Key Sorting Algorithms Every Coder Should Know - 2

🌀 1. Quick Sort

Divide-and-conquer: pick a  pivot, partition the array into elements ≤ pivot (left) and > pivot (right), then recursively sort the two halves. Average-case efficiency comes from balanced partitions.

1.1. Time Complexity

• Average / Best case: O(n log n)

• Worst case: O(n²) (already-sorted or all equal elements with naïve pivot)

1.2. Space Complexity

• O(log n) extra (call stack) if in-place partitioning is used.

1.3. Code

def quick_sort(arr):
    if len(arr) <= 1:                   # base case
        return arr
    pivot = arr[0]                      # simple pivot choice
    tail  = arr[1:]

    left  = [x for x in tail if x <= pivot]
    right = [x for x in tail if x >  pivot]

    return quick_sort(left) + [pivot] + quick_sort(right)

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🪄 2. Merge Sort

Recursively divide the array in half, sort each half, then merge the two sorted halves back together in linear time.

2.1. Time Complexity

• All cases: O(n log n)

2.2. Space Complexity

• O(n) extra for the temporary merge buffer.

2.3. Code

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):
    merged = []
    i = j = 0
    while i < len(left) and j < len(right):
        if left[i] <= right[j]:
            merged.append(left[i]);  i += 1
        else:
            merged.append(right[j]); j += 1
    merged.extend(left[i:]); merged.extend(right[j:])
    return merged

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🏧 3. Heap Sort

Build a  max-heap from the input array, then repeatedly swap the root (largest element) with the last unsorted element and heap-reduce the remaining array.

3.1. Time Complexity

• All cases: O(n log n)

3.2. Space Complexity

• O(1) extra if performed in place (array-backed heap).

3.3. Code

import heapq

def heap_sort(arr):
    heapq.heapify(arr)              # Min-heap by default
    sorted_arr = [heapq.heappop(arr) for _ in range(len(arr))]
    return sorted_arr

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📊 4. Counting Sort

For a small integer range, count the occurrences of each value, then iterate through the counts to rebuild the sorted array. Works only for discrete, non-negative keys of limited range.

4.1. Time Complexity

• O(n + k) where k is the value range (max − min + 1).

4.2. Space Complexity

• O(n + k) for the count array and (optionally) the output array.

4.3. Code

def counting_sort(arr):
    if not arr:
        return []
    max_val = max(arr)
    count = [0] * (max_val + 1)

    for num in arr:
        count[num] += 1

    sorted_arr = []
    for i in range(len(count)):
        sorted_arr.extend([i] * count[i])

    return sorted_arr

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✨ Summary

🔗 References

• Quick sort in 4 minutes

• Merge sort in 3 minutes

• Heap sort in 4 minutes

• Learn Counting Sort Algorithm in LESS THAN 6 MINUTES!