Maximize Score After N Operations

arraymathdynamic programming

You are given nums , an array of positive integers of size 2 * n . You must perform n operations on this array.

In the i ^th operation (1-indexed) , you will:

Choose two elements, x and y .

Receive a score of i * gcd(x, y) .

Remove x and y from nums .

Return the maximum score you can receive after performing n operations.

The function gcd(x, y) is the greatest common divisor of x and y .

Example 1

Input: nums = [1,2]
Output: 1
The optimal choice of operations is:
(1 * gcd(1, 2)) = 1

Example 2

Input: nums = [3,4,6,8]
Output: 11
The optimal choice of operations is:
(1 * gcd(3, 6)) + (2 * gcd(4, 8)) = 3 + 8 = 11

Example 3

Input: nums = [1,2,3,4,5,6]
Output: 14
The optimal choice of operations is:
(1 * gcd(1, 5)) + (2 * gcd(2, 4)) + (3 * gcd(3, 6)) = 1 + 4 + 9 = 14

1 <= n <= 7

nums.length == 2 * n

1 <= nums[i] <= 10 ^6

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Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicMath