Implement Tim Sort Algorithm

Implements koii-network#12858

Implements koii-network#12829

Implements koii-network#12825

Implements koii-network#12786

Implements koii-network#12770

Implements koii-network#12725

Implements koii-network#12648

# Implement Tim Sort Algorithm

## Task
Write a function to implement the tim sort algorithm.

## Acceptance Criteria
All tests must pass.

## Summary of Changes
Added a comprehensive implementation of Tim Sort algorithm, which is a hybrid sorting algorithm derived from merge sort and insertion sort. The implementation includes optimizations for small arrays and provides efficient sorting with O(n log n) time complexity.

## Test Cases
 - Verify Tim Sort correctly sorts an array of integers in ascending order
 - Verify Tim Sort handles an empty array without errors
 - Verify Tim Sort correctly sorts an array with duplicate elements
 - Check Tim Sort performance with large randomly generated arrays
 - Ensure Tim Sort maintains stability of element ordering
 - Validate Tim Sort works with different data types (integers, floats, strings)

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

Author: beso

prometheus/sorting_algorithms.py

@@ -0,0 +1,86 @@
+def tim_sort(array, n=None, bucket_size=32):
+    """
+    Implement Tim Sort algorithm.
+
+    Tim Sort is a hybrid sorting algorithm derived from merge sort and insertion sort.
+    It includes optimizations for small arrays and provides efficient sorting with O(n log n)
+    time complexity.
+
+    :param array: The array to be sorted.
+    :param n: Optional. The length of the array. If not provided, it will be determined
+               automatically.
+    :param bucket_size: Optional. The bucket size for initial sorting. Default is 32.
+    :return: None
+    """
+    if n is None:
+        n = len(array)
+
+    if n <= 1:
+        return
+
+    # Split the array into smaller chunks and sort them using insertion sort
+    for i in range(0, n, bucket_size):
+        end = min(i + bucket_size, n)
+        insertion_sort(array, i, end)
+
+    # Merge the sorted chunks using the merge sort algorithm
+    for size in range(bucket_size, n, bucket_size):
+        for start in range(0, n, 2 * size):
+            mid = start + size
+            end = min(start + 2 * size, n)
+            merge(array, start, mid, end)
+
+
+def insertion_sort(array, start, end):
+    """
+    Perform insertion sort on the given subarray.
+
+    :param array: The array to be sorted.
+    :param start: The start index of the subarray.
+    :param end: The end index of the subarray.
+    :return: None
+    """
+    for i in range(start + 1, end):
+        key = array[i]
+        j = i - 1
+        while j >= start and array[j] > key:
+            array[j + 1] = array[j]
+            j -= 1
+        array[j + 1] = key
+
+
+def merge(array, start, mid, end):
+    """
+    Merge two sorted subarrays into a single sorted array.
+
+    :param array: The array to be merged.
+    :param start: The start index of the first subarray.
+    :param mid: The end index of the first subarray and the start index of the second subarray.
+    :param end: The end index of the second subarray.
+    :return: None
+    """
+    left_array = array[start:mid]
+    right_array = array[mid:end]
+
+    left_index = 0
+    right_index = 0
+    current_index = start
+
+    while left_index < len(left_array) and right_index < len(right_array):
+        if left_array[left_index] <= right_array[right_index]:
+            array[current_index] = left_array[left_index]
+            left_index += 1
+        else:
+            array[current_index] = right_array[right_index]
+            right_index += 1
+        current_index += 1
+
+    while left_index < len(left_array):
+        array[current_index] = left_array[left_index]
+        left_index += 1
+        current_index += 1
+
+    while right_index < len(right_array):
+        array[current_index] = right_array[right_index]
+        right_index += 1
+        current_index += 1