If the given input array is sorted or nearly sorted, which of the following algorithm gives the best performance?Insertion sortSelection sortQuick sortMerge sort

Insertion sort gives the best performance when the input array is sorted or nearly sorted. This is because insertion sort can recognize the existing order in the array and has a best-case time complexity of O(n) when the array is already sorted. Other algorithms like selection sort, quick sort, and merge sort do not take advantage of existing order in the same way and have a best-case time complexity of O(n log n).

Insertion sort is the best algorithm for a sorted or nearly sorted array. Here's why:

1. Insertion sort works by comparing each element in the list with the element next to it, and swapping them if required.

2. In a sorted or nearly sorted array, the number of comparisons and swaps required would be minimal, making the algorithm very efficient.

3. Other sorting algorithms like Selection sort, Quick sort, and Merge sort do not take into account the existing order of elements, and hence, would not be as efficient as Insertion sort in this case.

4. Selection sort always looks for the minimum element and places it at the beginning, regardless of the existing order. Quick sort and Merge sort divide the array into smaller parts and sort them individually, again not taking into account the existing order.

5. Therefore, for a sorted or nearly sorted array, Insertion sort would give the best performance.

Insertion sort is the best algorithm for a sorted or nearly sorted array. Here's why:

1. Insertion sort works by comparing each element in the list with the element next to it, and swapping them if required.

2. In a sorted or nearly sorted array, the number of comparisons and swaps required would be minimal, making the algorithm very efficient.

3. On the other hand, algorithms like Quick sort and Merge sort have a time complexity of O(n log n) regardless of whether the input is sorted or not.

4. Selection sort is not a good choice either because it always takes O(n^2) time, even if the input is sorted.

So, for a sorted or nearly sorted array, Insertion sort would give the best performance.

The best algorithm for a sorted or nearly sorted array would be the Insertion Sort.

Here's why:

1. Insertion Sort: This algorithm iterates through the array and maintains a sorted sublist in the lower positions of the list. Each new item is then "inserted" back into the previous sublist such that the sorted sublist is one item larger. In the best case scenario, when the array is already sorted, the complexity of this algorithm is O(n), which is the most efficient among these options.

2. Selection Sort: This algorithm sorts an array by repeatedly finding the minimum element from the unsorted part and putting it at the beginning. The algorithm maintains two subarrays in a given array. Even if the array is sorted or nearly sorted, it will still go through all the elements, making its time complexity O(n^2).

3. Quick Sort: This algorithm is a divide and conquer algorithm. It picks an element as pivot and partitions the given array around the picked pivot. The worst case occurs when the partition process always picks greatest or smallest element as pivot causing an O(n^2) complexity. However, in the best case scenario, the complexity is O(n log n).

4. Merge Sort: This is also a divide and conquer algorithm. It divides the input array into two halves, calls itself for the two halves, and then merges the two sorted halves. The merge process is the most expensive part of the algorithm and will be performed even if the array is already sorted, leading to a time complexity of O(n log n).

So, for a sorted or nearly sorted array, Insertion Sort would give the best performance.