throw new IllegalArgumentException("Speed must be lower than the speed of light");
+ }
+ return 1.0 / Math.sqrt(1 - v * v / (SPEED_OF_LIGHT * SPEED_OF_LIGHT));
+ }
+
+ /**
+ * Calculates the length of an object in the moving frame.
+ *
+ * @param length The length of an object in its own frame (m).
+ * @param v The velocity of the object (m/s).
+ * @return The length of an object in the laboratory frame (m).
+ */
+ public static double lengthContraction(double length, double v) {
+ if (length < 0) {
+ throw new IllegalArgumentException("Length must be non-negative");
+ }
+ return length / gamma(v);
+ }
+
+ /**
+ * Calculates the time that has passed in the moving frame.
+ *
+ * @param length The time that has passed in the object's own frame (s).
+ * @param v The velocity of the object (m/s).
+ * @return The time that has passed in the laboratory frame (s).
+ */
+ public static double timeDilation(double time, double v) {
+ if (time < 0) {
+ throw new IllegalArgumentException("Time must be non-negative");
+ }
+ return time * gamma(v);
+ }
+
+ /**
+ * Calculates the velocity with respect to the moving frame.
+ *
+ * @param v1 The velocity of the object with respect to laboratory frame (m/s).
+ * @param v The velocity of the moving frame (m/s).
+ * @return The velocity with respect to the moving frame (m/s).
+ */
+ public static double velocityAddition(double v1, double v) {
+ if (Math.abs(v1) > SPEED_OF_LIGHT) {
+ throw new IllegalArgumentException("Speed must not exceed the speed of light");
+ }
+ if (Math.abs(v) >= SPEED_OF_LIGHT) {
+ throw new IllegalArgumentException("Frame speed must be lower than the speed of light");
+ }
+ return (v1 - v) / (1 - v1 * v / (SPEED_OF_LIGHT * SPEED_OF_LIGHT));
+ }
+}
diff --git a/src/main/java/com/thealgorithms/searches/BinarySearch.java b/src/main/java/com/thealgorithms/searches/BinarySearch.java
index 7a5361b280ea..ca873fc6eafa 100644
--- a/src/main/java/com/thealgorithms/searches/BinarySearch.java
+++ b/src/main/java/com/thealgorithms/searches/BinarySearch.java
@@ -58,11 +58,18 @@ class BinarySearch implements SearchAlgorithm {
*/
@Override
public > int find(T[] array, T key) {
- // Handle edge case: empty array
+ // Handle edge case: null or empty array
if (array == null || array.length == 0) {
return -1;
}
+ // Handle edge case: null key
+ // Searching for null in an array of Comparables is undefined behavior
+ // Return -1 to indicate not found rather than throwing NPE
+ if (key == null) {
+ return -1;
+ }
+
// Delegate to the core search implementation
return search(array, key, 0, array.length - 1);
}
diff --git a/src/main/java/com/thealgorithms/searches/InterpolationSearch.java b/src/main/java/com/thealgorithms/searches/InterpolationSearch.java
index 3ac6be25bf53..d24cc1c774bc 100644
--- a/src/main/java/com/thealgorithms/searches/InterpolationSearch.java
+++ b/src/main/java/com/thealgorithms/searches/InterpolationSearch.java
@@ -1,3 +1,14 @@
+/**
+ * Interpolation Search estimates the position of the target value
+ * based on the distribution of values.
+ *
+ * Example:
+ * Input: [10, 20, 30, 40], target = 30
+ * Output: Index = 2
+ *
+ * Time Complexity: O(log log n) (average case)
+ * Space Complexity: O(1)
+ */
package com.thealgorithms.searches;
/**
diff --git a/src/main/java/com/thealgorithms/searches/IterativeBinarySearch.java b/src/main/java/com/thealgorithms/searches/IterativeBinarySearch.java
index 05fab0534267..d051dbc7b823 100644
--- a/src/main/java/com/thealgorithms/searches/IterativeBinarySearch.java
+++ b/src/main/java/com/thealgorithms/searches/IterativeBinarySearch.java
@@ -3,50 +3,53 @@
import com.thealgorithms.devutils.searches.SearchAlgorithm;
/**
- * Binary search is one of the most popular algorithms This class represents
- * iterative version {@link BinarySearch} Iterative binary search is likely to
- * have lower constant factors because it doesn't involve the overhead of
- * manipulating the call stack. But in java the recursive version can be
- * optimized by the compiler to this version.
+ * Binary search is one of the most popular algorithms.
+ * This class represents the iterative version of {@link BinarySearch}.
*
- *
- * Worst-case performance O(log n) Best-case performance O(1) Average
- * performance O(log n) Worst-case space complexity O(1)
+ *
Iterative binary search avoids recursion overhead and uses constant space.
*
- * @author Gabriele La Greca : https://github.com/thegabriele97
- * @author Podshivalov Nikita (https://github.com/nikitap492)
+ *
Performance:
+ *
+ * - Best-case: O(1)
+ * - Average-case: O(log n)
+ * - Worst-case: O(log n)
+ * - Space complexity: O(1)
+ *
+ *
+ * @author Gabriele La Greca
+ * @author Podshivalov Nikita
* @see SearchAlgorithm
* @see BinarySearch
*/
public final class IterativeBinarySearch implements SearchAlgorithm {
/**
- * This method implements an iterative version of binary search algorithm
+ * Performs iterative binary search on a sorted array.
*
- * @param array a sorted array
- * @param key the key to search in array
- * @return the index of key in the array or -1 if not found
+ * @param array the sorted array
+ * @param key the element to search
+ * @param type of elements (must be Comparable)
+ * @return index of the key if found, otherwise -1
*/
@Override
public > int find(T[] array, T key) {
- int l;
- int r;
- int k;
- int cmp;
+ if (array == null || array.length == 0 || key == null) {
+ return -1;
+ }
- l = 0;
- r = array.length - 1;
+ int left = 0;
+ int right = array.length - 1;
- while (l <= r) {
- k = (l + r) >>> 1;
- cmp = key.compareTo(array[k]);
+ while (left <= right) {
+ int mid = (left + right) >>> 1;
+ int cmp = key.compareTo(array[mid]);
if (cmp == 0) {
- return k;
+ return mid;
} else if (cmp < 0) {
- r = --k;
+ right = mid - 1;
} else {
- l = ++k;
+ left = mid + 1;
}
}
diff --git a/src/main/java/com/thealgorithms/searches/JumpSearch.java b/src/main/java/com/thealgorithms/searches/JumpSearch.java
index 8dcec3a819a4..5074aa7845c8 100644
--- a/src/main/java/com/thealgorithms/searches/JumpSearch.java
+++ b/src/main/java/com/thealgorithms/searches/JumpSearch.java
@@ -12,26 +12,57 @@
* Once the range is found, a linear search is performed within that block.
*
*
- * The Jump Search algorithm is particularly effective for large sorted arrays where the cost of
- * performing a linear search on the entire array would be prohibitive.
+ * How it works:
+ *
+ * - Calculate the optimal block size as √n (square root of array length)
+ * - Jump ahead by the block size until the current element is greater than the target
+ * - Perform a linear search backwards within the identified block
+ *
*
*
- * Worst-case performance: O(√N)
- * Best-case performance: O(1)
- * Average performance: O(√N)
- * Worst-case space complexity: O(1)
+ * Example:
+ * Array: [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], Target: 9
+ * Step 1: Jump from index 0 → 3 → 6 (9 < 13, so we found the block)
+ * Step 2: Linear search from index 3 to 6: found 9 at index 4
+ * Result: Index = 4
+ *
+ *
+ * Time Complexity:
+ * - Best-case: O(1) - element found at first position
+ * - Average: O(√n) - optimal block size reduces jumps
+ * - Worst-case: O(√n) - element at end of array or not present
+ *
+ *
+ * Space Complexity: O(1) - only uses a constant amount of extra space
+ *
+ *
+ * Edge Cases:
+ *
+ * - Empty array → returns -1
+ * - Element not present → returns -1
+ * - Single element array
+ *
+ *
+ * Note: Jump Search requires a sorted array. For unsorted arrays, use Linear Search.
+ * Compared to Linear Search (O(n)), Jump Search is faster for large arrays.
+ * Compared to Binary Search (O(log n)), Jump Search is less efficient but may be
+ * preferable when jumping through a linked list or when backward scanning is costly.
*
*
* This class implements the {@link SearchAlgorithm} interface, providing a generic search method
* for any comparable type.
