LeetCode in Kotlin

1799. Maximize Score After N Operations

Hard

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:

v(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

Constraints:

• 1 <= n <= 7
• nums.length == 2 * n
• 1 <= nums[i] <= 106

Solution

class Solution {
    fun maxScore(nums: IntArray): Int {
        val n = nums.size
        val memo = arrayOfNulls<Int>(1 shl n)
        return helper(1, 0, nums, memo)
    }

    private fun helper(operationNumber: Int, mask: Int, nums: IntArray, memo: Array<Int?>): Int {
        val n = nums.size
        if (memo[mask] != null) {
            return memo[mask]!!
        }
        if (operationNumber > n / 2) {
            return 0
        }
        var maxScore = Int.MIN_VALUE
        for (i in 0 until n) {
            if (mask and (1 shl i) == 0) {
                for (j in i + 1 until n) {
                    if (mask and (1 shl j) == 0) {
                        val score = operationNumber * gcd(nums[i], nums[j])
                        val score2 = helper(operationNumber + 1, mask or (1 shl i) or (1 shl j), nums, memo)
                        maxScore = Math.max(maxScore, score + score2)
                    }
                }
            }
        }
        memo[mask] = maxScore
        return maxScore
    }

    private fun gcd(a: Int, b: Int): Int {
        return if (b == 0) {
            a
        } else gcd(b, a % b)
    }
}

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