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Problem solution · Python

Number of Valid Move Combinations On Chessboard

Number of Valid Move Combinations On Chessboard: a Python solution using depth-first search. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Depth-first search
Source
walkccc LeetCode Solutions
Length
51 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Depth-first search

For Number of Valid Move Combinations On Chessboard, the implementation follows one branch at a time, making it suitable for components, trees, backtracking, or dependency exploration.

  1. Define the state carried into one recursive or stack frame.
  2. Mark or choose the current state before exploring children.
  3. Combine child results or undo the choice when the branch finishes.

Code notes

  • 51 lines of Python from the credited upstream file 2056.py.
  • The implementation visibly relies on sequence storage, ordered lookup.
  • No explicit loop blocks detected, together with recursive traversal.

Complexity

Count unique states for graph traversal; for backtracking, count the branching factor and maximum depth.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeNumber of Valid Move Combinations On Chessboard · PythonPython
Use this to learn the idea, then write your own version.
class Solution:  def countCombinations(      self,      pieces: list[str],      positions: list[list[int]],  ) -> int:    n = len(pieces)    moves = {"rook": [(1, 0), (-1, 0), (0, 1), (0, -1)],             "bishop": [(1, 1), (1, -1), (-1, 1), (-1, -1)],             "queen": [(1, 0), (-1, 0), (0, 1), (0, -1), (1, 1), (1, -1), (-1, 1), (-1, -1)]}    hashedBoards = set()     def getHash(board: list[list[int]]) -> Tuple:      return tuple([tuple(pos) for pos in board])     def dfs(        board: list[list[int]],        pieceMoves: list[tuple[int, int]],        activeMask: int,    ) -> None:      """Performs a depth-first search to explore all possible board states."""      if activeMask == 0:        return      hashedBoards.add(getHash(board))       for nextActiveMask in range(1, 1 << n):        if activeMask & nextActiveMask != nextActiveMask:          continue         # Copy the board.        nextBoard = [pos.copy() for pos in board]         # Move the pieces that are active in this turn.        for i in range(n):          if nextActiveMask >> i & 1:            nextBoard[i][0] += pieceMoves[i][0]            nextBoard[i][1] += pieceMoves[i][1]         # No two or more pieces occupy the same square.        if len(set(getHash(nextBoard))) < n:          continue         # Every piece needs to be in the boundary.        if all(1 <= x <= 8 and 1 <= y <= 8 for x, y in nextBoard):          dfs(nextBoard, pieceMoves, nextActiveMask)     for pieceMoves in itertools.product(*(moves[piece] for piece in pieces)):      dfs(positions, pieceMoves, (1 << n) - 1)     return len(hashedBoards)

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