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Problem solution · C++

Number of Valid Move Combinations On Chessboard

Number of Valid Move Combinations On Chessboard: a C++ 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
90 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

  • 90 lines of C++ from the credited upstream file 2056.cpp.
  • The implementation visibly relies on sequence storage, hash lookup.
  • 6 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 · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  int countCombinations(vector<string>& pieces,                        vector<vector<int>>& positions) {    const int n = pieces.size();    unordered_set<long long> hashedBoards;    // Stores all possible move combinations for `pieces`. Each element is a    // vector of moves, one for each piece in the input order. e.g., if pieces =    // ["rook", "bishop"], one element might be [[1,0], [1,1]], representing a    // rook moving right and a bishop moving diagonally up-right.    vector<vector<pair<int, int>>> pieceMovesList;     getPieceMovesList(pieces, 0, {}, pieceMovesList);     for (const vector<pair<int, int>>& pieceMoves : pieceMovesList)      dfs(positions, n, pieceMoves, (1 << n) - 1, hashedBoards);     return hashedBoards.size();  }  private:  const unordered_map<string, vector<pair<int, int>>> kPieceToMoves{      {"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}}}};   // Generates all possible combinations of moves.  void getPieceMovesList(const vector<string>& pieces, int i,                         vector<pair<int, int>>&& path,                         vector<vector<pair<int, int>>>& pieceMovesList) {    if (i == pieces.size()) {      pieceMovesList.push_back(path);      return;    }    for (const pair<int, int>& move : kPieceToMoves.at(pieces[i])) {      path.push_back(move);      getPieceMovesList(pieces, i + 1, std::move(path), pieceMovesList);      path.pop_back();    }  }   // Performs a depth-first search to explore all possible board states.  void dfs(const vector<vector<int>>& board, int n,           const vector<pair<int, int>>& pieceMoves, int activeMask,           unordered_set<long long>& hashedBoards) {    if (activeMask == 0)      return;    hashedBoards.insert(getHash(board));    for (int nextActiveMask = 1; nextActiveMask < 1 << n; ++nextActiveMask) {      if ((activeMask & nextActiveMask) != nextActiveMask)        continue;       // Copy the board.      vector<vector<int>> nextBoard = board;       // Move the pieces that are active in this turn.      for (int i = 0; i < n; ++i)        if (nextActiveMask >> i & 1) {          nextBoard[i][0] += pieceMoves[i].first;          nextBoard[i][1] += pieceMoves[i].second;        }       // No two or more pieces occupy the same square.      if (getUniqueSize(nextBoard) < n)        continue;       // Every piece needs to be in the boundary.      if (ranges::all_of(nextBoard, [](const vector<int>& pos) {        return 1 <= pos[0] && pos[0] <= 8 && 1 <= pos[1] && pos[1] <= 8;      }))        dfs(nextBoard, n, pieceMoves, nextActiveMask, hashedBoards);    }  }   long long getHash(const vector<vector<int>>& board) {    long long hash = 0;    for (const vector<int>& pos : board)      hash = (hash * 64) + ((pos[0] - 1) << 3) + (pos[1] - 1);    return hash;  }   int getUniqueSize(const vector<vector<int>>& board) {    unordered_set<int> unique;    for (const vector<int>& pos : board)      unique.insert(pos[0] * 8 + pos[1]);    return unique.size();  }};

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