What is the Big O Runtime of Binary Search?
Binary search is a search algorithm that repeatedly divides a sorted array in half until the target element is found or the array is empty. The worst-case time complexity of binary search is O(log n), where n is the number of elements in the array. This means that the maximum number of steps it takes to find an element in a sorted array using binary search is logarithmic with respect to the size of the array.
How Binary Search Works
Binary search works by comparing the target element to the element in the middle of the array. If the target element is less than the middle element, then the search continues in the lower half of the array. If the target element is greater than the middle element, then the search continues in the upper half of the array. This process is repeated until the target element is found or the array is empty.
Why the Runtime is O(log n)
The reason why the runtime of binary search is O(log n) is because the array is repeatedly divided in half. Each time the array is divided in half, the number of elements that need to be searched is reduced by half. Therefore, the maximum number of steps it takes to find an element in a sorted array using binary search is logarithmic with respect to the size of the array.
Related Questions
- What is the best-case time complexity of binary search? O(1)
- What is the average-case time complexity of binary search? O(log n)
- Can binary search be used to find an element in an unsorted array? No
- What is an example of a real-world application of binary search? Searching for a name in a phone book
- How is binary search implemented in programming? Using a while loop or recursion
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