🧠 Solving LeetCode Until I Become Top 1% — Day `76`

🔹 Problem: 1304 Find N Unique Integers Sum up to Zero

Difficulty: #Easy
Tags: #Math, #Constructive

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📝 Problem Summary

Given an integer n, return an array of n unique integers such that they sum up to 0.

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🧠 My Thought Process

• Brute Force Idea:
  Generate random numbers and try to adjust until their sum is zero. This would be messy and inefficient.

• Optimized Strategy:

  • Pair positive and negative integers: (1, -1), (2, -2), ...
  • If n is even, the pairs are enough.
  • If n is odd, just add 0 to balance everything out.
  • This guarantees uniqueness and ensures the sum is always 0.

• Algorithm Used:
  
  Constructive Math (pairing positives and negatives).

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⚙️ Code Implementation (Python)

class Solution:
    def sumZero(self, n: int) -> List[int]:
        ans = []
        for i in range(1, n // 2 + 1):
            ans.append(i)
            ans.append(-i)
        if n % 2 == 1:
            ans.append(0)
        return ans

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⏱️ Time & Space Complexity

• Time: O(n) — we generate n elements.
• Space: O(n) — storing the result array.

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🧩 Key Takeaways

• ✅ Learned how constructive math can directly give the answer without brute force.
• 💡 The “pairing” trick is a powerful way to balance sums.
• 💭 If a problem asks for sums = 0 (or balanced counts), think about symmetry.

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🔁 Reflection (Self-Check)

• [x] Could I solve this without help?
• [x] Did I write code from scratch?
• [x] Did I understand why it works?
• [x] Will I be able to recall this in a week?

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🚀 Progress Tracker

Metric	Value
Day	76
Total Problems Solved	440
Confidence Today	😃
Leetcode Rating	1530