To determine which of the algorithms has the smallest time complexity, we need to compare their time complexities:
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Merge Sort: O(n log n) - This is a divide-and-conquer algorithm that typically sorts an array or list.
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Binary Search: O(log n) - This algorithm is used to find an element in a sorted array or list, and it reduces the search space by half each time.
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Insertion Sort: O(n^2) - This sorting algorithm builds the final sorted array one item at a time, with a time complexity that can degrade to quadratic in the worst case.
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Linear Search: O(n) - This search algorithm checks each element one by one until it finds the target element or reaches the end of the list.
Among these algorithms, Binary Search has the smallest time complexity, which is O(log n).