Difficulty: Medium
Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.
Note: You can only move either down or right at any point in time.
Example:
Input:
[
[1,3,1],
[1,5,1],
[4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.
Language: Java
class Solution {
public int minPathSum(int[][] grid) {
int width = grid[0].length;
int[] dp = new int[width]; // 表示到达该位置的最短路径长度
for (int i = 0; i < grid.length; i++) {
int[] ints = grid[i];
for (int j = 0; j < ints.length; j++) {
if (j == 0) {
dp[0] += ints[j];
} else {
if (i == 0) {
dp[j] = dp[j - 1] + ints[j]; // 没有上，直接加
} else {
dp[j] = Math.min(dp[j - 1], dp[j]) + ints[j]; // 比较选择小的
}
}
}
}
return dp[width - 1];
}
}