Explain the insertion merge insertion sort algorithm.

The insertion merge insertion sort algorithm is a variation of the traditional insertion sort algorithm that incorporates the merge sort algorithm to improve its efficiency. This algorithm is particularly useful when dealing with large datasets.

To understand the insertion merge insertion sort algorithm, let's break it down into three main steps:

1. Initial Insertion Sort:
The first step involves performing an initial insertion sort on smaller subarrays of the given dataset. This is done by dividing the dataset into multiple subarrays of a fixed size (let's say k). Each subarray is then sorted individually using the insertion sort algorithm. This step helps in reducing the overall number of comparisons and swaps required in the subsequent steps.

2. Merge Sort:
After the initial insertion sort, we have multiple sorted subarrays of size k. The next step is to merge these subarrays using the merge sort algorithm. The merge sort algorithm works by repeatedly dividing the subarrays into halves until we have subarrays of size 1. Then, it merges these subarrays in a sorted manner to obtain a single sorted array.

3. Final Insertion Sort:
Once the merge step is completed, we have a single sorted array. However, this array may still contain some unsorted elements due to the initial insertion sort step. To ensure that the entire array is sorted, we perform a final insertion sort on the entire array. This step is necessary because the merge step may introduce some unsorted elements during the merging process.

Overall, the insertion merge insertion sort algorithm combines the benefits of both insertion sort and merge sort. The initial insertion sort reduces the number of comparisons and swaps required, while the merge sort ensures a more efficient merging process. The final insertion sort guarantees that the entire array is sorted correctly.

It is important to note that the efficiency of the insertion merge insertion sort algorithm depends on the choice of the initial subarray size (k). Choosing an optimal value for k can significantly impact the overall performance of the algorithm.