Minimum Path Sum

Java

public class Solution {
		public int minPathSum(int[][] grid) {
			//corner case 
		if (grid == null || grid.length == 0 || grid[0].length == 0) {
			return 0;
		}
			
		int m = grid.length, n = grid[0].length;
			int[][] dp = new int[m][n];
			
			dp[0][0] = grid[0][0];
			
			//function need to prepare for three different situations
			for (int i = 1; i < n; ++i) {
				dp[0][i] = dp[0][i - 1] + grid[0][i];
			}
		
			for (int i = 1; i < m; ++i) {
				dp[i][0] = dp[i - 1][0] + grid[i][0];
		}
		
		for (int i = 1; i < m; ++i) {
				for (int j = 1; j < n; ++j) {
					dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
				}
		}
		
		return dp[m - 1][n - 1];
		}
}


Time Complexity: O(mn);
Space Complexity: O(mn);