+ *
+ * @see SearchAlgorithm
+ * @see BinarySearch
+ * @see LinearSearch
*/
public class JumpSearch implements SearchAlgorithm {
/**
* Jump Search algorithm implementation.
*
- * @param array the sorted array containing elements
- * @param key the element to be searched
+ * @param array the sorted array containing elements (must be sorted in ascending order)
+ * @param key the element to be searched for
* @return the index of {@code key} if found, otherwise -1
*/
@Override
diff --git a/src/main/java/com/thealgorithms/searches/LinearSearch.java b/src/main/java/com/thealgorithms/searches/LinearSearch.java
index cb483d8dfedc..3f273e167f0a 100644
--- a/src/main/java/com/thealgorithms/searches/LinearSearch.java
+++ b/src/main/java/com/thealgorithms/searches/LinearSearch.java
@@ -1,6 +1,20 @@
+/**
+ * Performs Linear Search on an array.
+ *
+ * Linear search checks each element one by one until the target is found
+ * or the array ends.
+ *
+ * Example:
+ * Input: [2, 4, 6, 8], target = 6
+ * Output: Index = 2
+ *
+ * Time Complexity: O(n)
+ * Space Complexity: O(1)
+ */
package com.thealgorithms.searches;
import com.thealgorithms.devutils.searches.SearchAlgorithm;
+
/**
* Linear Search is a simple searching algorithm that checks
* each element of the array sequentially until the target
@@ -20,7 +34,6 @@
* @see BinarySearch
* @see SearchAlgorithm
*/
-
public class LinearSearch implements SearchAlgorithm {
/**
@@ -28,15 +41,22 @@ public class LinearSearch implements SearchAlgorithm {
*
* @param array List to be searched
* @param value Key being searched for
- * @return Location of the key
+ * @return Location of the key, -1 if array is null or empty, or key not found
*/
@Override
public > int find(T[] array, T value) {
+
+ if (array == null || array.length == 0 || value == null) {
+ return -1;
+ }
+
for (int i = 0; i < array.length; i++) {
- if (array[i].compareTo(value) == 0) {
+ T currentElement = array[i];
+ if (currentElement != null && currentElement.compareTo(value) == 0) {
return i;
}
}
+
return -1;
}
}
diff --git a/src/main/java/com/thealgorithms/stacks/StockSpanProblem.java b/src/main/java/com/thealgorithms/stacks/StockSpanProblem.java
new file mode 100644
index 000000000000..2e9f6863c90a
--- /dev/null
+++ b/src/main/java/com/thealgorithms/stacks/StockSpanProblem.java
@@ -0,0 +1,67 @@
+package com.thealgorithms.stacks;
+
+import java.util.Stack;
+
+/**
+ * Calculates the stock span for each day in a series of stock prices.
+ *
+ * The span of a price on a given day is the number of consecutive days ending on that day
+ * for which the price was less than or equal to the current day's price.
+ *
+ *
Idea: keep a stack of indices whose prices are strictly greater than the current price.
+ * While processing each day, pop smaller or equal prices because they are part of the current
+ * span. After popping, the nearest greater price left on the stack tells us where the span stops.
+ *
+ *
Time complexity is O(n) because each index is pushed onto the stack once and popped at most
+ * once, so the total number of stack operations grows linearly with the number of prices. This
+ * makes the stack approach efficient because it avoids rechecking earlier days repeatedly, unlike
+ * a naive nested-loop solution that can take O(n^2) time.
+ *
+ *
Example: for prices [100, 80, 60, 70, 60, 75, 85], the spans are
+ * [1, 1, 1, 2, 1, 4, 6].
+ */
+public final class StockSpanProblem {
+ private StockSpanProblem() {
+ }
+
+ /**
+ * Calculates the stock span for each price in the input array.
+ *
+ * @param prices the stock prices
+ * @return the span for each day
+ * @throws IllegalArgumentException if the input array is null
+ */
+ public static int[] calculateSpan(int[] prices) {
+ if (prices == null) {
+ throw new IllegalArgumentException("Input prices cannot be null");
+ }
+
+ int[] spans = new int[prices.length];
+ Stack stack = new Stack<>();
+
+ // Small example:
+ // prices = [100, 80, 60, 70]
+ // spans = [ 1, 1, 1, 2]
+ // When we process 70, we pop 60 because 60 <= 70, so the span becomes 2.
+ //
+ // The stack stores indices of days with prices greater than the current day's price.
+ for (int index = 0; index < prices.length; index++) {
+ // Remove all previous days whose prices are less than or equal to the current price.
+ while (!stack.isEmpty() && prices[stack.peek()] <= prices[index]) {
+ stack.pop();
+ }
+
+ // If the stack is empty, there is no earlier day with a greater price,
+ // so the count will be from day 0 to this day (index + 1).
+ //
+ // Otherwise, the span is the number of days between
+ // the nearest earlier day with a greater price and the current day.
+ spans[index] = stack.isEmpty() ? index + 1 : index - stack.peek();
+
+ // Store the current index as a candidate for future span calculations.
+ stack.push(index);
+ }
+
+ return spans;
+ }
+}
diff --git a/src/main/java/com/thealgorithms/strings/Alphabetical.java b/src/main/java/com/thealgorithms/strings/Alphabetical.java
index ef2974eb427d..37b1fb068b44 100644
--- a/src/main/java/com/thealgorithms/strings/Alphabetical.java
+++ b/src/main/java/com/thealgorithms/strings/Alphabetical.java
@@ -1,32 +1,58 @@
package com.thealgorithms.strings;
+import java.util.Locale;
+
/**
- * Utility class for checking if a string's characters are in alphabetical order.
+ * Utility class for checking whether a string's characters are in non-decreasing
+ * lexicographical order based on Unicode code points (case-insensitive).
+ *
+ * This does NOT implement language-aware alphabetical ordering (collation rules).
+ * It simply compares lowercase Unicode character values.
*
- * Alphabetical order is a system whereby character strings are placed in order
- * based on the position of the characters in the conventional ordering of an
- * alphabet.
+ * Non-letter characters are not allowed and will cause the check to fail.
*
- * Reference: Wikipedia: Alphabetical Order
+ * Reference:
+ * Wikipedia: Alphabetical order
*/
public final class Alphabetical {
+
private Alphabetical() {
}
/**
- * Checks whether the characters in the given string are in alphabetical order.
- * Non-letter characters will cause the check to fail.
+ * Checks whether the characters in the given string are in non-decreasing
+ * lexicographical order (case-insensitive).
+ *
+ * Rules:
+ *
+ * - String must not be null or blank
+ * - All characters must be letters
+ * - Comparison is based on lowercase Unicode values
+ * - Order must be non-decreasing (equal or increasing allowed)
+ *
*
- * @param s the input string
- * @return {@code true} if all characters are in alphabetical order (case-insensitive), otherwise {@code false}
+ * @param s input string
+ * @return {@code true} if characters are in non-decreasing order, otherwise {@code false}
*/
public static boolean isAlphabetical(String s) {
- s = s.toLowerCase();
- for (int i = 0; i < s.length() - 1; ++i) {
- if (!Character.isLetter(s.charAt(i)) || s.charAt(i) > s.charAt(i + 1)) {
+ if (s == null || s.isBlank()) {
+ return false;
+ }
+
+ String normalized = s.toLowerCase(Locale.ROOT);
+
+ if (!Character.isLetter(normalized.charAt(0))) {
+ return false;
+ }
+
+ for (int i = 1; i < normalized.length(); i++) {
+ char prev = normalized.charAt(i - 1);
+ char curr = normalized.charAt(i);
+
+ if (!Character.isLetter(curr) || prev > curr) {
return false;
}
}
- return !s.isEmpty() && Character.isLetter(s.charAt(s.length() - 1));
+ return true;
}
}
diff --git a/src/main/java/com/thealgorithms/strings/KasaiAlgorithm.java b/src/main/java/com/thealgorithms/strings/KasaiAlgorithm.java
new file mode 100644
index 000000000000..b8b10dcf4538
--- /dev/null
+++ b/src/main/java/com/thealgorithms/strings/KasaiAlgorithm.java
@@ -0,0 +1,79 @@
+package com.thealgorithms.strings;
+
+/**
+ * Kasai's Algorithm for constructing the Longest Common Prefix (LCP) array.
