LeetCode 64: Minimum Path Sum Solution

Master LeetCode problem 64 (Minimum Path Sum), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

64. Minimum Path Sum

Medium

Array Dynamic Programming Matrix

Problem Explanation

Explanation

To solve this problem, we can use dynamic programming. We will create a 2D array to store the minimum path sum at each cell. We will iterate over the grid and update the minimum path sum for each cell based on the minimum of the path sum from the cell above and the cell on the left. Finally, the value at the bottom right cell will be the minimum path sum from the top left to the bottom right.

Time complexity: O(mn)
Space complexity: O(mn)

Solution Code

class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        
        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];
        
        for (int i = 1; i < m; i++) {
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        }
        
        for (int j = 1; j < n; j++) {
            dp[0][j] = dp[0][j - 1] + grid[0][j];
        }
        
        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]);
            }
        }
        
        return dp[m - 1][n - 1];
    }
}

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