最小路径和

64. 最小路径和

/**
 * @author realzhaijiayu on 2020/7/23
 * @project leetcode
 */
/*
典型的动态规划问题
二维的
dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + grid[i][j];

一维的
dp[j] = min(dp[j], dp[j-1]) + grid[i][j];

*/
//一维的
class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        if(m == 0){
            return 0;
        }
        int n = grid[0].length;
        int[][] dp = new int[m + 1][n + 1];
        for(int i = 1; i <= m; i++){
            for(int j = 1; j <= n; j++){
                if(i == 1){
                    dp[i][j] = dp[i][j-1] + grid[i-1][j-1];
                }
                else if(j == 1){
                    dp[i][j] = dp[i-1][j] + grid[i-1][j-1];
                }
                else{
                    dp[i][j] = Math.min(dp[i-1][j],dp[i][j-1]) + grid[i-1][j-1];
                }
            }
        }
        return dp[m][n];
    }
}

//二维的
class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        if(m == 0){
            return 0;
        }
        int n = grid[0].length;
        int[] dp = new int[n + 1];
        for(int i = 1; i <= m; i++){
            for(int j = 1; j <= n; j++){
                if(i == 1){
                    dp[j] = dp[j - 1] + grid[i - 1][j - 1];
                }
                else if(j == 1){
                    dp[j] = dp[j] + grid[i - 1][j - 1];
                }
                else{
                    dp[j] = Math.min(dp[j], dp[j - 1]) + grid[i - 1][j - 1];
                }
            }
        }
        return dp[n];
    }
}