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Problem solution · C++

Find the Maximum Factor Score of Array

Find the Maximum Factor Score of Array: 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
58 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 Find the Maximum Factor Score of Array, 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

  • 58 lines of C++ from the credited upstream file 3334.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 codeFind the Maximum Factor Score of Array · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  long long maxScore(vector<int>& nums) {    const int n = nums.size();    // prefixGcd[i] := GCD of nums[0..i]    // prefixLcm[i] := LCM of nums[0..i]    const auto [prefixGcd, prefixLcm] = getPrefix(nums);    // suffixGcd[i] := GCD of nums[i..n - 1]    // suffixLcm[i] := LCM of nums[i..n - 1]    const auto [suffixGcd, suffixLcm] = getSuffix(nums);    long ans = suffixGcd[0] * suffixLcm[0];     for (int i = 0; i < n; ++i) {      const long gcd1 = i > 0 ? prefixGcd[i - 1] : 0;      const long gcd2 = i + 1 < n ? suffixGcd[i + 1] : 0;      const long lcm1 = i > 0 ? prefixLcm[i - 1] : 1;      const long lcm2 = i + 1 < n ? suffixLcm[i + 1] : 1;      const long score = gcd(gcd1, gcd2) * lcm(lcm1, lcm2);      ans = max(ans, score);    }     return ans;  }  private:  // Returns the prefix GCD and LCM arrays.  pair<vector<long>, vector<long>> getPrefix(const vector<int>& nums) {    vector<long> prefixGcd;    vector<long> prefixLcm;    long currGcd = 0;    long currLcm = 1;    for (const int num : nums) {      currGcd = gcd(currGcd, num);      currLcm = lcm(currLcm, num);      prefixGcd.push_back(currGcd);      prefixLcm.push_back(currLcm);    }    return {prefixGcd, prefixLcm};  }   // Returns the suffix GCD and LCM arrays.  pair<vector<long>, vector<long>> getSuffix(const vector<int>& nums) {    vector<long> suffixGcd;    vector<long> suffixLcm;    long currGcd = 0;    long currLcm = 1;    for (int i = nums.size() - 1; i >= 0; --i) {      currGcd = gcd(currGcd, nums[i]);      currLcm = lcm(currLcm, nums[i]);      suffixGcd.push_back(currGcd);      suffixLcm.push_back(currLcm);    }    ranges::reverse(suffixGcd);    ranges::reverse(suffixLcm);    return {suffixGcd, suffixLcm};  }};

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