How do you solve Append K Integers With Minimal Sum on LeetCode?

Append K Integers With Minimal Sum (LeetCode #2195) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: The smallest k unique integers will always yield the minimal sum.

What is the brute force solution for Append K Integers With Minimal Sum?

The brute force approach for Append K Integers With Minimal Sum is Brute Force, with O(n²) time complexity and O(n) space complexity. The brute force approach involves checking every positive integer starting from 1 to see if it is in the given array. If it's not, we add it to our list of unique integers until we have k of them. This is simple but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Append K Integers With Minimal Sum?

Append K Integers With Minimal Sum uses the following concepts: Array, Math, Greedy, Sorting. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Append K Integers With Minimal Sum?

Always think about the data structures that can optimize your solution. Clarify the problem requirements, especially regarding uniqueness and positivity of integers. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Append K Integers With Minimal Sum?

Not using a set for quick lookups, leading to inefficient checks. Failing to account for the case when all integers from 1 to k are already in nums.

#2195

Append K Integers With Minimal Sum

Medium

ArrayMathGreedySortingHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(n)	O(n)

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Intuition

Time O(n)Space O(n)

The optimal approach leverages the fact that the smallest k unique positive integers not in nums will always yield the minimum sum. We can efficiently find these integers by iterating through positive integers and checking against a set of existing numbers.

⚙️

Algorithm

5 steps

1Step 1: Create a set from nums for O(1) lookups.
2Step 2: Initialize a variable to keep track of the sum of the k unique integers.
3Step 3: Use a loop starting from 1 to find the first k integers not in the set.
4Step 4: Add these integers to the sum.
5Step 5: Return the sum.

solution.py12 lines

1# Full working Python code
2
3def minimal_sum(nums, k):
4    num_set = set(nums)
5    sum_unique = 0
6    current = 1
7    while k > 0:
8        if current not in num_set:
9            sum_unique += current
10            k -= 1
11        current += 1
12    return sum_unique

ℹ

Complexity note: The time complexity is O(n) because we are iterating through the integers and checking against the set, which is O(1) per check. The space complexity is O(n) for storing the elements of nums in the set.

1The smallest k unique integers will always yield the minimal sum.
2Using a set allows for quick lookups to check if an integer is already in nums.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.