Merge sort has a O(n log₂(n)) complexity. If a computer can sort 1,024 elements in an amount of time x, approximately how much longer will it take the computer to sort 1,024 times that many, or 1,048,576 elements? A) 1,024 times longer B) 2,048 times longer C) 8,192 times longer D) 1,048,576 times longer

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Merge sort has a time complexity of O(n log n). So, if the time taken to sort n elements is x, then the time taken to sort m elements is O(m log m). Therefore, the time taken to sort 1,048,576 elements is O(1,048,576 log 1,048,576) = O(1,048,576 * 20) = O(20,971,520). Since 20,971,520 is approximately 8,192 times larger than x, the answer is C.

Merge Sort Has a O(n Log2(n)) Complexity

Merge Sort Has a O(n Log₂(n)) Complexity