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sorting/README.md

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+## sorting and searching
+
+<br>
+
+* **inversions** in a sequence is a pair of elements that are out of order with respect to the ordering relation. a sorting algorithm is a sequence of operations that reduces inversions to zero.
+* a **topological sort** of a diretect graph is a way of ordering the list of nodes such that if `(a, b)` is a edge of the graph, then `a` appears before `b`. it does not work if a graph has cycles or is not directed.
+
+
+<br>
+
+----
+
+### `sorting_algorithms.py`
+
+<br>
+
+```python
+> python3 sorting_algorithms.py
+
+
+Array: [3, 5, 1, 2, 10, 6]
+Testing merge sort: [1, 2, 3, 5, 6, 10]
+Testing quick sort: [1, 2, 3, 5, 6, 10]
+```
+
+<br>
+
+### `binary_search.py`
+
+<br>
+
+```python
+> python binary_search.py
+Recursive:  6
+Iterative:  6
+```
+

sorting/sorting_algorithms.py

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+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+# author: bt3gl
+
+
+def merge_sort(array):
+    """Sort an array using merge sort"""
+
+    # part 1: recursively divide the array into subarrays
+    if len(array) < 2:
+        return array
+    
+    mid = len(array) // 2
+    left = merge_sort(array[:mid])
+    right = merge_sort(array[mid:])
+
+    # part 2: merge the subarrays
+    result = []
+    i, j = 0, 0
+    
+    while i < len(left) and j < len(right):
+        if left[i] <= right[j]:
+            result.append(left[i])
+            i +=1
+        else:
+            result.append(right[j])
+            j +=1
+    
+    if left[i:]:
+        result.extend(left[i:])
+    if right[j:]:
+        result.extend(right[j:])
+    
+    return result
+
+
+def quick_sort_partition(array):
+    """Sort an array using quick sort"""
+
+    pivot, array = array[0], array[1:]
+
+    lower = [i for i in array if i <= pivot]
+    higher = [i for i in array if i > pivot]
+
+    return lower, pivot, higher
+
+
+def quick_sort_divided(array):
+    """Sort an array using quick sort"""
+
+    if len(array) < 2:
+        return array
+
+    lower, pivot, higher = quick_sort_partition(array)
+    return quick_sort_divided(lower) + [pivot] + quick_sort_divided(higher)
+
+
+if __name__ == '__main__':
+
+    array = [3, 5, 1, 2, 10, 6]
+    print(f'Array: {array}')
+
+    print(f'Testing merge sort: {merge_sort(array)}')
+    print(f'Testing quick sort: {quick_sort_divided(array)}')