CPMagical CP Library

Problem solution · Python

Find the Maximum Factor Score of Array

Find the Maximum Factor Score of Array: a Python 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
47 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

  • 47 lines of Python from the credited upstream file 3334.py.
  • The implementation visibly relies on sequence storage.
  • No explicit 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 · PythonPython
Use this to learn the idea, then write your own version.
class Solution:  def maxScore(self, nums: list[int]) -> int:    n = len(nums)    # prefixGcd[i] := GCD of nums[0..i]    # prefixLcm[i] := LCM of nums[0..i]    prefixGcd, prefixLcm = self._getPrefix(nums)    # suffixGcd[i] := GCD of nums[i..n - 1]    # suffixLcm[i] := LCM of nums[i..n - 1]    suffixGcd, suffixLcm = self._getSuffix(nums)    ans = suffixGcd[0] * suffixLcm[0]     for i in range(n):      gcd1 = prefixGcd[i - 1] if i > 0 else 0      gcd2 = suffixGcd[i + 1] if i + 1 < n else 0      lcm1 = prefixLcm[i - 1] if i > 0 else 1      lcm2 = suffixLcm[i + 1] if i + 1 < n else 1      score = math.gcd(gcd1, gcd2) * math.lcm(lcm1, lcm2)      ans = max(ans, score)     return ans   def _getPrefix(self, nums: list[int]) -> tuple[list[int], list[int]]:    """Returns the prefix GCD and LCM arrays."""    prefixGcd = []    prefixLcm = []    currGcd = 0    currLcm = 1    for num in nums:      currGcd = math.gcd(currGcd, num)      currLcm = math.lcm(currLcm, num)      prefixGcd.append(currGcd)      prefixLcm.append(currLcm)    return prefixGcd, prefixLcm   def _getSuffix(self, nums: list[int]) -> tuple[list[int], list[int]]:    """Returns the suffix GCD and LCM arrays."""    suffixGcd = []    suffixLcm = []    currGcd = 0    currLcm = 1    for num in reversed(nums):      currGcd = math.gcd(currGcd, num)      currLcm = math.lcm(currLcm, num)      suffixGcd.append(currGcd)      suffixLcm.append(currLcm)    return list(reversed(suffixGcd)), list(reversed(suffixLcm))

Keep practising

Did this explanation save you time? I'm a Grade 11 student building this free library to make difficult algorithms easier to understand.

Buy me a coffee ↗