leetcode--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 {
    /**This is a simple implementation of dynamic programming methodology. We use int[][] minGrid to denote the 
	 * minimum path sum from cell (0,0) to (i,j). 
	 * For each cell (i,j), there are two ways to reach it:
	 * 1. go one step vertically from cell (i - 1 ,j)
	 * 2. go one step horizontally from cell (i, j - 1).
	 * 3. So the minimum path sum from cell (0,0) to (i,j) is 
	 *  minGrid[i][j] = min{grid[i][j] + minGrid[i - 1][j], grid[i][j] + minGrid[i][j - 1]};
	 * @param grid
	 * @return
	 */
	public int minPathSum(int[][] grid) {
		int min = 0;
        int row = grid.length;
        if(row > 0){
        	int column = grid[0].length;
        	int[][] minGrid = new int[row][column];
        	minGrid[0][0] = grid[0][0];
        	for(int i = 1; i < row; ++i)
        		minGrid[i][0] = grid[i][0]+ minGrid[i- 1][0];
        	for(int i = 1; i < column; ++i)
        		minGrid[0][i] = grid[0][i] + minGrid[0][i - 1];
        	for(int i = 1; i < row; ++i){
        		for(int j = 1; j < column; ++j)
        			minGrid[i][j] = Math.min(grid[i][j] + minGrid[i - 1][j], grid[i][j] + minGrid[i][j - 1]);
        	}
        	min = minGrid[row - 1][column - 1];
        }
        return min;	    
    }
}