The time complexity of running merge sort on an array of size n which is already sorted is O(n log n). Here's why: 1. Merge sort is a divide and conquer algorithm. It works by dividing the array into two halves, sorting them separately, and then merging them. 2. Even if the array is already sorted, merge sort doesn't know this and will still perform the same steps. 3. The division step is O(log n) because each division splits the array in half. This will be done log n times until each array is of size 1. 4. The merge step is O(n) because in the worst case, we have to look at every element in both halves of the array to merge them back together. 5. Since these steps are done together for each division and merge, we multiply their time complexities together, giving us a total time complexity of O(n log n). So, even if the array is already sorted, merge sort will still take O(n log n) time.

Running merge sort on an array of size n which is already sorted isO(n)O(nlogn)O(n2) None

Question

Running merge sort on an array of size n which is already sorted isO(n)O(nlogn)O(n2) None

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Solution 1

The time complexity of running merge sort on an array of size n which is already sorted is O(n log n).

Here's why:

Merge sort is a divide and conquer algorithm. It works by dividing the array into two halves, sorting them separately, and then merging them.
Even if the array is already sorted, merge sort doesn't know this and will still perform the same steps.
The division step is O(log n) because each division splits the array in half. This will be done log n times until each array is of size 1.
The merge step is O(n) because in the worst case, we have to look at every element in both halves of the array to merge them back together.
Since these steps are done together for each division and merge, we multiply their time complexities together, giving us a total time complexity of O(n log n).

So, even if the array is already sorted, merge sort will still take O(n log n) time.

This problem has been solved

Solution 2

The time complexity of running merge sort on an array of size n which is already sorted is O(n log n). This is because merge sort has a time complexity of O(n log n) in all cases (best, average, and worst). Even if the array is already sorted, merge sort will still divide the array into halves and merge them back together, resulting in a time complexity of O(n log n).

Solution 3

Solution 4

Similar Questions

What is the time complexity for executing merge sort on an array of size n which is already sorted isSelect one:O(n log n)O(log n)OO(n^2)

What is the run time of Merge Sort algorithm in terms of Big O? a. O(logN) b. O(N) c. O(N!) d. O(NlogN) e. O(N^2)

You are given two integer arrays nums1 and nums2, sorted in non-decreasing order, and two integers m and n, representing the number of elements in nums1 and nums2 respectively.Merge nums1 and nums2 into a single array sorted in non-decreasing order.The final sorted array should not be returned by the function, but instead be stored inside the array nums1. To accommodate this, nums1 has a length of m + n, where the first m elements denote the elements that should be merged, and the last n elements are set to 0 and should be ignored. nums2 has a length of n. Example 1:Input: nums1 = [1,2,3,0,0,0], m = 3, nums2 = [2,5,6], n = 3Output: [1,2,2,3,5,6]Explanation: The arrays we are merging are [1,2,3] and [2,5,6].The result of the merge is [1,2,2,3,5,6] with the underlined elements coming from nums1.Example 2:Input: nums1 = [1], m = 1, nums2 = [], n = 0Output: [1]Explanation: The arrays we are merging are [1] and [].The result of the merge is [1].Example 3:Input: nums1 = [0], m = 0, nums2 = [1], n = 1Output: [1]Explanation: The arrays we are merging are [] and [1].The result of the merge is [1].Note that because m = 0, there are no elements in nums1. The 0 is only there to ensure the merge result can fit in nums1. Constraints:nums1.length == m + nnums2.length == n0 <= m, n <= 2001 <= m + n <= 200-109 <= nums1[i], nums2[j] <= 109 Follow up: Can you come up with an algorithm that runs in O(m + n) time?

What is the worst case time complexity of mergesort

Given two sorted arrays arr1[] and arr2[] of sizes n and m in non-decreasing order. Merge them in sorted order without using any extra space. Modify arr1 so that it contains the first N elements and modify arr2 so that it contains the last M elements.

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