Minimum Path Sum

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.

public class Solution {
    public int minPathSum(int[][] grid) {
        // Start typing your Java solution below
        // DO NOT write main() function
        //[m,n] = (m,n) + min([m-1,n],[m,n-1])
        //only can move right or down
        if(grid == null || grid.length == 0 || grid[0].length == 0)return 0;
        int m = grid.length;
        int n = grid[0].length;
        int[][] map = new int[m][n];
        for(int i = 0; i < m; i ++){
            map[i][0] = grid[i][0];
            if(i > 0) map[i][0] += map[i - 1][0];
        }
        for(int j = 1; j < n; j ++){
            map[0][j] = map[0][j - 1] + grid[0][j];
        }
        for(int i = 1; i < m; i ++){
            for(int j = 1; j < n; j ++){
                map[i][j] = grid[i][j] + Math.min(map[i - 1][j], map[i][j - 1]);
            }
        }
        return map[m - 1][n - 1];
    }
}

 第二遍：

public class Solution {
    public int minPathSum(int[][] grid) {
        // Start typing your Java solution below
        // DO NOT write main() function
        //[m,n] = (m,n) + min([m-1,n],[m,n-1])
        //only can move right or down
        if(grid == null || grid.length == 0 || grid[0].length == 0)return 0;
        int m = grid.length;
        int n = grid[0].length;
        int[][] map = new int[m][n];
        for(int i = 0; i < m; i ++){
            for(int j = 0; j < n; j ++){
                map[i][j] = grid[i][j];
                if(i > 0 && j > 0) map[i][j] += Math.min(map[i - 1][j], map[i][j - 1]);
                else if(i > 0) map[i][j] += map[i - 1][j];
                else if(j > 0) map[i][j] += map[i][j - 1];
            }
        }
        return map[m - 1][n - 1];
    }
}

 第三遍：

public class Solution {
    public int minPathSum(int[][] grid) {
        if(grid == null || grid.length == 0 || grid[0].length == 0) return 0;
        int m = grid.length, n = grid[0].length;
        int[][] result = new int[m][n];
        result[0][0] = grid[0][0];
        for(int i = 0; i < m; i ++)
            for(int j = 0; j < n; j ++)
                if(i != 0 || j != 0){
                    int aa = i > 0 ? result[i - 1][j] : Integer.MAX_VALUE;
                    int bb = j > 0 ? result[i][j - 1] : Integer.MAX_VALUE;
                    result[i][j] = Math.min(aa, bb) + grid[i][j];
                }
        return result[m - 1][n - 1];
    }
}