Why is the time complexity of merge sort O(n log n)?
Merge sort is a divide-and-conquer sorting algorithm that follows the principle of recursion. It is known for its reliable performance and is often considered one of the most efficient sorting algorithms, especially when dealing with large datasets.
The time complexity of merge sort is O(n log n), meaning that the running time of the algorithm increases logarithmically with the size of the input data. This is because merge sort operates by recursively dividing the input array into smaller subarrays, sorting them, and then merging them back together.
During each recursive call, the input array of size n is divided into two halves, each of size n/2. The merge operation, which combines the sorted subarrays, takes O(n) time. The recursion continues until the subarrays reach a size of 1, at which point they are trivially sorted.
The total time complexity can be calculated using the recursion tree method:
- The root of the tree represents the initial merge sort operation, which takes O(n) time.
- Each level of the tree represents a recursive call, and the time taken at each level is O(n).
- The height of the tree is log n, as each level represents dividing the input size by 2.
Therefore, the total time complexity of merge sort is the sum of the time taken at each level, which is O(n) * log n = O(n log n).
Related Questions
- What is the worst-case time complexity of merge sort? O(n log n)
- What is the best-case time complexity of merge sort? O(n)
- Is merge sort a stable sorting algorithm? Yes
- What is the space complexity of merge sort? O(n)
- Which sorting algorithm is faster than merge sort? Quick sort
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