LeetCode Minimum Path Sum

Description:

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.

Solution:

经典的DP题目

还有一种出法是给一个长得像杨辉三角的三角形，求从顶端到最底层的最短路径和。

这里的状态转移方程就是dp[i][j] = Math.min(dp[i-1][j], dp[i][j-1]) + grid[i][j];

import java.util.*;public class Solution {public int minPathSum(int[][] grid) {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 < n; i++)dp[0][i] = dp[0][i - 1] + grid[0][i];for (int i = 1; i < m; i++)dp[i][0] = dp[i - 1][0] + grid[i][0];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];}}