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Problem solution · C++

Zuma Game

Zuma Game: 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
53 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 Zuma Game, 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

  • 53 lines of C++ from the credited upstream file 488.cpp.
  • The implementation visibly relies on hash lookup.
  • 4 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 codeZuma Game · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  int findMinStep(string board, string hand) {    const int ans = dfs(board + "#", hand, {});    return ans == INT_MAX ? -1 : ans;  }  private:  int dfs(string&& board, const string& hand,          unordered_map<string, int>&& mem) {    const string hashKey = board + '#' + hand;    if (const auto it = mem.find(hashKey); it != mem.cend())      return it->second;    board = deDup(board);    if (board == "#")      return 0;     unordered_set<char> boardSet = unordered_set(board.begin(), board.end());     string hs;  // hand that is in board    for (const char h : hand)      if (boardSet.contains(h))        hs += h;    if (hs.empty())  // infeasible      return INT_MAX;     int ans = INT_MAX;     for (int i = 0; i < board.size(); ++i)      for (int j = 0; j < hs.size(); ++j) {        // Place hs[j] in board[i].        const string& newHand = hs.substr(0, j) + hs.substr(j + 1);        string newBoard = board.substr(0, i) + hs[j] + board.substr(i);        const int res = dfs(std::move(newBoard), newHand, std::move(mem));        if (res < INT_MAX)          ans = min(ans, 1 + res);      }     return mem[hashKey] = ans;  }   string deDup(string board) {    int start = 0;  // the start index of a color sequenece    for (int i = 0; i < board.size(); ++i)      if (board[i] != board[start]) {        if (i - start >= 3)          return deDup(board.substr(0, start) + board.substr(i));        start = i;  // Meet a new sequence.      }    return board;  }};

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