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Problem solution · C++

Number of Ways of Cutting a Pizza

Number of Ways of Cutting a Pizza: a C++ solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Direct simulation
Source
walkccc LeetCode Solutions
Length
54 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

Direct simulation

For Number of Ways of Cutting a Pizza, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 54 lines of C++ from the credited upstream file 1444.cpp.
  • The implementation visibly relies on sequence storage.
  • 4 loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

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 Ways of Cutting a Pizza · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  int ways(vector<string>& pizza, int k) {    const int M = pizza.size();    const int N = pizza[0].size();    vector<vector<vector<int>>> mem(M,                                    vector<vector<int>>(N, vector<int>(k, -1)));    vector<vector<int>> prefix(M + 1, vector<int>(N + 1));     for (int i = 0; i < M; ++i)      for (int j = 0; j < N; ++j)        prefix[i + 1][j + 1] = (pizza[i][j] == 'A') + prefix[i][j + 1] +                               prefix[i + 1][j] - prefix[i][j];     return ways(0, 0, k - 1, M, N, prefix, mem);  }  private:  static constexpr int kMod = 1'000'000'007;   // Returns the number of ways to cut pizza[m..M)[n..N) with k cuts.  int ways(int m, int n, int k, const int M, const int N,           const vector<vector<int>>& prefix,           vector<vector<vector<int>>>& mem) {    if (k == 0)      return hasApple(prefix, m, M, n, N) ? 1 : 0;    if (mem[m][n][k] != -1)      return mem[m][n][k];     mem[m][n][k] = 0;     for (int i = m + 1; i < M; ++i)  // Cut horizontally.      if (hasApple(prefix, m, i, n, N) && hasApple(prefix, i, M, n, N)) {        mem[m][n][k] += ways(i, n, k - 1, M, N, prefix, mem);        mem[m][n][k] %= kMod;      }     for (int j = n + 1; j < N; ++j)  // Cut vertically.      if (hasApple(prefix, m, M, n, j) && hasApple(prefix, m, M, j, N)) {        mem[m][n][k] += ways(m, j, k - 1, M, N, prefix, mem);        mem[m][n][k] %= kMod;      }     return mem[m][n][k];  }   // Returns true if pizza[row1..row2)[col1..col2) has apple.  bool hasApple(const vector<vector<int>>& prefix, int row1, int row2, int col1,                int col2) {    return (prefix[row2][col2] - prefix[row1][col2] -  //            prefix[row2][col1] + prefix[row1][col1]) > 0;  };};

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