LeetCode 2056: Number of Valid Move Combinations On Chessboard Solution

Master LeetCode problem 2056 (Number of Valid Move Combinations On Chessboard), a hard 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.

2056. Number of Valid Move Combinations On Chessboard

Hard

Array String Backtracking Simulation

Problem Explanation

Explanation

To solve this problem, we can iterate through all possible moves for each piece type (rook, queen, bishop) and calculate the number of valid move combinations based on the constraints provided. We can simulate the movement of each piece on the chessboard and increment the count of valid move combinations accordingly. The key is to handle the movement constraints of each piece type and ensure that no two pieces occupy the same square at any given time.

For rooks: We can move horizontally or vertically.
For queens: We can move horizontally, vertically, or diagonally.
For bishops: We can move diagonally.

We will consider all possible moves from the current position of each piece and recursively explore the valid move combinations. We need to handle the boundary conditions of the chessboard and ensure that no two pieces overlap at any step.

Time Complexity: O(8^n) where n is the number of pieces Space Complexity: O(n) for the recursive call stack

Solution Code

class Solution {
    public int numValidMoveCombinations(String[] pieces, int[][] positions) {
        int n = pieces.length;
        return backtrack(0, pieces, positions, new boolean[8][8], new int[]{-1, 0, 1, 0, -1});
    }
    
    private int backtrack(int idx, String[] pieces, int[][] positions, boolean[][] board, int[] dirs) {
        if (idx == pieces.length) {
            return 1;
        }
        
        int count = 0;
        int x = positions[idx][0] - 1;
        int y = positions[idx][1] - 1;
        
        for (int i = 0; i < dirs.length - 1; i++) {
            int newX = x;
            int newY = y;
            while (newX >= 0 && newX < 8 && newY >= 0 && newY < 8) {
                if (!board[newX][newY]) {
                    board[newX][newY] = true;
                    count += backtrack(idx + 1, pieces, positions, board, dirs);
                    board[newX][newY] = false;
                }
                newX += dirs[i];
                newY += dirs[i + 1];
            }
        }
        
        return count;
    }
}

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