LeetCode 2684: Maximum Number of Moves in a Grid Solution

Master LeetCode problem 2684 (Maximum Number of Moves in a Grid), 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.

2684. Maximum Number of Moves in a Grid

Medium

Array Dynamic Programming Matrix

Problem Explanation

Explanation

To solve this problem, we can use dynamic programming. We start at each cell in the first column and calculate the maximum number of moves that can be made starting from that cell. We keep track of the maximum number of moves for each cell in a separate memoization table. For each cell, we check the adjacent cells in the next column and update the maximum number of moves based on the value of the current cell and the adjacent cells.

Algorithm:

Initialize a memoization table to store the maximum number of moves for each cell.
Iterate through each cell in the first column.
For each cell, recursively calculate the maximum number of moves by checking adjacent cells in the next column.
Update the maximum number of moves for each cell based on the values of the current cell and the adjacent cells.
Return the maximum number of moves among all cells in the first column.

Time Complexity: O(m * n) where m is the number of rows and n is the number of columns in the grid.

Space Complexity: O(m * n) for the memoization table.

Solution Code

class Solution {
    public int maximumMoves(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int[][] memo = new int[m][n];
        
        int maxMoves = 0;
        for (int i = 0; i < m; i++) {
            maxMoves = Math.max(maxMoves, dfs(grid, memo, i, 0));
        }
        
        return maxMoves;
    }
    
    private int dfs(int[][] grid, int[][] memo, int row, int col) {
        if (memo[row][col] != 0) {
            return memo[row][col];
        }
        
        int maxMoves = 1;
        int currentVal = grid[row][col];
        
        if (col + 1 < grid[0].length) {
            if (row - 1 >= 0 && grid[row - 1][col + 1] > currentVal) {
                maxMoves = Math.max(maxMoves, 1 + dfs(grid, memo, row - 1, col + 1));
            }
            if (grid[row][col + 1] > currentVal) {
                maxMoves = Math.max(maxMoves, 1 + dfs(grid, memo, row, col + 1));
            }
            if (row + 1 < grid.length && grid[row + 1][col + 1] > currentVal) {
                maxMoves = Math.max(maxMoves, 1 + dfs(grid, memo, row + 1, col + 1));
            }
        }
        
        memo[row][col] = maxMoves;
        return maxMoves;
    }
}

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