Maximum Factor Score After Removing At Most One Element
Intuition\nWhen I first saw this problem, I realized we need to calculate the (GCD \times LCM) for different subarrays after removing at most one element. The k
# Intuition\nWhen I first saw this problem, I realized we need to calculate the $$(GCD \\times LCM)$$ for different subarrays after removing at most one element. The key insight is that we need to compare the factor score of the original array with the scores after removing each element one by one to find the maximum possible score.\n\n\n# Approach\n1. First, create helper functions for calculating:\n    - LCM of two numbers using the formula: LCM = (a*b)/GCD\n    - GCD of array using reduce function\n    - LCM of array using reduce function\n    - Factor score (GCD * LCM) for an array\n\n2. In the main function:\n    - Handle the base case (single element array) where factor score is number.\n    - Calculate initial factor score without removing any element\n    - For each element in array:\n        - Create a new array excluding that element\n        - Calculate its factor score\n        - Update maximum score if current score is higher\n    - Return the maximum score found\n\n# Complexity\n- **Time complexity:**\n    - $$O(n^2 \\log m)$$ where $$n$$ is the length of array and m is the maximum number in array.\n        - We try removing each element: $$O(n)$$\n        - For each removal, we calculate GCD and LCM of remaining elements: $$O(n log m)$$\n\n- **Space complexity:**\n    - $$O(n)$$ to store new arrays when removing elements\n\n# Code\n```python3 []\nfrom math import gcd\nfrom functools import reduce\n\nclass Solution:\n    def maxScore(self, nums: List[int]) -> int:\n\n        def lcm(a, b):\n            return abs(a * b) // gcd(a, b)\n        \n        def array_gcd(arr):\n            return reduce(gcd, arr)\n        \n        def array_lcm(arr):\n            return reduce(lcm, arr)\n        \n        def get_factor_score(arr):\n            if not arr:\n                return 0\n            if len(arr) == 1:\n                return arr[0] * arr[0]\n            return array_gcd(arr) * array_lcm(arr)\n        \n        n = len(nums)\n        if n == 1:\n            return nums[0] * nums[0]\n        \n        # Try removing each element and calculate factor score\n        max_score = get_factor_score(nums)  # Score without removing any element\n        \n        for i in range(n):\n            # Create new array without element at index i\n            new_nums = nums[:i] + nums[i+1:]\n            score = get_factor_score(new_nums)\n            max_score = max(max_score, score)\n        \n        return max_score\n```
['Python3']