【LeetCode】64. Minimum Path Sum

問題描述

https://leetcode.com/problems/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.

算法

矩陣m x n，從左上角到右下角有很多條路徑，每個位置都有一個數字，求路徑上數字之和的最小值。

設(i,j)表示從(0,0)到(i,j)的所有路徑上數字之和中的最小值，則有：

1. f(0,0) = grid[0][0]
2. f(i,0) = f(i-1,0) + grid[i-1][0],0<i<m，第一列
3. f(0,j) = f(0,j-1) + grid[0][j-1],0<j<n，第一行
4. f(i,j) = min(f(i-1,j), f(i,j-1)) + grid[i][j]，1<=i<m, 1<=j<n

代碼

        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[][] f = new int[m][n];
            f[0][0] = grid[0][0];
            for(int i=1;i<m;i++) {
                f[i][0] = f[i-1][0] + grid[i][0];
            }
            for(int j=1;j<n;j++) {
                f[0][j] = f[0][j-1] + grid[0][j];
            }
            for(int i=1;i<m;i++) {
                for(int j=1;j<n;j++) {
                    f[i][j] = Math.min(f[i-1][j], f[i][j-1]) + grid[i][j];
                }
            }
            return f[m-1][n-1];
        }