package leetcode;
/*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 Minimum_path_sum {
     public static void main(String[] args) {
        int[][] a = {{1,3,1},{1,5,1},{4,2,1}};
        System.out.println(minPathSum(a));
    }
     
     public static int minPathSum(int[][] grid) {
         for(int i = 0 ; i < grid.length ; i ++) {
             for(int j = 0 ; j < grid[i].length ; j ++) {
                 if(i == 0 && j == 0) {    //當為左上角元素時跳過
                     continue;
                 }else if( i == 0 ) {
                     grid[i][j] += grid[i][j-1];  //第一行元素,只能向右走
                 }else if( j == 0 ) {
                     grid[i][j] += grid[i-1][j];  //第一列元素,只能向下走
                 }else {
                     int min = Math.min(grid[i][j-1], grid[i-1][j]);  //每一個方格都來自上或者左的和的最小值來替代,這樣最後一個方格選好之後,及時路徑和最短值
                     grid[i][j] += min; 
                 }
             }
         }
        return grid[grid.length-1][grid[0].length-1];
         
     }
}