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.

MinPathSum.java

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