64. Minimum Path Sum

Leetcode Array Dynamic Programming

Given a $m \times n$ 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.

分析

典型的动态规划，非常简单直接。类似于LeetCode 62. Unique Paths.

public int minPathSum(int[][] grid) {
    if (grid == null || grid.length == 0 || grid[0].length == 0) return 0;
    int[][] pathSums = grid.clone();
    int m = grid.length, n = grid[0].length;
    for (int i = 1; i < m; i++)
        pathSums[i][0] += pathSums[i - 1][0];

    for (int j = 1; j < n; j++)
        pathSums[0][j] += pathSums[0][j - 1];

    for (int i = 1; i < m; i++)
        for (int j = 1; j < n; j++)
            pathSums[i][j] += Math.min(pathSums[i - 1][j], pathSums[i][j - 1]);
    return pathSums[m - 1][n - 1];
}