+ *
+ *
+ * The LCP array stores the lengths of the longest common prefixes between
+ * lexicographically adjacent suffixes of a string. Kasai's algorithm computes
+ * this array in O(N) time given the string and its suffix array.
+ *
+ *
+ * @see LCP array - Wikipedia
+ */
+public final class KasaiAlgorithm {
+
+ private KasaiAlgorithm() {
+ }
+
+ /**
+ * Computes the LCP array using Kasai's algorithm.
+ *
+ * @param text the original string
+ * @param suffixArr the suffix array of the string
+ * @return the LCP array of length N, where LCP[i] is the length of the longest
+ * common prefix of the suffixes indexed by suffixArr[i] and suffixArr[i+1].
+ * The last element LCP[N-1] is always 0.
+ * @throws IllegalArgumentException if text or suffixArr is null, or their lengths differ
+ */
+ public static int[] kasai(String text, int[] suffixArr) {
+ if (text == null || suffixArr == null) {
+ throw new IllegalArgumentException("Text and suffix array must not be null.");
+ }
+ int n = text.length();
+ if (suffixArr.length != n) {
+ throw new IllegalArgumentException("Suffix array length must match text length.");
+ }
+ if (n == 0) {
+ return new int[0];
+ }
+
+ // Compute the inverse suffix array
+ // invSuff[i] stores the index of the suffix text.substring(i) in the suffix array
+ int[] invSuff = new int[n];
+ for (int i = 0; i < n; i++) {
+ if (suffixArr[i] < 0 || suffixArr[i] >= n) {
+ throw new IllegalArgumentException("Suffix array contains out-of-bounds index.");
+ }
+ invSuff[suffixArr[i]] = i;
+ }
+
+ int[] lcp = new int[n];
+ int k = 0; // Length of the longest common prefix
+
+ for (int i = 0; i < n; i++) {
+ // Suffix at index i has not a next suffix in suffix array
+ int rank = invSuff[i];
+ if (rank == n - 1) {
+ k = 0;
+ continue;
+ }
+
+ int nextSuffixIndex = suffixArr[rank + 1];
+
+ // Directly match characters to find LCP
+ while (i + k < n && nextSuffixIndex + k < n && text.charAt(i + k) == text.charAt(nextSuffixIndex + k)) {
+ k++;
+ }
+
+ lcp[rank] = k;
+
+ // Delete the starting character from the string
+ if (k > 0) {
+ k--;
+ }
+ }
+
+ return lcp;
+ }
+}
diff --git a/src/main/java/com/thealgorithms/strings/MoveHashToEnd.java b/src/main/java/com/thealgorithms/strings/MoveHashToEnd.java
new file mode 100644
index 000000000000..bd686a0c5ba0
--- /dev/null
+++ b/src/main/java/com/thealgorithms/strings/MoveHashToEnd.java
@@ -0,0 +1,56 @@
+package com.thealgorithms.strings;
+
+/**
+ * Moves all '#' characters to the end of the given string while preserving
+ * the order of the other characters.
+ *
+ * Example:
+ * Input : "h#e#l#llo"
+ * Output : "helllo###"
+ *
+ * The algorithm works by iterating through the string and collecting
+ * all non-# characters first, then filling the remaining positions
+ * with '#'.
+ *
+ * Time Complexity: O(n)
+ * Space Complexity: O(n)
+ *
+ * @see Move all special characters to end - GeeksForGeeks
+ */
+public final class MoveHashToEnd {
+
+ /**
+ * Private constructor to prevent instantiation of utility class.
+ */
+ private MoveHashToEnd() {
+ }
+
+ /**
+ * Moves all '#' characters in the input string to the end.
+ *
+ * @param str the input string containing characters and '#'
+ * @return a new string with all '#' characters moved to the end
+ */
+ public static String moveHashToEnd(String str) {
+ if (str == null || str.isEmpty()) {
+ return str;
+ }
+
+ char[] arr = str.toCharArray();
+ int insertPos = 0;
+
+ // Place all non-# characters at the beginning
+ for (char ch : arr) {
+ if (ch != '#') {
+ arr[insertPos++] = ch;
+ }
+ }
+
+ // Fill remaining positions with '#'
+ while (insertPos < arr.length) {
+ arr[insertPos++] = '#';
+ }
+
+ return new String(arr);
+ }
+}
diff --git a/src/test/java/com/thealgorithms/datastructures/trees/SegmentTree2DTest.java b/src/test/java/com/thealgorithms/datastructures/trees/SegmentTree2DTest.java
new file mode 100644
index 000000000000..db081da2550a
--- /dev/null
+++ b/src/test/java/com/thealgorithms/datastructures/trees/SegmentTree2DTest.java
@@ -0,0 +1,71 @@
+package com.thealgorithms.datastructures.trees;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.api.Test;
+
+public class SegmentTree2DTest {
+
+ @Test
+ void testInitialEmptyQueries() {
+ SegmentTree2D segmentTree = new SegmentTree2D(4, 4);
+
+ // Initial tree should return 0 for any query
+ assertEquals(0, segmentTree.query(0, 4, 0, 4));
+ assertEquals(0, segmentTree.query(1, 3, 1, 3));
+ }
+
+ @Test
+ void testUpdateAndPointQuery() {
+ SegmentTree2D segmentTree = new SegmentTree2D(5, 5);
+
+ segmentTree.update(2, 3, 10);
+ segmentTree.update(0, 0, 5);
+
+ // Querying single points [row, row+1) x [col, col+1)
+ assertEquals(10, segmentTree.query(2, 3, 3, 4));
+ assertEquals(5, segmentTree.query(0, 1, 0, 1));
+
+ // Empty point should be 0
+ assertEquals(0, segmentTree.query(1, 2, 1, 2));
+ }
+
+ @Test
+ void testSubmatrixQuery() {
+ SegmentTree2D segmentTree = new SegmentTree2D(4, 4);
+
+ // Matrix simulation:
+ // [1, 2, 0, 0]
+ // [3, 4, 0, 0]
+ // [0, 0, 0, 0]
+ // [0, 0, 0, 0]
+ segmentTree.update(0, 0, 1);
+ segmentTree.update(0, 1, 2);
+ segmentTree.update(1, 0, 3);
+ segmentTree.update(1, 1, 4);
+
+ // Top-left 2x2 sum: 1+2+3+4 = 10
+ assertEquals(10, segmentTree.query(0, 2, 0, 2));
+
+ // First row sum: 1+2 = 3
+ assertEquals(3, segmentTree.query(0, 1, 0, 4));
+
+ // Second column sum: 2+4 = 6
+ assertEquals(6, segmentTree.query(0, 4, 1, 2));
+ }
+
+ @Test
+ void testUpdateOverwriting() {
+ SegmentTree2D segmentTree = new SegmentTree2D(3, 3);
+
+ segmentTree.update(1, 1, 5);
+ assertEquals(5, segmentTree.query(1, 2, 1, 2));
+
+ // Overwrite the same point
+ segmentTree.update(1, 1, 20);
+ assertEquals(20, segmentTree.query(1, 2, 1, 2));
+
+ // Full matrix sum should just be this point
+ assertEquals(20, segmentTree.query(0, 3, 0, 3));
+ }
+}
diff --git a/src/test/java/com/thealgorithms/dynamicprogramming/OptimalBinarySearchTreeTest.java b/src/test/java/com/thealgorithms/dynamicprogramming/OptimalBinarySearchTreeTest.java
new file mode 100644
index 000000000000..17ff3ec728dc
--- /dev/null
+++ b/src/test/java/com/thealgorithms/dynamicprogramming/OptimalBinarySearchTreeTest.java
@@ -0,0 +1,73 @@
+package com.thealgorithms.dynamicprogramming;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import java.util.Arrays;
