Problem Statement
Compare linear search and binary search. In what scenarios is each algorithm preferred?
Explanation
Linear search and binary search are fundamental searching algorithms with different requirements, performance characteristics, and use cases.
Linear search examines each element sequentially from start to end until the target is found or the array ends. It works by checking if the current element equals the target, returning the index if found, or continuing to the next element. Time complexity is O of 1 best case when element is first, O of n average and worst case. Space complexity is O of 1 as no extra space is needed. Linear search works on both sorted and unsorted arrays, and it works on any data structure with sequential access including linked lists.
Binary search divides the search space in half repeatedly by comparing the target with the middle element. It requires a sorted array. If the middle element equals target, return it. If target is smaller, search left half. If larger, search right half. Time complexity is O of log n for all cases. Space complexity is O of 1 for iterative implementation or O of log n for recursive due to call stack. Binary search only works on sorted arrays and requires random access, making it unsuitable for linked lists.
Use linear search when the array is unsorted and sorting overhead exceeds search benefit, when the array is very small where O of n is acceptable, when searching linked lists or data structures without random access, when you need to find all occurrences of an element, and when implementing simple search without complexity. Linear search is also useful when the target is likely to be near the beginning.
Use binary search when the array is already sorted or will be searched multiple times justifying the sorting cost, when dealing with large datasets where O of log n significantly outperforms O of n, when you need to find first or last occurrence in sorted array, when implementing range queries or finding closest elements, and when memory allows random access. Binary search is essential in scenarios requiring logarithmic performance like database indexing.
For example, with an array of 1 million elements, linear search might examine up to 1 million elements in worst case, while binary search examines at most 20 elements, demonstrating the massive performance difference for large datasets.