How do you solve Number of Valid Move Combinations On Chessboard on LeetCode?

Number of Valid Move Combinations On Chessboard (LeetCode #2056) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding piece movement is crucial.

What is the brute force solution for Number of Valid Move Combinations On Chessboard?

The brute force approach for Number of Valid Move Combinations On Chessboard is Brute Force, with O(n²) time complexity and O(1) space complexity. We can generate all possible move combinations for each piece and check if they result in any collisions. This approach is straightforward but can be inefficient as it explores all potential movements. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Number of Valid Move Combinations On Chessboard?

Number of Valid Move Combinations On Chessboard uses the following concepts: Array, String, Backtracking, Simulation. The recommended patterns to study are: Backtracking, Simulation.

What are the interview tips for Number of Valid Move Combinations On Chessboard?

Clarify the movement rules for each piece. Discuss edge cases, like corner positions. Practice generating combinations efficiently.

What are common mistakes when solving Number of Valid Move Combinations On Chessboard?

Not considering all potential moves. Failing to check for collisions properly.

#2056

Number of Valid Move Combinations On Chessboard

Hard

ArrayStringBacktrackingSimulationBacktrackingSimulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

Instead of generating all combinations, we can simulate the movements of the pieces and track their positions using a set to ensure no collisions occur. This is more efficient as it avoids redundant checks.

⚙️

Algorithm

3 steps

1Step 1: Create a set to track occupied positions on the board.
2Step 2: For each piece, calculate its potential moves and check if they collide with already occupied positions.
3Step 3: Count valid combinations based on non-collision moves.

solution.py34 lines

1def count_valid_combinations_optimized(pieces, positions):
2    from itertools import product
3    valid_count = 0
4    n = len(pieces)
5    occupied = set()
6
7    def generate_moves(piece, position):
8        moves = []
9        r, c = position
10        if piece == 'rook':
11            for i in range(1, 9):
12                moves.append((r, i))
13                moves.append((i, c))
14        elif piece == 'queen':
15            for i in range(1, 9):
16                moves.append((r, i))
17                moves.append((i, c))
18                moves.append((r + i, c + i))
19                moves.append((r + i, c - i))
20                moves.append((r - i, c + i))
21                moves.append((r - i, c - i))
22        elif piece == 'bishop':
23            for i in range(1, 9):
24                moves.append((r + i, c + i))
25                moves.append((r + i, c - i))
26                moves.append((r - i, c + i))
27                moves.append((r - i, c - i))
28        return moves
29
30    for combination in product(*[generate_moves(pieces[i], positions[i]) for i in range(n)]):
31        if len(set(combination)) == len(combination):
32            valid_count += 1
33    return valid_count
34

ℹ

Complexity note: The time complexity is O(n) as we only iterate through the pieces and their moves once, while the space complexity is O(n) due to the storage of occupied positions.

1Understanding piece movement is crucial.
2Simulating moves helps avoid collisions.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.