+import java.util.stream.Stream;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.Arguments;
+import org.junit.jupiter.params.provider.MethodSource;
+
+class OptimalBinarySearchTreeTest {
+
+ @ParameterizedTest
+ @MethodSource("validTestCases")
+ void testFindOptimalCost(int[] keys, int[] frequencies, long expectedCost) {
+ assertEquals(expectedCost, OptimalBinarySearchTree.findOptimalCost(keys, frequencies));
+ }
+
+ private static Stream validTestCases() {
+ return Stream.of(Arguments.of(new int[] {}, new int[] {}, 0L), Arguments.of(new int[] {15}, new int[] {9}, 9L), Arguments.of(new int[] {10, 12}, new int[] {34, 50}, 118L), Arguments.of(new int[] {20, 10, 30}, new int[] {50, 34, 8}, 134L),
+ Arguments.of(new int[] {12, 10, 20, 42, 25, 37}, new int[] {8, 34, 50, 3, 40, 30}, 324L), Arguments.of(new int[] {1, 2, 3}, new int[] {0, 0, 0}, 0L));
+ }
+
+ @ParameterizedTest
+ @MethodSource("crossCheckTestCases")
+ void testFindOptimalCostAgainstBruteForce(int[] keys, int[] frequencies) {
+ assertEquals(bruteForceOptimalCost(keys, frequencies), OptimalBinarySearchTree.findOptimalCost(keys, frequencies));
+ }
+
+ private static Stream crossCheckTestCases() {
+ return Stream.of(Arguments.of(new int[] {3, 1, 2}, new int[] {4, 2, 6}), Arguments.of(new int[] {5, 2, 8, 6}, new int[] {3, 7, 1, 4}), Arguments.of(new int[] {9, 4, 11, 2}, new int[] {1, 8, 2, 5}));
+ }
+
+ @ParameterizedTest
+ @MethodSource("invalidTestCases")
+ void testFindOptimalCostInvalidInput(int[] keys, int[] frequencies) {
+ assertThrows(IllegalArgumentException.class, () -> OptimalBinarySearchTree.findOptimalCost(keys, frequencies));
+ }
+
+ private static Stream invalidTestCases() {
+ return Stream.of(Arguments.of(null, new int[] {}), Arguments.of(new int[] {}, null), Arguments.of(new int[] {1, 2}, new int[] {3}), Arguments.of(new int[] {1, 1}, new int[] {2, 3}), Arguments.of(new int[] {1, 2}, new int[] {3, -1}));
+ }
+
+ private static long bruteForceOptimalCost(int[] keys, int[] frequencies) {
+ int[][] sortedNodes = new int[keys.length][2];
+ for (int index = 0; index < keys.length; index++) {
+ sortedNodes[index][0] = keys[index];
+ sortedNodes[index][1] = frequencies[index];
+ }
+ Arrays.sort(sortedNodes, java.util.Comparator.comparingInt(node -> node[0]));
+
+ int[] sortedFrequencies = new int[sortedNodes.length];
+ for (int index = 0; index < sortedNodes.length; index++) {
+ sortedFrequencies[index] = sortedNodes[index][1];
+ }
+
+ return bruteForceOptimalCost(sortedFrequencies, 0, sortedFrequencies.length - 1, 1);
+ }
+
+ private static long bruteForceOptimalCost(int[] frequencies, int start, int end, int depth) {
+ if (start > end) {
+ return 0L;
+ }
+
+ long minimumCost = Long.MAX_VALUE;
+ for (int root = start; root <= end; root++) {
+ long currentCost = (long) depth * frequencies[root] + bruteForceOptimalCost(frequencies, start, root - 1, depth + 1) + bruteForceOptimalCost(frequencies, root + 1, end, depth + 1);
+ minimumCost = Math.min(minimumCost, currentCost);
+ }
+ return minimumCost;
+ }
+}
diff --git a/src/test/java/com/thealgorithms/geometry/LineIntersectionTest.java b/src/test/java/com/thealgorithms/geometry/LineIntersectionTest.java
new file mode 100644
index 000000000000..9f60df51b65f
--- /dev/null
+++ b/src/test/java/com/thealgorithms/geometry/LineIntersectionTest.java
@@ -0,0 +1,101 @@
+package com.thealgorithms.geometry;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertFalse;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import java.awt.geom.Point2D;
+import java.util.Optional;
+import org.junit.jupiter.api.Test;
+
+class LineIntersectionTest {
+
+ @Test
+ void testCrossingSegments() {
+ Point p1 = new Point(0, 0);
+ Point p2 = new Point(4, 4);
+ Point q1 = new Point(0, 4);
+ Point q2 = new Point(4, 0);
+
+ assertTrue(LineIntersection.intersects(p1, p2, q1, q2));
+ Optional intersection = LineIntersection.intersectionPoint(p1, p2, q1, q2);
+ assertTrue(intersection.isPresent());
+ assertEquals(2.0, intersection.orElseThrow().getX(), 1e-9);
+ assertEquals(2.0, intersection.orElseThrow().getY(), 1e-9);
+ }
+
+ @Test
+ void testParallelSegments() {
+ Point p1 = new Point(0, 0);
+ Point p2 = new Point(3, 3);
+ Point q1 = new Point(0, 1);
+ Point q2 = new Point(3, 4);
+
+ assertFalse(LineIntersection.intersects(p1, p2, q1, q2));
+ assertTrue(LineIntersection.intersectionPoint(p1, p2, q1, q2).isEmpty());
+ }
+
+ @Test
+ void testTouchingAtEndpoint() {
+ Point p1 = new Point(0, 0);
+ Point p2 = new Point(2, 2);
+ Point q1 = new Point(2, 2);
+ Point q2 = new Point(4, 0);
+
+ assertTrue(LineIntersection.intersects(p1, p2, q1, q2));
+ Optional intersection = LineIntersection.intersectionPoint(p1, p2, q1, q2);
+ assertTrue(intersection.isPresent());
+ assertEquals(2.0, intersection.orElseThrow().getX(), 1e-9);
+ assertEquals(2.0, intersection.orElseThrow().getY(), 1e-9);
+ }
+
+ @Test
+ void testCollinearOverlapHasNoUniquePoint() {
+ Point p1 = new Point(0, 0);
+ Point p2 = new Point(4, 4);
+ Point q1 = new Point(2, 2);
+ Point q2 = new Point(6, 6);
+
+ assertTrue(LineIntersection.intersects(p1, p2, q1, q2));
+ assertTrue(LineIntersection.intersectionPoint(p1, p2, q1, q2).isEmpty());
+ }
+
+ @Test
+ void testCollinearDisjointSegments() {
+ Point p1 = new Point(0, 0);
+ Point p2 = new Point(2, 2);
+ Point q1 = new Point(3, 3);
+ Point q2 = new Point(5, 5);
+
+ assertFalse(LineIntersection.intersects(p1, p2, q1, q2));
+ assertTrue(LineIntersection.intersectionPoint(p1, p2, q1, q2).isEmpty());
+ }
+
+ @Test
+ void testCollinearSegmentsTouchingAtEndpointHaveUniquePoint() {
+ Point p1 = new Point(0, 0);
+ Point p2 = new Point(2, 2);
+ Point q1 = new Point(2, 2);
+ Point q2 = new Point(4, 4);
+
+ assertTrue(LineIntersection.intersects(p1, p2, q1, q2));
+ Optional intersection = LineIntersection.intersectionPoint(p1, p2, q1, q2);
+ assertTrue(intersection.isPresent());
+ assertEquals(2.0, intersection.orElseThrow().getX(), 1e-9);
+ assertEquals(2.0, intersection.orElseThrow().getY(), 1e-9);
+ }
+
+ @Test
+ void testVerticalAndHorizontalCrossingSegments() {
+ Point p1 = new Point(2, 0);
+ Point p2 = new Point(2, 5);
+ Point q1 = new Point(0, 3);
+ Point q2 = new Point(4, 3);
+
+ assertTrue(LineIntersection.intersects(p1, p2, q1, q2));
+ Optional intersection = LineIntersection.intersectionPoint(p1, p2, q1, q2);
