mediumBinary SearchBinary Search

Single Element in Sorted Array

mediumTime: O(log n)Space: O(1)

Recognize the pattern

single non-duplicate in sorted paired arrayO(log n)pairing pattern disrupted

Brute force idea

XOR all — O(n). Doesn't use sorted structure.

Better approach

Binary search: before the single element, pairs start at even indices. After, at odd. Check mid's pair to determine which side. O(log n).

Key invariant

The single element shifts all subsequent pairs. Binary search identifies where the shift occurs.

Watch out for

Not normalizing mid to even — if mid is odd, check mid-1. If even, check mid+1.

Binary Search Pattern