Append K Integers With Minimal Sum

Problem Description

You are given an integer array nums and an integer k. Append k unique positive integers that do not appear in nums to nums such that the resulting total sum is minimal. Return the sum of the k integers appended to nums.

Key Insights

• To minimize the sum, the integers to be appended should be the smallest positive integers not present in nums.
• The use of a set can help efficiently track which integers are already in nums.
• A simple iteration can be used to find the first k unique integers that do not exist in nums.

Space and Time Complexity

Time Complexity: O(n + k), where n is the length of nums. We need O(n) to create a set of existing numbers and O(k) to find the missing integers.

Space Complexity: O(n), for storing the unique integers in a set.

Solution

The solution uses a set to keep track of the integers already present in nums. We then iterate through positive integers starting from 1, checking if they are present in the set. If not, we add them to our result until we have collected k unique integers. Finally, we return the sum of these k integers.

Code Solutions