+ assertTrue(intersection.isPresent());
+ assertEquals(2.0, intersection.orElseThrow().getX(), 1e-9);
+ assertEquals(3.0, intersection.orElseThrow().getY(), 1e-9);
+ }
+}
diff --git a/src/test/java/com/thealgorithms/graph/AccountMergeTest.java b/src/test/java/com/thealgorithms/graph/AccountMergeTest.java
new file mode 100644
index 000000000000..291be677d894
--- /dev/null
+++ b/src/test/java/com/thealgorithms/graph/AccountMergeTest.java
@@ -0,0 +1,61 @@
+package com.thealgorithms.graph;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import java.util.List;
+import org.junit.jupiter.api.Test;
+
+class AccountMergeTest {
+
+ @Test
+ void testMergeAccountsWithSharedEmails() {
+ List> accounts = List.of(List.of("abc", "abc@mail.com", "abx@mail.com"), List.of("abc", "abc@mail.com", "aby@mail.com"), List.of("Mary", "mary@mail.com"), List.of("John", "johnnybravo@mail.com"));
+
+ List> merged = AccountMerge.mergeAccounts(accounts);
+
+ List> expected = List.of(List.of("John", "johnnybravo@mail.com"), List.of("Mary", "mary@mail.com"), List.of("abc", "abc@mail.com", "abx@mail.com", "aby@mail.com"));
+
+ assertEquals(expected, merged);
+ }
+
+ @Test
+ void testAccountsWithSameNameButNoSharedEmailStaySeparate() {
+ List> accounts = List.of(List.of("Alex", "alex1@mail.com"), List.of("Alex", "alex2@mail.com"));
+
+ List> merged = AccountMerge.mergeAccounts(accounts);
+ List> expected = List.of(List.of("Alex", "alex1@mail.com"), List.of("Alex", "alex2@mail.com"));
+
+ assertEquals(expected, merged);
+ }
+
+ @Test
+ void testEmptyInput() {
+ assertEquals(List.of(), AccountMerge.mergeAccounts(List.of()));
+ }
+
+ @Test
+ void testNullInput() {
+ assertEquals(List.of(), AccountMerge.mergeAccounts(null));
+ }
+
+ @Test
+ void testTransitiveMergeAndDuplicateEmails() {
+ List> accounts = List.of(List.of("A", "a1@mail.com", "a2@mail.com"), List.of("A", "a2@mail.com", "a3@mail.com"), List.of("A", "a3@mail.com", "a4@mail.com", "a4@mail.com"));
+
+ List> merged = AccountMerge.mergeAccounts(accounts);
+
+ List> expected = List.of(List.of("A", "a1@mail.com", "a2@mail.com", "a3@mail.com", "a4@mail.com"));
+
+ assertEquals(expected, merged);
+ }
+
+ @Test
+ void testAccountsWithNoEmailsArePreserved() {
+ List> accounts = List.of(List.of("Alex"), List.of("Alex", "alex1@mail.com"), List.of("Bob"));
+
+ List> merged = AccountMerge.mergeAccounts(accounts);
+ List> expected = List.of(List.of("Alex"), List.of("Alex", "alex1@mail.com"), List.of("Bob"));
+
+ assertEquals(expected, merged);
+ }
+}
diff --git a/src/test/java/com/thealgorithms/graph/TarjanBridgesTest.java b/src/test/java/com/thealgorithms/graph/TarjanBridgesTest.java
new file mode 100644
index 000000000000..8608bfb2dfc9
--- /dev/null
+++ b/src/test/java/com/thealgorithms/graph/TarjanBridgesTest.java
@@ -0,0 +1,207 @@
+package com.thealgorithms.graph;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import java.util.ArrayList;
+import java.util.Comparator;
+import java.util.List;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Unit tests for {@link TarjanBridges}.
+ *
+ * Tests cover a wide range of graph configurations including simple graphs,
+ * cycles, trees, disconnected components, multigraph-like structures, and
+ * various edge cases to ensure correct bridge detection.
+ */
+class TarjanBridgesTest {
+
+ /**
+ * Helper to build a symmetric adjacency list for an undirected graph.
+ */
+ private static List> buildGraph(int vertexCount, int[][] edges) {
+ List> adj = new ArrayList<>();
+ for (int i = 0; i < vertexCount; i++) {
+ adj.add(new ArrayList<>());
+ }
+ for (int[] edge : edges) {
+ adj.get(edge[0]).add(edge[1]);
+ adj.get(edge[1]).add(edge[0]);
+ }
+ return adj;
+ }
+
+ /**
+ * Sorts bridges for deterministic comparison.
+ */
+ private static void sortBridges(List bridges) {
+ bridges.sort(Comparator.comparingInt((int[] a) -> a[0]).thenComparingInt(a -> a[1]));
+ }
+
+ @Test
+ void testSimpleGraphWithOneBridge() {
+ // Graph: 0-1-2-3 where 1-2 is the only bridge
+ // 0---1---2---3
+ // | |
+ // +-------+ (via 0-2 would make cycle, but not here)
+ // Actually: 0-1 in a cycle with 0-1, and 2-3 in a cycle with 2-3
+ // Let's use: 0--1--2 (linear chain). All edges are bridges.
+ List> adj = buildGraph(3, new int[][] {{0, 1}, {1, 2}});
+ List bridges = TarjanBridges.findBridges(3, adj);
+ sortBridges(bridges);
+ assertEquals(2, bridges.size());
+ assertEquals(0, bridges.get(0)[0]);
+ assertEquals(1, bridges.get(0)[1]);
+ assertEquals(1, bridges.get(1)[0]);
+ assertEquals(2, bridges.get(1)[1]);
+ }
+
+ @Test
+ void testCycleGraphHasNoBridges() {
+ // Graph: 0-1-2-0 (triangle). No bridges.
+ List> adj = buildGraph(3, new int[][] {{0, 1}, {1, 2}, {2, 0}});
+ List bridges = TarjanBridges.findBridges(3, adj);
+ assertTrue(bridges.isEmpty());
+ }
+
+ @Test
+ void testTreeGraphAllEdgesAreBridges() {
+ // Tree: 0
+ // / \
+ // 1 2
+ // / \
+ // 3 4
+ List> adj = buildGraph(5, new int[][] {{0, 1}, {0, 2}, {1, 3}, {1, 4}});
+ List bridges = TarjanBridges.findBridges(5, adj);
+ assertEquals(4, bridges.size());
+ }
+
+ @Test
+ void testGraphWithMixedBridgesAndCycles() {
+ // Graph:
+ // 0---1
+ // | |
+ // 3---2---4---5
+ // |
+ // 6
+ // Cycle: 0-1-2-3-0 (no bridges within)
+ // Bridges: 2-4, 4-5, 5-6
+ List> adj = buildGraph(7, new int[][] {{0, 1}, {1, 2}, {2, 3}, {3, 0}, {2, 4}, {4, 5}, {5, 6}});
+ List bridges = TarjanBridges.findBridges(7, adj);
+ sortBridges(bridges);
+ assertEquals(3, bridges.size());
+ assertEquals(2, bridges.get(0)[0]);
+ assertEquals(4, bridges.get(0)[1]);
+ assertEquals(4, bridges.get(1)[0]);
+ assertEquals(5, bridges.get(1)[1]);
+ assertEquals(5, bridges.get(2)[0]);
+ assertEquals(6, bridges.get(2)[1]);
+ }
+
+ @Test
+ void testDisconnectedGraphWithBridges() {
+ // Component 1: 0-1 (bridge)
+ // Component 2: 2-3-4-2 (cycle, no bridges)
+ List> adj = buildGraph(5, new int[][] {{0, 1}, {2, 3}, {3, 4}, {4, 2}});
+ List bridges = TarjanBridges.findBridges(5, adj);
+ assertEquals(1, bridges.size());
+ assertEquals(0, bridges.get(0)[0]);
+ assertEquals(1, bridges.get(0)[1]);
+ }
+
+ @Test
+ void testSingleVertex() {
+ List> adj = buildGraph(1, new int[][] {});
+ List bridges = TarjanBridges.findBridges(1, adj);
+ assertTrue(bridges.isEmpty());
+ }
+
+ @Test
+ void testTwoVerticesWithOneEdge() {
+ List> adj = buildGraph(2, new int[][] {{0, 1}});
