Added timsort.py Algorithm

[shaik-amanullah-codelaunch]

Tim Sort Algorithms
The main idea behind Tim Sort is to exploit the existing order in the data to minimize the number of comparisons and swaps. It achieves this by dividing the array into small subarrays called runs, which are already sorted, and then merging these runs using a modified merge sort algorithm.

How does Tim Sort work?

Let’s consider the following array as an example: arr[] = {4, 2, 8, 6, 1, 5, 9, 3, 7}.

Step 1: Define the size of the run

Minimum run size: 32 (we’ll ignore this step since our array is small)

Step 2: Divide the array into runs

In this step, we’ll use insertion sort to sort the small subsequences (runs) within the array.
The initial array: [4, 2, 8, 6, 1, 5, 9, 3, 7]
No initial runs are present, so we’ll create runs using insertion sort.
Sorted runs: [2, 4], [6, 8], [1, 5, 9], [3, 7]
Updated array: [2, 4, 6, 8, 1, 5, 9, 3, 7]

Step 3: Merge the runs

In this step, we’ll merge the sorted runs using a modified merge sort algorithm.
Merge the runs until the entire array is sorted.
Merged runs: [2, 4, 6, 8], [1, 3, 5, 7, 9]
Updated array: [2, 4, 6, 8, 1, 3, 5, 7, 9]

Step 4: Adjust the run size

After each merge operation, we double the size of the run until it exceeds the length of the array.
The run size doubles: 32, 64, 128 (we’ll ignore this step since our array is small)

Step 5: Continue merging

Repeat the merging process until the entire array is sorted.
Final merged run: [1, 2, 3, 4, 5, 6, 7, 8, 9]

The final sorted array is [1, 2, 3, 4, 5, 6, 7, 8, 9].