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10. Single Number

easyAsked at Mercury

Find the one element that appears exactly once where every other element appears twice.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given a non-empty array of integers where every element except one appears exactly twice, find that single one. Your algorithm should run in linear time and ideally use constant extra space.

Constraints

  • 1 <= nums.length <= 3*10^4
  • -3*10^4 <= nums[i] <= 3*10^4
  • Exactly one element appears once

Examples

Example 1

Input
nums = [2,2,1]
Output
1

Example 2

Input
nums = [4,1,2,1,2]
Output
4

Approaches

1. Hash count

Tally occurrences and return the key with count 1.

Time
O(n)
Space
O(n)
const c=new Map();
for(const x of nums) c.set(x,(c.get(x)||0)+1);
for(const [k,v] of c) if(v===1) return k;

Tradeoff:

2. XOR fold

XOR all values together: duplicates cancel, leaving the unique value. Linear time, O(1) space.

Time
O(n)
Space
O(1)
function singleNumber(nums) {
  let acc = 0;
  for (const n of nums) acc ^= n;
  return acc;
}

Tradeoff:

Mercury-specific tips

Mercury maps this onto reconciliation: every ACH credit should pair with a debit, so the surviving 'single' is the unmatched leg that needs human review.

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Output

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