2829. Determine the Minimum Sum of a k-avoiding Array

Problem

You are given two integers, n and k.

An array of distinct positive integers is called a k-avoiding array if there does not exist any pair of distinct elements that sum to k.

Return **the *minimum* possible sum of a k-avoiding array of length **n.

Example 1:

Input: n = 5, k = 4
Output: 18
Explanation: Consider the k-avoiding array [1,2,4,5,6], which has a sum of 18.
It can be proven that there is no k-avoiding array with a sum less than 18.

Example 2:

Input: n = 2, k = 6
Output: 3
Explanation: We can construct the array [1,2], which has a sum of 3.
It can be proven that there is no k-avoiding array with a sum less than 3.

Constraints:

• 1 <= n, k <= 50

Solution (Java)

class Solution {
    int calculateSumInRange(int a, int n) {
        int sum = (n * (2 * a + (n - 1))) / 2;
        return sum;
    }

    public int minimumSum(int quantity, int k) {
        int middle = k / 2;

        if (quantity <= middle) {
            return quantity * (quantity + 1) / 2;
        }

        int leftSum = middle * (middle + 1) / 2;

        int remainingNumbers = quantity - middle;

        return leftSum + calculateSumInRange(k, remainingNumbers);
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).