LeetcodeMinimum Path Sum

Posted 2020-07-13 wuezs

题目链接：https://leetcode.com/problems/minimum-path-sum/

题目：

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.

思路：

c[i][j]表示从左上到i,j这个位置最小路径和，则状态转移方程：c[i][j]=min{c[i-1][j],c[i][j-1]}

算法：

public int minPathSum(int[][] grid) {  
    int c[][] = new int[grid.length][grid[0].length];  
    c[0][0] = grid[0][0];  
    for (int i = 1; i <grid.length; i++) {  
        c[i][0] = c[i-1][0]+grid[i][0];  
    }  
    for(int j=1;j<grid[0].length;j++){  
        c[0][j] = c[0][j-1]+grid[0][j];  
    }  
      
    for (int i = 1; i <grid.length; i++) {  
        for (int j = 1; j <grid[0].length; j++) {  
            c[i][j] = Math.min(c[i-1][j], c[i][j-1])+grid[i][j];  
        }  
    }  
    return c[grid.length-1][grid[0].length-1];  
}