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Problem solution · C++

Stone Game V

Stone Game V: 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
41 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 Stone Game V, 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

  • 41 lines of C++ from the credited upstream file 1563.cpp.
  • The implementation visibly relies on sequence storage.
  • 1 loop block 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 codeStone Game V · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  int stoneGameV(vector<int>& stoneValue) {    const int n = stoneValue.size();    vector<vector<int>> mem(n, vector<int>(n, INT_MIN));    vector<int> prefix(n + 1);    partial_sum(stoneValue.begin(), stoneValue.end(), prefix.begin() + 1);    return stoneGameV(stoneValue, 0, n - 1, prefix, mem);  }  private:  // Returns the maximum score that Alice can obtain from stoneValue[i..j].  int stoneGameV(const vector<int>& stoneValue, int i, int j,                 const vector<int>& prefix, vector<vector<int>>& mem) {    if (i == j)      return 0;    if (mem[i][j] > 0)      return mem[i][j];     // Try all the possible partitions.    for (int p = i; p < j; ++p) {      // sum(stoneValue[i..p])      const int leftSum = prefix[p + 1] - prefix[i];      const int throwRight =          leftSum + stoneGameV(stoneValue, i, p, prefix, mem);      // sum(stoneValue[p + 1..j])      const int rightSum = prefix[j + 1] - prefix[p + 1];      const int throwLeft =          rightSum + stoneGameV(stoneValue, p + 1, j, prefix, mem);      if (leftSum < rightSum)  // Bob throws the right row.        mem[i][j] = max(mem[i][j], throwRight);      else if (leftSum > rightSum)  // Bob throws the left row.        mem[i][j] = max(mem[i][j], throwLeft);      else  // Alice decides which row to throw.        mem[i][j] = max({mem[i][j], throwLeft, throwRight});    }     return mem[i][j];  }};

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