|
| 1 | +# LeetCode 684. Redundant Connection's Solution |
| 2 | +LeetCode problem link: [684. Redundant Connection](https://leetcode.com/problems/redundant-connection) |
| 3 | + |
| 4 | +## LeetCode problem description |
| 5 | +In this problem, a tree is an **undirected graph** that is connected and has no cycles. |
| 6 | + |
| 7 | +You are given a graph that started as a tree with `n` nodes labeled from `1` to `n`, with one additional edge added. The added edge has two **different** vertices chosen from `1` to `n`, and was not an edge that already existed. The graph is represented as an array `edges` of length `n` where `edges[i] = [ai, bi]` indicates that there is an edge between nodes `ai` and `bi` in the graph. |
| 8 | + |
| 9 | +Return an edge that can be removed so that the resulting graph is a tree of `n` nodes. If there are multiple answers, return the answer that occurs last in the input. |
| 10 | + |
| 11 | +### Example 1 |
| 12 | + |
| 13 | +``` |
| 14 | +Input: edges = [[1,2],[1,3],[2,3]] |
| 15 | +Output: [2,3] |
| 16 | +``` |
| 17 | + |
| 18 | +### Example 2 |
| 19 | + |
| 20 | +``` |
| 21 | +Input: edges = [[1,2],[2,3],[3,4],[1,4],[1,5]] |
| 22 | +Output: [1,4] |
| 23 | +``` |
| 24 | + |
| 25 | +### Constraints |
| 26 | +- `n == edges.length` |
| 27 | +- `3 <= n <= 1000` |
| 28 | +- `edges[i].length == 2` |
| 29 | +- `1 <= ai < bi <= edges.length` |
| 30 | +- `ai != bi` |
| 31 | +- There are no repeated edges. |
| 32 | +- The given graph is connected. |
| 33 | + |
| 34 | +## Intuition |
| 35 | +- This undirected graph has only **one** **connected component**, which is a tree. |
| 36 | +- When an edge is added to the graph, its two nodes are also added to the graph. |
| 37 | +- If the two nodes are already in the graph, then they must be on the same tree. At this time, a cycle is bound to be formed. |
| 38 | + |
| 39 | + |
| 40 | + |
| 41 | +- We are given `edges` data and need to divide them into multiple groups, each group can be abstracted into a **tree**. |
| 42 | +- Finally, those trees will be merged into one tree. |
| 43 | +- `UnionFind` algorithm is designed for grouping and searching data. |
| 44 | + |
| 45 | +### 'UnionFind' algorithm |
| 46 | +- `UnionFind` algorithm typically has three methods: |
| 47 | + - The `unite(node1, node2)` operation can be used to merge two trees. |
| 48 | + - The `find_root(node)` method can be used to return the root of a node. |
| 49 | + - The `same_root(node1, node2)` method can be used to judge if two nodes are in the same tree. |
| 50 | + |
| 51 | +## Approach (UnionFind algorithm) |
| 52 | +1. Initially, each node is in its own group. |
| 53 | +1. Iterate `edges` data and `unite(node1, node2)`. |
| 54 | +1. As soon as `same_root(node1, node2)`, return `[node1, node2]`. |
| 55 | + |
| 56 | +## Complexity |
| 57 | +* Time: `O(n)`. |
| 58 | +* Space: `O(n)`. |
| 59 | + |
| 60 | +## Python |
| 61 | +```python |
| 62 | +class Solution: |
| 63 | + def __init__(self): |
| 64 | + self.fathers = None |
| 65 | + |
| 66 | + def findRedundantConnection(self, edges: List[List[int]]) -> List[int]: |
| 67 | + self.fathers = list(range(len(edges) + 1)) |
| 68 | + |
| 69 | + for x, y in edges: |
| 70 | + if self.same_root(x, y): |
| 71 | + return [x, y] |
| 72 | + |
| 73 | + self.unite(x, y) |
| 74 | + |
| 75 | + def unite(self, x, y): |
| 76 | + root_x = self.find_root(x) |
| 77 | + root_y = self.find_root(y) |
| 78 | + |
| 79 | + self.fathers[root_y] = root_x # Error-prone point |
| 80 | + |
| 81 | + def find_root(self, x): |
| 82 | + if x == self.fathers[x]: |
| 83 | + return x |
| 84 | + |
| 85 | + self.fathers[x] = self.find_root(self.fathers[x]) |
| 86 | + |
| 87 | + return self.fathers[x] |
| 88 | + |
| 89 | + def same_root(self, x, y): |
| 90 | + return self.find_root(x) == self.find_root(y) |
