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.

Example 1:

Input: grid = [[1,3,1],[1,5,1],[4,2,1]]
Output: 7
Explanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.

Example 2:

Input: grid = [[1,2,3],[4,5,6]]
Output: 12

Constraints:

• m == grid.length
• n == grid[i].length
• 1 <= m, n <= 200
• 0 <= grid[i][j] <= 200

Approach - Bottom Up 1D DP

• put nth element as infinity and base condition rest is easy dp[j] means what is the value at dp[i-1][j] top left and dp[j+1] is bottom right

class Solution {
    public int minPathSum(int[][] grid) {
        int r = grid.length, c = grid[0].length;
        int[] dp = new int[c+1];
        Arrays.fill(dp, Integer.MAX_VALUE);
        dp[c-1] = 0;
 
        for (int i = r - 1; i >= 0; i--) {
            for (int j = c - 1; j >=0; j--) {
                dp[j] = grid[i][j] + Math.min(dp[j],dp[j+1]);
            }
        }
 
        return dp[0];
    }
}