CODE 69. Minimum Path Sum

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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 int minPathSum(int[][] grid) {
	// Start typing your Java solution below
	// DO NOT write main() function
	int[][] sum = new int[grid.length][grid[0].length];
	sum[0][0] = grid[0][0];
	for (int i = 1; i < grid.length; i++) {
		sum[i][0] = grid[i][0] + sum[i - 1][0];
	}
	for (int i = 1; i < grid[0].length; i++) {
		sum[0][i] = grid[0][i] + sum[0][i - 1];
	}
	for (int i = 1; i < grid.length; i++) {
		for (int j = 1; j < grid[0].length; j++) {
			sum[i][j] = grid[i][j] + Math.min(sum[i - 1][j], sum[i][j - 1]);
		}
	}
	return sum[sum.length - 1][sum[0].length - 1];
}