MinPathSumDP.java

//https://leetcode.com/problems/minimum-path-sum

public int minPathSum(int[][] grid) {
        
                int m = grid.length;
        int n = grid[0].length;

        // Create a dp array to store the minimum path sum to each cell
        int[][] dp = new int[m][n];

        // Initialize the top-left cell
        dp[0][0] = grid[0][0];

        // Fill the first row (can only come from the left)
        for (int j = 1; j < n; j++) {
            dp[0][j] = dp[0][j - 1] + grid[0][j];
        }

        // Fill the first column (can only come from above)
        for (int i = 1; i < m; i++) {
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        }

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

        // The bottom-right cell contains the minimum path sum
        return dp[m - 1][n - 1];
    }