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  1. Python provides a rich ecosystem for implementing various algorithms, ranging from sorting and searching to graph traversal and dynamic programming. Below are some key algorithms with examples to help you understand their implementation and use cases.

    Sorting Algorithms

    Quicksort

    Quicksort is a divide-and-conquer algorithm that selects a pivot element, partitions the array into elements less than and greater than the pivot, and recursively sorts the partitions.

    def quicksort(arr):
    if len(arr) <= 1:
    return arr
    pivot = arr[len(arr) // 2]
    left = [x for x in arr if x < pivot]
    middle = [x for x in arr if x == pivot]
    right = [x for x in arr if x > pivot]
    return quicksort(left) + middle + quicksort(right)

    # Example usage
    arr = [3, 6, 8, 10, 1, 2, 1]
    print(quicksort(arr)) # Output: [1, 1, 2, 3, 6, 8, 10]
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    Merge Sort

    Merge Sort splits the array into halves, recursively sorts them, and merges the sorted halves.

    def merge_sort(arr):
    if len(arr) <= 1:
    return arr
    mid = len(arr) // 2
    left = merge_sort(arr[:mid])
    right = merge_sort(arr[mid:])
    return merge(left, right)

    def merge(left, right):
    result = []
    i = j = 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
    result.extend(left[i:])
    result.extend(right[j:])
    return result

    # Example usage
    arr = [3, 6, 8, 10, 1, 2, 1]
    print(merge_sort(arr)) # Output: [1, 1, 2, 3, 6, 8, 10]
    Copied!
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