Chapter 9: Sorting Algorithms (Part 1)

Vol 2: Algorithm Forest Adventure · Station 9

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Metadata Card

Attribute	Value
Difficulty	(Foundation)
Prerequisites	Arrays, Linked Lists, Recursion
Keywords	Selection Sort Bubble Sort Insertion Sort Shell Sort Merge Sort Divide and Conquer Stable Sort

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Your Progress

Master Chen taught you how to use data, but not how to organize it. Before you lies a chaotic pile of items (input). To find the smallest, largest, or median — sorting is your first weapon.

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Breakthrough · Origins

Selection Sort: Find the Minimum Each Round

def selection_sort(arr):
    for i in range(len(arr) - 1):
        min_idx = i
        for j in range(i + 1, len(arr)):
            if arr[j] < arr[min_idx]:
                min_idx = j
        arr[i], arr[min_idx] = arr[min_idx], arr[i]
    return arr

Bubble Sort: Adjacent Comparison (As a Counterexample)

def bubble_sort(arr):
    for i in range(len(arr) - 1):
        swapped = False
        for j in range(len(arr) - 1 - i):
            if arr[j] > arr[j + 1]:
                arr[j], arr[j + 1] = arr[j + 1], arr[j]
                swapped = True
        if not swapped:
            break
    return arr

Insertion Sort: Like Organizing Playing Cards

def insertion_sort(arr):
    for i in range(1, len(arr)):
        key = arr[i]
        j = i - 1
        while j >= 0 and arr[j] > key:
            arr[j + 1] = arr[j]
            j -= 1
        arr[j + 1] = key
    return arr

Key insight: Insertion sort is O(n) on nearly-sorted data — used as the fallback in advanced sorts (Timsort).

Merge Sort: The First O(n log n) Divide and Conquer

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

Complexity Comparison

Algorithm	Best	Average	Worst	Space	Stable
Selection	O(n²)	O(n²)	O(n²)	O(1)	No
Bubble	O(n)	O(n²)	O(n²)	O(1)	Yes
Insertion	O(n)	O(n²)	O(n²)	O(1)	Yes
Merge	O(n log n)	O(n log n)	O(n log n)	O(n)	Yes

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Verification Checklist

• [ ] Can hand-write selection, bubble, insertion, merge sort
• [ ] Can explain why insertion sort is O(n) on nearly-sorted data
• [ ] Can draw the recursion tree for merge sort (n=8)
• [ ] Can explain merge sort's stability

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Traveler's Notes

• Selection: most honest O(n²), always O(n²)
• Bubble: most intuitive, but worst performer
• Insertion: most practical O(n²), foundation for advanced sorts
• Merge: divide and conquer perfected, stable, O(n log n) guaranteed

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→ Next Stop Preview

Chapter 10: Sorting Algorithms (Part 2) — "Quicksort, Heapsort, and linear-time sorting."