#1799
Maximize Score After N Operations
hard · verified · 58% accepted · 1,712 likes · top 54%
array · math · dynamic programming · backtracking · bit manipulation · number theory · bitmask
Description
You are given nums, an array of positive integers of size 2 * n. You must perform n operations on this array.
In the ith 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
Explanation: The optimal choice of operations is:
(1 * gcd(1, 2)) = 1
Example 2:
Input: nums = [3,4,6,8]
Output: 11
Explanation: 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
Explanation: The optimal choice of operations is:
(1 * gcd(1, 5)) + (2 * gcd(2, 4)) + (3 * gcd(3, 6)) = 1 + 4 + 9 = 14
Solution