+ List bridges = TarjanBridges.findBridges(2, adj);
+ assertEquals(1, bridges.size());
+ assertEquals(0, bridges.get(0)[0]);
+ assertEquals(1, bridges.get(0)[1]);
+ }
+
+ @Test
+ void testEmptyGraph() {
+ List> adj = buildGraph(0, new int[][] {});
+ List bridges = TarjanBridges.findBridges(0, adj);
+ assertTrue(bridges.isEmpty());
+ }
+
+ @Test
+ void testIsolatedVertices() {
+ // 5 vertices, no edges — all isolated
+ List> adj = buildGraph(5, new int[][] {});
+ List bridges = TarjanBridges.findBridges(5, adj);
+ assertTrue(bridges.isEmpty());
+ }
+
+ @Test
+ void testLargeCycleNoBridges() {
+ // Cycle: 0-1-2-3-4-5-6-7-0
+ int n = 8;
+ int[][] edges = new int[n][2];
+ for (int i = 0; i < n; i++) {
+ edges[i] = new int[] {i, (i + 1) % n};
+ }
+ List> adj = buildGraph(n, edges);
+ List bridges = TarjanBridges.findBridges(n, adj);
+ assertTrue(bridges.isEmpty());
+ }
+
+ @Test
+ void testComplexGraphWithMultipleCyclesAndBridges() {
+ // Two cycles connected by a single bridge edge:
+ // Cycle A: 0-1-2-0
+ // Cycle B: 3-4-5-3
+ // Bridge: 2-3
+ List> adj = buildGraph(6, new int[][] {{0, 1}, {1, 2}, {2, 0}, {3, 4}, {4, 5}, {5, 3}, {2, 3}});
+ List bridges = TarjanBridges.findBridges(6, adj);
+ assertEquals(1, bridges.size());
+ assertEquals(2, bridges.get(0)[0]);
+ assertEquals(3, bridges.get(0)[1]);
+ }
+
+ @Test
+ void testNegativeVertexCountThrowsException() {
+ assertThrows(IllegalArgumentException.class, () -> TarjanBridges.findBridges(-1, new ArrayList<>()));
+ }
+
+ @Test
+ void testNullAdjacencyListThrowsException() {
+ assertThrows(IllegalArgumentException.class, () -> TarjanBridges.findBridges(3, null));
+ }
+
+ @Test
+ void testMismatchedAdjacencyListSizeThrowsException() {
+ List> adj = buildGraph(2, new int[][] {{0, 1}});
+ assertThrows(IllegalArgumentException.class, () -> TarjanBridges.findBridges(5, adj));
+ }
+
+ @Test
+ void testStarGraphAllEdgesAreBridges() {
+ // Star graph: center vertex 0 connected to 1, 2, 3, 4
+ List> adj = buildGraph(5, new int[][] {{0, 1}, {0, 2}, {0, 3}, {0, 4}});
+ List bridges = TarjanBridges.findBridges(5, adj);
+ assertEquals(4, bridges.size());
+ }
+
+ @Test
+ void testBridgeBetweenTwoCycles() {
+ // Two squares connected by one bridge:
+ // Square 1: 0-1-2-3-0
+ // Square 2: 4-5-6-7-4
+ // Bridge: 3-4
+ List> adj = buildGraph(8, new int[][] {{0, 1}, {1, 2}, {2, 3}, {3, 0}, {4, 5}, {5, 6}, {6, 7}, {7, 4}, {3, 4}});
+ List bridges = TarjanBridges.findBridges(8, adj);
+ assertEquals(1, bridges.size());
+ assertEquals(3, bridges.get(0)[0]);
+ assertEquals(4, bridges.get(0)[1]);
+ }
+}
diff --git a/src/test/java/com/thealgorithms/maths/CorrelationTest.java b/src/test/java/com/thealgorithms/maths/CorrelationTest.java
new file mode 100644
index 000000000000..96867d56ad5e
--- /dev/null
+++ b/src/test/java/com/thealgorithms/maths/CorrelationTest.java
@@ -0,0 +1,51 @@
+package com.thealgorithms.maths;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+/**
+ * Test class for Correlation class
+ */
+public class CorrelationTest {
+
+ public static final double DELTA = 1e-9;
+
+ // Regular correlation test
+ public void testCorrelationFirst() {
+ double[] x = {1, 2, 3, 4};
+ double[] y = {7, 1, 4, 9};
+ int n = 4;
+ assertEquals(0.3319700011, Correlation.correlation(x, y, n), DELTA);
+ }
+
+ // Regular correlation test (zero correlation)
+ public void testCorrelationSecond() {
+ double[] x = {1, 2, 3, 4};
+ double[] y = {5, 0, 9, 2};
+ int n = 4;
+ assertEquals(0, Correlation.correlation(x, y, n), DELTA);
+ }
+
+ // Correlation with a constant variable is taken to be zero
+ public void testCorrelationConstant() {
+ double[] x = {1, 2, 3};
+ double[] y = {4, 4, 4};
+ int n = 3;
+ assertEquals(0, Correlation.correlation(x, y, n), DELTA);
+ }
+
+ // Linear dependence gives correlation 1
+ public void testCorrelationLinearDependence() {
+ double[] x = {1, 2, 3, 4};
+ double[] y = {6, 8, 10, 12};
+ int n = 4;
+ assertEquals(1, Correlation.correlation(x, y, n), DELTA);
+ }
+
+ // Inverse linear dependence gives correlation -1
+ public void testCorrelationInverseLinearDependence() {
+ double[] x = {1, 2, 3, 4, 5};
+ double[] y = {18, 15, 12, 9, 6};
+ int n = 5;
+ assertEquals(-1, Correlation.correlation(x, y, n), DELTA);
+ }
+}
diff --git a/src/test/java/com/thealgorithms/maths/FactorialTest.java b/src/test/java/com/thealgorithms/maths/FactorialTest.java
index 3ff7097b8113..a393136696e1 100644
--- a/src/test/java/com/thealgorithms/maths/FactorialTest.java
+++ b/src/test/java/com/thealgorithms/maths/FactorialTest.java
@@ -3,6 +3,7 @@
import static org.junit.jupiter.api.Assertions.assertEquals;
import static org.junit.jupiter.api.Assertions.assertThrows;
+import java.math.BigInteger;
import org.junit.jupiter.api.Test;
public class FactorialTest {
@@ -16,9 +17,9 @@ public void testWhenInvalidInoutProvidedShouldThrowException() {
@Test
public void testCorrectFactorialCalculation() {
- assertEquals(1, Factorial.factorial(0));
- assertEquals(1, Factorial.factorial(1));
- assertEquals(120, Factorial.factorial(5));
- assertEquals(3628800, Factorial.factorial(10));
+ assertEquals(BigInteger.ONE, Factorial.factorial(0));
+ assertEquals(BigInteger.ONE, Factorial.factorial(1));
+ assertEquals(BigInteger.valueOf(120), Factorial.factorial(5));
+ assertEquals(BigInteger.valueOf(3628800), Factorial.factorial(10));
}
}
diff --git a/src/test/java/com/thealgorithms/maths/VolumeTest.java b/src/test/java/com/thealgorithms/maths/VolumeTest.java
index c159d7566b46..c0b02d6ba28e 100644
--- a/src/test/java/com/thealgorithms/maths/VolumeTest.java
+++ b/src/test/java/com/thealgorithms/maths/VolumeTest.java
@@ -41,5 +41,8 @@ public void volume() {
/* test torus */
assertEquals(39.47841760435743, Volume.volumeTorus(2, 1));
+
+ /* test ellipsoid */
+ assertEquals(25.1327412287183459, Volume.volumeEllipsoid(3, 2, 1));
}
}
diff --git a/src/test/java/com/thealgorithms/physics/RelativityTest.java b/src/test/java/com/thealgorithms/physics/RelativityTest.java
new file mode 100644
index 000000000000..44c17bdbd40f
--- /dev/null
+++ b/src/test/java/com/thealgorithms/physics/RelativityTest.java
@@ -0,0 +1,73 @@
+package com.thealgorithms.physics;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.DisplayName;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Unit tests for the Relativity utility class.
