Given an array of numbers where every number occurs twice except one, how would you find the unique number in O(log n) time?

To find the unique number in an array where all other numbers appear twice, in O(log n) time, we must assume the array is sorted. This allows us to use a binary search approach. The key insight is that in a sorted array with pairs, the first occurrence of a number will always be at an even index, and its duplicate will be at the next odd index. If the unique number disrupts this pattern, we can use binary search to narrow down the search space. We check the middle element: if it's at an even index and equal to the next element, the unique number is in the right half; otherwise, it's in the left half. We continue this process until the search space is reduced to a single element, which will be our unique number.