| 91 | +``` |
| 92 | + |
| 93 | +## Java |
| 94 | +```java |
| 95 | +class Solution { |
| 96 | + private int[] fathers; |
| 97 | + |
| 98 | + public int[] findRedundantConnection(int[][] edges) { |
| 99 | + fathers = new int[edges.length + 1]; |
| 100 | + |
| 101 | + for (var i = 0; i < fathers.length; i++) { |
| 102 | + fathers[i] = i; |
| 103 | + } |
| 104 | + |
| 105 | + for (var edge : edges) { |
| 106 | + if (sameRoot(edge[0], edge[1])) { |
| 107 | + return edge; |
| 108 | + } |
| 109 | + |
| 110 | + unite(edge[0], edge[1]); |
| 111 | + } |
| 112 | + |
| 113 | + return null; |
| 114 | + } |
| 115 | + |
| 116 | + private void unite(int x, int y) { |
| 117 | + int rootX = findRoot(x); |
| 118 | + int rootY = findRoot(y); |
| 119 | + |
| 120 | + fathers[rootY] = rootX; // Error-prone point 1 |
| 121 | + } |
| 122 | + |
| 123 | + private int findRoot(int x) { |
| 124 | + if (x == fathers[x]) { |
| 125 | + return x; |
| 126 | + } |
| 127 | + |
| 128 | + fathers[x] = findRoot(fathers[x]); // Error-prone point 2 |
| 129 | + |
| 130 | + return fathers[x]; |
| 131 | + } |
| 132 | + |
| 133 | + private boolean sameRoot(int x, int y) { |
| 134 | + return findRoot(x) == findRoot(y); |
| 135 | + } |
| 136 | +} |
| 137 | +``` |
| 138 | + |
| 139 | +## C++ |
| 140 | +```cpp |
| 141 | +class Solution { |
| 142 | +public: |
| 143 | + vector<int> findRedundantConnection(vector<vector<int>>& edges) { |
| 144 | + for (auto i = 0; i <= edges.size(); i++) { |
| 145 | + fathers.push_back(i); |
| 146 | + } |
| 147 | + |
| 148 | + for (auto& edge : edges) { |
| 149 | + if (sameRoot(edge[0], edge[1])) { |
| 150 | + return edge; |
| 151 | + } |
| 152 | + |
| 153 | + unite(edge[0], edge[1]); |
| 154 | + } |
| 155 | + |
| 156 | + return {}; |
| 157 | + } |
| 158 | + |
| 159 | +private: |
| 160 | + vector<int> fathers; |
| 161 | + |
| 162 | + void unite(int x, int y) { |
| 163 | + int root_x = findRoot(x); |
| 164 | + int root_y = findRoot(y); |
| 165 | + |
| 166 | + fathers[root_y] = root_x; // Error-prone point 1 |
| 167 | + } |
| 168 | + |
| 169 | + int findRoot(int x) { |
| 170 | + if (x == fathers[x]) { |
| 171 | + return x; |
| 172 | + } |
| 173 | + |
| 174 | + fathers[x] = findRoot(fathers[x]); // Error-prone point 2 |
| 175 | + |
| 176 | + return fathers[x]; |
| 177 | + } |
| 178 | + |
| 179 | + bool sameRoot(int x, int y) { |
| 180 | + return findRoot(x) == findRoot(y); |
| 181 | + } |
| 182 | +}; |
| 183 | +``` |
| 184 | +
|
| 185 | +## JavaScript |
| 186 | +```javascript |
| 187 | +let fathers |
| 188 | +
|
| 189 | +var findRedundantConnection = function(edges) { |
| 190 | + fathers = [] |
| 191 | + for (let i = 0; i <= edges.length; i++) { |
| 192 | + fathers.push(i) |
| 193 | + } |
| 194 | +
|
| 195 | + for (let [x, y] of edges) { |
| 196 | + if (sameRoot(x, y)) { |
| 197 | + return [x, y] |
| 198 | + } |
| 199 | +
|
| 200 | + unite(x, y) |
| 201 | + } |
| 202 | +
|
| 203 | + return sameRoot(source, destination) |
| 204 | +}; |
| 205 | +
|
| 206 | +function unite(x, y) { |
| 207 | + rootX = findRoot(x) |
| 208 | + rootY = findRoot(y) |
| 209 | +
|
| 210 | + fathers[rootY] = rootX // Error-prone point 1 |
| 211 | +} |
| 212 | +
|
| 213 | +function findRoot(x) { |
| 214 | + if (x == fathers[x]) { |
| 215 | + return x |
| 216 | + } |
| 217 | +
|
| 218 | + fathers[x] = findRoot(fathers[x]) // Error-prone point 2 |
| 219 | +
|
| 220 | + return fathers[x] |
| 221 | +} |
| 222 | +
|
| 223 | +function sameRoot(x, y) { |
| 224 | + return findRoot(x) == findRoot(y) |
| 225 | +} |
| 226 | +``` |
| 227 | + |
| 228 | +## C# |
| 229 | +```c# |
| 230 | +public class Solution |
| 231 | +{ |
| 232 | + int[] fathers; |
| 233 | + |
| 234 | + public int[] FindRedundantConnection(int[][] edges) |
| 235 | + { |
| 236 | + fathers = new int[edges.Length + 1]; |
| 237 | + |
