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Maximize Pair Strength Using GCD - Video Solutions

EasyArrayMathEnumerationNumber Theory

Maximize Pair Strength Using GCD | LeetCode 4010 | Weekly Contest 513 | Java Code | Developer Coder

Developer Coder
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2 video solutions available

Maximize Pair Strength Using GCD - Video Solution

Watch 2 video solutions for Maximize Pair Strength Using GCD, a easy level problem involving Array, Math, Enumeration. This walkthrough by Developer Coder has 121 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.

Problem Statement

You are given an integer array nums.

Choose exactly one pair of distinct indices i and j. The strength of the pair is defined as (nums[i] * nums[j]) / gcd(nums[i], nums[j])2.

Return the maximum strength over all possible pairs.

 

Example 1:

Input: nums = [2,3,5]

Output: 15

Explanation:

Choosing i = 1 and j = 2 gives strength (3 * 5) / gcd(3, 5)2 = 15 / 1 = 15, which is the maximum over all pairs.

Example 2:

Input: nums = [4,6,8]

Output: 12

Explanation:

Choosing i = 1 and j = 2 gives strength (6 * 8) / gcd(6, 8)2 = 48 / 4 = 12, which is the maximum over all pairs.

Example 3:

Input: nums = [3,3]

Output: 1

Explanation:

Choosing i = 0 and j = 1 gives strength (3 * 3) / gcd(3, 3)2 = 9 / 9 = 1, the maximum over all pairs.

 

Constraints:

  • 2 <= nums.length <= 2000
  • 1 <= nums[i] <= 105
Read full problem with examples

Approach Overview

Problem Overview: Given an array of integers, find the maximum pair strength where strength is defined as the sum of the pair multiplied by their GCD.

Approach 1: Enumeration (O(n^2))

Iterate through all possible pairs in the array, compute their GCD, and calculate the strength. Track the maximum strength encountered. This approach is straightforward but inefficient for large arrays. Use it when the array size is small or when simplicity is preferred over performance.

Recommended for interviews: Start with the enumeration approach to demonstrate understanding, but be prepared to discuss optimization strategies. Interviewers expect you to recognize the inefficiency and suggest improvements.

For more advanced topics, explore GCD and Enumeration on FleetCode.

Complexity Analysis

ApproachTimeSpaceWhen to Use
EnumerationO(n^2)O(1)Small arrays or simplicity