+ */
+final class RelativityTest {
+
+ // A small tolerance (delta) for comparing floating-point numbers
+ private static final double DELTA = 1e-6;
+ private static final double C = Relativity.SPEED_OF_LIGHT;
+
+ @Test
+ @DisplayName("Test the gamma parameter")
+ void testGamma() {
+ double myGamma = Relativity.gamma(0.6 * C);
+ assertEquals(1.25, myGamma, DELTA);
+ }
+
+ @Test
+ @DisplayName("Test the length contraction")
+ void testLengthContraction() {
+ double myLength = Relativity.lengthContraction(5.0, 0.8 * C);
+ assertEquals(3.0, myLength, DELTA);
+ }
+
+ @Test
+ @DisplayName("Test the time dilation")
+ void testTimeDilation() {
+ double myTime = Relativity.timeDilation(4.0, 0.6 * C);
+ assertEquals(5.0, myTime, DELTA);
+ }
+
+ @Test
+ @DisplayName("Test the velocity addition in the same direction")
+ void testVelocityAdditionSameDirection() {
+ double myVelocity = Relativity.velocityAddition(0.8 * C, 0.75 * C);
+ assertEquals(0.125 * C, myVelocity, DELTA);
+ }
+
+ @Test
+ @DisplayName("Test the velocity addition in different directions")
+ void testVelocityAdditionDifferentDirections() {
+ double myVelocity = Relativity.velocityAddition(0.8 * C, -0.75 * C);
+ assertEquals(0.96875 * C, myVelocity, DELTA);
+ }
+
+ @Test
+ @DisplayName("Test the velocity addition with the speed of light")
+ void testVelocityAdditionWithSpeedOfLight() {
+ double myVelocity = Relativity.velocityAddition(C, 0.7 * C);
+ assertEquals(C, myVelocity, DELTA);
+ }
+
+ @Test
+ @DisplayName("Test invalid inputs throw exception")
+ void testInvalidOrbitalVelocityInputs() {
+ assertThrows(IllegalArgumentException.class, () -> Relativity.gamma(1.2 * C));
+ assertThrows(IllegalArgumentException.class, () -> Relativity.gamma(-C));
+ assertThrows(IllegalArgumentException.class, () -> Relativity.lengthContraction(-1.0, 0.6 * C));
+ assertThrows(IllegalArgumentException.class, () -> Relativity.lengthContraction(1.0, 1.5 * C));
+ assertThrows(IllegalArgumentException.class, () -> Relativity.timeDilation(-5.0, -0.8 * C));
+ assertThrows(IllegalArgumentException.class, () -> Relativity.timeDilation(5.0, C));
+ assertThrows(IllegalArgumentException.class, () -> Relativity.velocityAddition(0.3 * C, -C));
+ assertThrows(IllegalArgumentException.class, () -> Relativity.velocityAddition(1.4 * C, 0.2 * C));
+ assertThrows(IllegalArgumentException.class, () -> Relativity.velocityAddition(-0.4 * C, 1.2 * C));
+ }
+}
diff --git a/src/test/java/com/thealgorithms/searches/BinarySearchTest.java b/src/test/java/com/thealgorithms/searches/BinarySearchTest.java
index bd4620a7fa7d..00bed165734e 100644
--- a/src/test/java/com/thealgorithms/searches/BinarySearchTest.java
+++ b/src/test/java/com/thealgorithms/searches/BinarySearchTest.java
@@ -105,4 +105,90 @@ void testBinarySearchLargeArray() {
int expectedIndex = 9999; // Index of the last element
assertEquals(expectedIndex, binarySearch.find(array, key), "The index of the last element should be 9999.");
}
+
+ /**
+ * Test for binary search with null array.
+ */
+ @Test
+ void testBinarySearchNullArray() {
+ BinarySearch binarySearch = new BinarySearch();
+ Integer[] array = null;
+ int key = 5; // Key to search
+ int expectedIndex = -1; // Key not found
+ assertEquals(expectedIndex, binarySearch.find(array, key), "The element should not be found in a null array.");
+ }
+
+ /**
+ * Test for binary search with duplicate elements.
+ */
+ @Test
+ void testBinarySearchWithDuplicates() {
+ BinarySearch binarySearch = new BinarySearch();
+ Integer[] array = {1, 2, 2, 2, 3};
+ int key = 2; // Element present multiple times
+
+ int result = binarySearch.find(array, key);
+ assertEquals(2, array[result], "The returned index should contain the searched element.");
+ }
+
+ /**
+ * Test for binary search where all elements are the same.
+ */
+ @Test
+ void testBinarySearchAllElementsSame() {
+ BinarySearch binarySearch = new BinarySearch();
+ Integer[] array = {5, 5, 5, 5, 5};
+ int key = 5; // All elements match
+
+ int result = binarySearch.find(array, key);
+ assertEquals(5, array[result], "The returned index should contain the searched element.");
+ }
+
+ /**
+ * Test for binary search with negative numbers.
+ */
+ @Test
+ void testBinarySearchNegativeNumbers() {
+ BinarySearch binarySearch = new BinarySearch();
+ Integer[] array = {-10, -5, 0, 5, 10};
+ int key = -5; // Element present
+ int expectedIndex = 1; // Index of the element
+ assertEquals(expectedIndex, binarySearch.find(array, key), "The index of the element should be 1.");
+ }
+
+ /**
+ * Test for binary search when key is smaller than all elements.
+ */
+ @Test
+ void testBinarySearchKeySmallerThanAll() {
+ BinarySearch binarySearch = new BinarySearch();
+ Integer[] array = {10, 20, 30};
+ int key = 5; // Smaller than all elements
+ int expectedIndex = -1; // Key not found
+ assertEquals(expectedIndex, binarySearch.find(array, key), "The element should not be found in the array.");
+ }
+
+ /**
+ * Test for binary search when key is larger than all elements.
+ */
+ @Test
+ void testBinarySearchKeyLargerThanAll() {
+ BinarySearch binarySearch = new BinarySearch();
+ Integer[] array = {10, 20, 30};
+ int key = 40; // Larger than all elements
+ int expectedIndex = -1; // Key not found
+ assertEquals(expectedIndex, binarySearch.find(array, key), "The element should not be found in the array.");
+ }
+
+ /**
+ * Test for binary search with String array.
+ */
+ @Test
+ void testBinarySearchStrings() {
+ BinarySearch binarySearch = new BinarySearch();
+ String[] array = {"apple", "banana", "cherry", "date"};
+ String key = "cherry"; // Element present
+ int expectedIndex = 2; // Index of the element
+ assertEquals(expectedIndex, binarySearch.find(array, key), "The index of the element should be 2.");
+ }
}
diff --git a/src/test/java/com/thealgorithms/searches/IterativeBinarySearchTest.java b/src/test/java/com/thealgorithms/searches/IterativeBinarySearchTest.java
index b2e121ac1ba0..f291610b298b 100644
--- a/src/test/java/com/thealgorithms/searches/IterativeBinarySearchTest.java
+++ b/src/test/java/com/thealgorithms/searches/IterativeBinarySearchTest.java
@@ -87,6 +87,26 @@ void testBinarySearchEmptyArray() {
assertEquals(-1, binarySearch.find(array, key), "The element should not be found in an empty array.");
}
+ /**
+ * Test for binary search with a null array.
+ */
+ @Test
+ void testBinarySearchNullArray() {
+ IterativeBinarySearch binarySearch = new IterativeBinarySearch();
+ Integer key = 1;
+ assertEquals(-1, binarySearch.find(null, key), "The element should not be found in a null array.");
+ }
+
+ /**
+ * Test for binary search with a null key.
+ */
+ @Test
+ void testBinarySearchNullKey() {
+ IterativeBinarySearch binarySearch = new IterativeBinarySearch();
+ Integer[] array = {1, 2, 4, 8, 16};
+ assertEquals(-1, binarySearch.find(array, null), "A null search key should return -1.");
+ }
+
/**
* Test for binary search on a large array.
