64 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.

Example:

Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.


public int minPathSum(int[][] grid) {

       if(grid.length==0)return 0;
        
       //first row
        for(int i=1;i<grid[0].length;i++){
            grid[0][i] =  grid[0][i]+  grid[0][i-1];
        }
        
       //first col
       for(int i=1;i<grid.length;i++){
            grid[i][0] =  grid[i][0]+  grid[i-1][0];
        }
       //whole grid
        
        for(int i=1;i<grid.length;i++){
            for(int j=1;j<grid[0].length;j++){
                grid[i][j] =  grid[i][j] + Math.min(grid[i][j-1],grid[i-1][j]);
            }
        }
        
        int n = grid.length-1;
        int m = grid[0].length-1;
        
        return grid[n][m];
    
        
    }