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Problem solution · C++

Count the Number of Square-Free Subsets

Count the Number of Square-Free Subsets: 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
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

Direct simulation

For Count the Number of Square-Free Subsets, 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

  • 53 lines of C++ from the credited upstream file 2572.cpp.
  • The implementation visibly relies on sequence storage.
  • 3 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 codeCount the Number of Square-Free Subsets · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  int squareFreeSubsets(vector<int>& nums) {    vector<vector<int>> mem(nums.size(),                            vector<int>(1 << (kPrimesCount + 1), -1));    vector<int> masks;     for (const int num : nums)      masks.push_back(getMask(num));     // -1 means that we take no number.    // `used` is initialized to 1 so that -1 & 1 = 1 instead of 0.    return (squareFreeSubsets(masks, 0, /*used=*/1, mem) - 1 + kMod) % kMod;  }  private:  static constexpr int kMod = 1'000'000'007;  static constexpr int kPrimesCount = 10;  static constexpr int primes[] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29};   int squareFreeSubsets(const vector<int>& masks, int i, int used,                        vector<vector<int>>& mem) {    if (i == masks.size())      return 1;    if (mem[i][used] != -1)      return mem[i][used];    const int pick = (masks[i] & used) == 0                         ? squareFreeSubsets(masks, i + 1, used | masks[i], mem)                         : 0;    const int skip = squareFreeSubsets(masks, i + 1, used, mem);    return mem[i][used] = (pick + skip) % kMod;  }   // e.g. num = 10 = 2 * 5, so mask = 0b101 -> 0b1010 (append a 0)  //      num = 15 = 3 * 5, so mask = 0b110 -> 0b1100 (append a 0)  //      num = 25 = 5 * 5, so mask =  0b-1 -> 0b1..1 (invalid)  int getMask(int num) {    int mask = 0;    for (int i = 0; i < sizeof(primes) / sizeof(int); ++i) {      int rootCount = 0;      while (num % primes[i] == 0) {        num /= primes[i];        ++rootCount;      }      if (rootCount >= 2)        return -1;      if (rootCount == 1)        mask |= 1 << i;    }    return mask << 1;  }};

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