*/
diff --git a/src/test/java/com/thealgorithms/stacks/StockSpanProblemTest.java b/src/test/java/com/thealgorithms/stacks/StockSpanProblemTest.java
new file mode 100644
index 000000000000..2e4ea74691da
--- /dev/null
+++ b/src/test/java/com/thealgorithms/stacks/StockSpanProblemTest.java
@@ -0,0 +1,34 @@
+package com.thealgorithms.stacks;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import java.util.stream.Stream;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.Arguments;
+import org.junit.jupiter.params.provider.MethodSource;
+
+class StockSpanProblemTest {
+
+ @ParameterizedTest
+ @MethodSource("validTestCases")
+ void testCalculateSpan(int[] prices, int[] expectedSpans) {
+ assertArrayEquals(expectedSpans, StockSpanProblem.calculateSpan(prices));
+ }
+
+ private static Stream validTestCases() {
+ return Stream.of(Arguments.of(new int[] {10, 4, 5, 90, 120, 80}, new int[] {1, 1, 2, 4, 5, 1}), Arguments.of(new int[] {100, 50, 60, 70, 80, 90}, new int[] {1, 1, 2, 3, 4, 5}), Arguments.of(new int[] {5, 4, 3, 2, 1}, new int[] {1, 1, 1, 1, 1}),
+ Arguments.of(new int[] {1, 2, 3, 4, 5}, new int[] {1, 2, 3, 4, 5}), Arguments.of(new int[] {10, 20, 30, 40, 50}, new int[] {1, 2, 3, 4, 5}), Arguments.of(new int[] {100, 80, 60, 70, 60, 75, 85}, new int[] {1, 1, 1, 2, 1, 4, 6}),
+ Arguments.of(new int[] {7, 7, 7, 7}, new int[] {1, 2, 3, 4}), Arguments.of(new int[] {}, new int[] {}), Arguments.of(new int[] {42}, new int[] {1}));
+ }
+
+ @ParameterizedTest
+ @MethodSource("invalidTestCases")
+ void testCalculateSpanInvalidInput(int[] prices) {
+ assertThrows(IllegalArgumentException.class, () -> StockSpanProblem.calculateSpan(prices));
+ }
+
+ private static Stream invalidTestCases() {
+ return Stream.of(Arguments.of((int[]) null));
+ }
+}
diff --git a/src/test/java/com/thealgorithms/strings/AlphabeticalTest.java b/src/test/java/com/thealgorithms/strings/AlphabeticalTest.java
index 7b41e11ef22f..0c7d7e4701cf 100644
--- a/src/test/java/com/thealgorithms/strings/AlphabeticalTest.java
+++ b/src/test/java/com/thealgorithms/strings/AlphabeticalTest.java
@@ -1,15 +1,45 @@
package com.thealgorithms.strings;
import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.params.provider.Arguments.arguments;
+import java.util.stream.Stream;
+import org.junit.jupiter.api.DisplayName;
+import org.junit.jupiter.api.Test;
import org.junit.jupiter.params.ParameterizedTest;
-import org.junit.jupiter.params.provider.CsvSource;
+import org.junit.jupiter.params.provider.Arguments;
+import org.junit.jupiter.params.provider.MethodSource;
-public class AlphabeticalTest {
+@DisplayName("Alphabetical.isAlphabetical()")
+class AlphabeticalTest {
- @ParameterizedTest(name = "\"{0}\" → Expected: {1}")
- @CsvSource({"'abcdefghijklmno', true", "'abcdxxxyzzzz', true", "'123a', false", "'abcABC', false", "'abcdefghikjlmno', false", "'aBC', true", "'abc', true", "'xyzabc', false", "'abcxyz', true", "'', false", "'1', false"})
- void testIsAlphabetical(String input, boolean expected) {
- assertEquals(expected, Alphabetical.isAlphabetical(input));
+ static Stream testCases() {
+ // Workaround for SpotBugs false positive (NAB_NEEDLESS_BOOLEAN_CONSTANT_CONVERSION)
+ // due to JUnit Arguments.of(Object...) auto-boxing
+ return Stream.of(arguments("", Boolean.FALSE, "Should return false for empty string"), arguments(" ", Boolean.FALSE, "Should return false for blank string"), arguments("a1b2", Boolean.FALSE, "Should return false when string contains numbers"),
+ arguments("abc!DEF", Boolean.FALSE, "Should return false when string contains symbols"), arguments("#abc", Boolean.FALSE, "Should return false when first character is not a letter"), arguments("abc", Boolean.TRUE, "Should return true for non-decreasing order"),
+ arguments("aBcD", Boolean.TRUE, "Should return true for mixed case increasing sequence"), arguments("a", Boolean.TRUE, "Should return true for single letter"), arguments("'", Boolean.FALSE, "Should return false for single symbol"),
+ arguments("aabbcc", Boolean.TRUE, "Should return true for repeated letters"), arguments("cba", Boolean.FALSE, "Should return false when order decreases"), arguments("abzba", Boolean.FALSE, "Should return false when middle breaks order"));
+ }
+
+ private void assertAlphabetical(String input, boolean expected, String message) {
+ // Arrange & Act
+ boolean result = Alphabetical.isAlphabetical(input);
+
+ // Assert
+ assertEquals(expected, result, message);
+ }
+
+ @Test
+ @DisplayName("Should return false for null input")
+ void nullInputTest() {
+ assertAlphabetical(null, false, "Should return false for null input");
+ }
+
+ @ParameterizedTest(name = "{2}")
+ @MethodSource("testCases")
+ @DisplayName("Alphabetical cases")
+ void isAlphabeticalTest(String input, boolean expected, String message) {
+ assertAlphabetical(input, expected, message);
}
}
diff --git a/src/test/java/com/thealgorithms/strings/KasaiAlgorithmTest.java b/src/test/java/com/thealgorithms/strings/KasaiAlgorithmTest.java
new file mode 100644
index 000000000000..c22cc77df18a
--- /dev/null
+++ b/src/test/java/com/thealgorithms/strings/KasaiAlgorithmTest.java
@@ -0,0 +1,75 @@
+package com.thealgorithms.strings;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.Test;
+
+public class KasaiAlgorithmTest {
+
+ @Test
+ public void testKasaiBanana() {
+ String text = "banana";
+ // Suffixes:
+ // 0: banana
+ // 1: anana
+ // 2: nana
+ // 3: ana
+ // 4: na
+ // 5: a
+ //
+ // Sorted Suffixes:
+ // 5: a
+ // 3: ana
+ // 1: anana
+ // 0: banana
+ // 4: na
+ // 2: nana
+ int[] suffixArr = {5, 3, 1, 0, 4, 2};
+
+ int[] expectedLcp = {1, 3, 0, 0, 2, 0};
+
+ assertArrayEquals(expectedLcp, KasaiAlgorithm.kasai(text, suffixArr));
+ }
+
+ @Test
+ public void testKasaiAaaa() {
+ String text = "aaaa";
+ // Sorted Suffixes:
+ // 3: a
+ // 2: aa
+ // 1: aaa
+ // 0: aaaa
+ int[] suffixArr = {3, 2, 1, 0};
+ int[] expectedLcp = {1, 2, 3, 0};
+
+ assertArrayEquals(expectedLcp, KasaiAlgorithm.kasai(text, suffixArr));
+ }
+
+ @Test
+ public void testKasaiEmptyString() {
+ assertArrayEquals(new int[0], KasaiAlgorithm.kasai("", new int[0]));
+ }
+
+ @Test
+ public void testKasaiSingleChar() {
+ assertArrayEquals(new int[] {0}, KasaiAlgorithm.kasai("A", new int[] {0}));
+ }
+
+ @Test
+ public void testKasaiNullTextOrSuffixArray() {
+ assertThrows(IllegalArgumentException.class, () -> KasaiAlgorithm.kasai(null, new int[] {0}));
+ assertThrows(IllegalArgumentException.class, () -> KasaiAlgorithm.kasai("A", null));
+ }
+
+ @Test
+ public void testKasaiInvalidSuffixArrayLength() {
+ assertThrows(IllegalArgumentException.class, () -> KasaiAlgorithm.kasai("A", new int[] {0, 1}));
+ }
+
+ @Test
+ public void testKasaiInvalidSuffixArrayIndex() {
+ assertThrows(IllegalArgumentException.class, () -> KasaiAlgorithm.kasai("A", new int[] {1})); // Out of bounds
+ assertThrows(IllegalArgumentException.class, () -> KasaiAlgorithm.kasai("A", new int[] {-1})); // Out of bounds
+ }
+}
diff --git a/src/test/java/com/thealgorithms/strings/MoveHashToEndTest.java b/src/test/java/com/thealgorithms/strings/MoveHashToEndTest.java
new file mode 100644
index 000000000000..016f72ff9d7f
--- /dev/null
+++ b/src/test/java/com/thealgorithms/strings/MoveHashToEndTest.java
@@ -0,0 +1,54 @@
+package com.thealgorithms.strings;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertNull;
+
+import org.junit.jupiter.api.Test;
+
+public class MoveHashToEndTest {
+
+ @Test
+ void testBasicCase() {
+ assertEquals("helllo###", MoveHashToEnd.moveHashToEnd("h#e#l#llo"));
+ }
+
+ @Test
+ void testNoHash() {
+ assertEquals("hello", MoveHashToEnd.moveHashToEnd("hello"));
+ }
+
+ @Test
+ void testAllHashes() {
+ assertEquals("###", MoveHashToEnd.moveHashToEnd("###"));
+ }
+
+ @Test
+ void testHashAtEnd() {
+ assertEquals("hello#", MoveHashToEnd.moveHashToEnd("hello#"));
+ }
+
+ @Test
+ void testHashAtStart() {
+ assertEquals("hello#", MoveHashToEnd.moveHashToEnd("#hello"));
+ }
+
+ @Test
+ void testEmptyString() {
+ assertEquals("", MoveHashToEnd.moveHashToEnd(""));
+ }
+
+ @Test
+ void testNullInput() {
+ assertNull(MoveHashToEnd.moveHashToEnd(null));
+ }
+
+ @Test
+ void testSingleHash() {
+ assertEquals("#", MoveHashToEnd.moveHashToEnd("#"));
+ }
+
+ @Test
+ void testSingleNonHashChar() {
+ assertEquals("a", MoveHashToEnd.moveHashToEnd("a"));
+ }
+}