| 238 | + for (int i = 0; i < fathers.Length; i++) |
| 239 | + fathers[i] = i; |
| 240 | + |
| 241 | + foreach (int[] edge in edges) |
| 242 | + { |
| 243 | + if (sameRoot(edge[0], edge[1])) |
| 244 | + { |
| 245 | + return edge; |
| 246 | + } |
| 247 | + |
| 248 | + unite(edge[0], edge[1]); |
| 249 | + } |
| 250 | + |
| 251 | + return null; |
| 252 | + } |
| 253 | + |
| 254 | + void unite(int x, int y) |
| 255 | + { |
| 256 | + int rootX = findRoot(x); |
| 257 | + int rootY = findRoot(y); |
| 258 | + |
| 259 | + fathers[rootY] = rootX; // Error-prone point 1 |
| 260 | + } |
| 261 | + |
| 262 | + int findRoot(int x) |
| 263 | + { |
| 264 | + if (x == fathers[x]) |
| 265 | + return x; |
| 266 | + |
| 267 | + fathers[x] = findRoot(fathers[x]); // Error-prone point 2 |
| 268 | +
|
| 269 | + return fathers[x]; |
| 270 | + } |
| 271 | + |
| 272 | + bool sameRoot(int x, int y) |
| 273 | + { |
| 274 | + return findRoot(x) == findRoot(y); |
| 275 | + } |
| 276 | +} |
| 277 | +``` |
| 278 | + |
| 279 | +## Go |
| 280 | +```go |
| 281 | +var fathers []int |
| 282 | + |
| 283 | +func findRedundantConnection(edges [][]int) []int { |
| 284 | + fathers = make([]int, len(edges) + 1) |
| 285 | + for i := 0; i < len(fathers); i++ { |
| 286 | + fathers[i] = i |
| 287 | + } |
| 288 | + |
| 289 | + for _, edge := range edges { |
| 290 | + if sameRoot(edge[0], edge[1]) { |
| 291 | + return edge |
| 292 | + } |
| 293 | + |
| 294 | + unite(edge[0], edge[1]) |
| 295 | + } |
| 296 | + |
| 297 | + return nil |
| 298 | +} |
| 299 | + |
| 300 | +func unite(x, y int) { |
| 301 | + rootX := findRoot(x) |
| 302 | + rootY := findRoot(y) |
| 303 | + |
| 304 | + fathers[rootY] = rootX // Error-prone point 1 |
| 305 | +} |
| 306 | + |
| 307 | +func findRoot(x int) int { |
| 308 | + if x == fathers[x] { |
| 309 | + return x |
| 310 | + } |
| 311 | + |
| 312 | + fathers[x] = findRoot(fathers[x]) // Error-prone point 2 |
| 313 | + |
| 314 | + return fathers[x] |
| 315 | +} |
| 316 | + |
| 317 | +func sameRoot(x, y int) bool { |
| 318 | + return findRoot(x) == findRoot(y) |
| 319 | +} |
| 320 | +``` |
| 321 | + |
| 322 | +## Ruby |
| 323 | +```ruby |
| 324 | +def find_redundant_connection(edges) |
| 325 | + @fathers = [] |
| 326 | + (0..edges.size).each { |i| @fathers << i } |
| 327 | + |
| 328 | + edges.each do |edge| |
| 329 | + if same_root(edge[0], edge[1]) |
| 330 | + return edge |
| 331 | + end |
| 332 | + |
| 333 | + unite(edge[0], edge[1]) |
| 334 | + end |
| 335 | +end |
| 336 | + |
| 337 | +def unite(x, y) |
| 338 | + root_x = find_root(x) |
| 339 | + root_y = find_root(y) |
| 340 | + |
| 341 | + @fathers[root_y] = root_x # Error-prone point 1 |
| 342 | +end |
| 343 | + |
| 344 | +def find_root(x) |
| 345 | + if x == @fathers[x] |
| 346 | + return x |
| 347 | + end |
| 348 | + |
| 349 | + @fathers[x] = find_root(@fathers[x]) # Error-prone point 2 |
| 350 | + |
| 351 | + @fathers[x] |
| 352 | +end |
| 353 | + |
| 354 | +def same_root(x, y) |
| 355 | + find_root(x) == find_root(y) |
| 356 | +end |
| 357 | +``` |
| 358 | + |
| 359 | +## C |
| 360 | +```c |
| 361 | +// Welcome to create a PR to complete the code of this language, thanks! |
| 362 | +``` |
| 363 | + |
| 364 | +## Kotlin |
| 365 | +```kotlin |
| 366 | +// Welcome to create a PR to complete the code of this language, thanks! |
| 367 | +``` |
| 368 | + |
| 369 | +## Swift |
| 370 | +```swift |
| 371 | +// Welcome to create a PR to complete the code of this language, thanks! |
| 372 | +``` |
| 373 | + |
| 374 | +## Rust |
| 375 | +```rust |
| 376 | +// Welcome to create a PR to complete the code of this language, thanks! |
| 377 | +``` |
| 378 | + |
| 379 | +## Other languages |
| 380 | +``` |
| 381 | +// Welcome to create a PR to complete the code of this language, thanks! |
| 382 | +``` |
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