How do you solve Find N Unique Integers Sum up to Zero on LeetCode?

Find N Unique Integers Sum up to Zero (LeetCode #1304) 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: Using pairs of integers that cancel each other out is a straightforward way to ensure the sum is zero.

What is the time complexity of Find N Unique Integers Sum up to Zero?

The optimal solution for Find N Unique Integers Sum up to Zero runs in O(n) time and uses O(n) space. This complexity is O(n) because we are iterating through n/2 integers to construct the result array, which is linear in terms of n.

What is the brute force solution for Find N Unique Integers Sum up to Zero?

The brute force approach for Find N Unique Integers Sum up to Zero is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach would involve generating all possible combinations of integers and checking which ones sum to zero. However, this is inefficient and not practical for larger values of n. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find N Unique Integers Sum up to Zero?

Find N Unique Integers Sum up to Zero uses the following concepts: Array, Math. The recommended patterns to study are: Array, Mathematical properties.

What are the interview tips for Find N Unique Integers Sum up to Zero?

Always consider the properties of numbers when dealing with sums and pairs. Think about edge cases, such as odd vs. even n, before starting to code. Communicate your thought process clearly; explain why you choose a particular approach.

What are common mistakes when solving Find N Unique Integers Sum up to Zero?

Overcomplicating the problem by trying to generate combinations instead of constructing the solution directly. Forgetting to handle the case when n is odd.

#1304

Find N Unique Integers Sum up to Zero

Easy

ArrayMathArrayMathematical properties

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

Instead of generating combinations, we can directly construct the required array by leveraging the properties of integers. For any n, we can use pairs of integers that cancel each other out.

⚙️

Algorithm

4 steps

1Step 1: Initialize an empty array.
2Step 2: For each integer from 1 to n/2, add both -i and i to the array.
3Step 3: If n is odd, append 0 to the array.
4Step 4: Return the constructed array.

solution.py10 lines

1# Full working Python code
2
3def find_n_unique_integers(n):
4    result = []
5    for i in range(1, n // 2 + 1):
6        result.append(i)
7        result.append(-i)
8    if n % 2 == 1:
9        result.append(0)
10    return result

ℹ

Complexity note: This complexity is O(n) because we are iterating through n/2 integers to construct the result array, which is linear in terms of n.

1Using pairs of integers that cancel each other out is a straightforward way to ensure the sum is zero.
2For odd n, including zero balances the array.

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