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 1:
[[1,3,1], [1,5,1], [4,2,1]]
Given the above grid map, return 7. Because the path 1→3→1→1→1 minimizes the sum.
解题思路：
依然用动态归化(Dynamic Programming)，我们使用dp[i][j]表明从(0, 0)到(i, j)最小的路径和，那么dp方程为:
dp[i][j] = min(dp[i][j-1], dp[i - 1][j]) + grid[i][j]
Java:
public class Solution {
public int minPathSum(int[][] grid) {
if (grid == null || grid.length == 0 || grid[0].length == 0) {
return 0;
}
int M = grid.length;
int N = grid[0].length;
int[][] dp = new int[M][N];
dp[0][0] = grid[0][0];
for (int i = 1; i < M; i++) {
dp[i][0] = dp[i - 1][0] + grid[i][0];
}
for (int i = 1; i < N; i++) {
dp[0][i] = dp[0][i - 1] + grid[0][i];
}
for (int i = 1; i < M; i++) {
for (int j = 1; j < N; j++) {
dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
}
}
return dp[M - 1][N - 1];
}
}
