LeetCode 64. Minimum Path Sum（动态规划）

题目来源：https://leetcode.com/problems/minimum-path-sum/

问题描述

64. Minimum Path Sum

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.

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题意

给定一个m×n的棋盘矩阵grid，规定只能向右或向下走。矩阵中的每个元素表示费用，求从左上角到右下角的最小费用。

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思路

同LeetCode 62. Unique Paths（动态规划）和LeetCode 63. Unique Paths II（动态规划），用时间复杂度为O(mn)的动态规划求解，可以直接使用了形参grid作为dp数组。区别只是在于状态转移方程变为：

dp[i][j] = grid[i][j] + min(dp[i-1][j], dp[i][j-1])

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代码

class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        if (m == 0)
        {
            return 0;
        }
        int n = grid[0].length;
        if (n == 0)
        {
            return 0;
        }
        int i = 0, j = 0;
        for (i=1; i<n; i++)
        {
            grid[0][i] += grid[0][i-1];
        }
        for (j=1; j<m; j++)
        {
            grid[j][0] += grid[j-1][0];
            for (i=1; i<n; i++)
            {
                grid[j][i] = grid[j][i] + Math.min(grid[j-1][i], grid[j][i-1]);
            }
        }
        return grid[m-1][n-1];
    }
}