LeetCode - Minimum Path Sum - 30Days Challenge

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.

Solution

Its a DP problem, Maintain previous states which gives minimum distance, Calculate current state based on the previous state.

Code


public class MinimumPathDistance {

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

		int n = grid.length, m = grid[0].length;

		int[][] dp = new int[n][m];

		dp[0][0] = grid[0][0];
		for (int i = 1; i < n; i++) {
			dp[i][0] = dp[i - 1][0] + grid[i][0];
		}
		for (int j = 1; j < m; j++) {
			dp[0][j] = dp[0][j - 1] + grid[0][j];
		}

		for (int i = 1; i < n; i++) {
			for (int j = 1; j < m; j++) {
				dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
			}
		}

		return dp[n - 1][m - 1];
	}

	public static void main(String[] args) {
		
		int [][] grid={
				  {1,3,1},
				  {1,5,1},
				  {4,2,1}
				};
		
		System.out.println(new MinimumPathDistance().minPathSum(grid));


	}

}