You are given an integer array nums.
The factor score of an array is defined as the product of the LCM and GCD of all elements of that array.
Return the maximum factor score of nums after removing at most one element from it.
Note that both the LCM and GCD of a single number are the number itself, and the factor score of an empty array is 0.
Example 1:
Input: nums = [2,4,8,16]
Output: 64
Explanation:
On removing 2, the GCD of the rest of the elements is 4 while the LCM is 16, which gives a maximum factor score of 4 * 16 = 64.
Example 2:
Input: nums = [1,2,3,4,5]
Output: 60
Explanation:
The maximum factor score of 60 can be obtained without removing any elements.
Example 3:
Input: nums = [3]
Output: 9
Constraints:
1 <= nums.length <= 1001 <= nums[i] <= 30In #3334 Find the Maximum Factor Score of Array, the challenge revolves around applying number theory concepts efficiently on an array. A direct brute‑force approach would try different element combinations and recompute factors repeatedly, which becomes expensive for large inputs.
A more optimized strategy relies on properties of greatest common divisor (GCD) and least common multiple (LCM). By precomputing prefix and suffix values, you can quickly determine how removing or considering a particular element affects the overall factor score of the remaining array. This avoids recomputing expensive operations multiple times.
Using prefix/suffix preprocessing allows each candidate configuration to be evaluated in constant time after preprocessing. Since computing GCD or LCM takes O(log V) time (where V is the value range), the overall approach becomes efficient for interview constraints. Careful handling of edge cases and integer overflow during LCM computation is also important.
| Approach | Time Complexity | Space Complexity |
|---|---|---|
| Prefix & Suffix GCD/LCM Precomputation | O(n log V) | O(n) |
NeetCode
Use these hints if you're stuck. Try solving on your own first.
Use brute force approach with two loops.
Optimize using prefix and suffix arrays.
Watch expert explanations and walkthroughs
Jot down your thoughts, approach, and key learnings
Prefix and suffix computations help avoid recalculating GCD or LCM for the entire array multiple times. By storing intermediate results, you can quickly combine values from the left and right sides of the array to evaluate each candidate efficiently.
Problems involving GCD, LCM, and prefix/suffix preprocessing are common in technical interviews, including FAANG-style rounds. While the exact problem may vary, the underlying number theory and optimization concepts are frequently tested.
Arrays are usually sufficient, especially for storing prefix and suffix GCD or LCM values. These structures allow constant-time lookups when evaluating how each index contributes to the overall factor score.
The optimal approach typically uses number theory techniques such as GCD and LCM along with prefix and suffix preprocessing. This allows you to evaluate the factor score efficiently for different positions without recomputing values repeatedly.