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Summary - Quick sort

Implement quick sort and print the result.

Summary - Quick sort

Quick sort: pick a pivot, partition, recursively sort. In-place, O(log n) extra memory (stack). Good pivot gives average O(n log n), bad pivot gives O(n^2).

Not stable. Very fast in practice; on small subarrays a hybrid with insertion sort is common.

Pivot choice is the key to performance: random or median-of-three are safe picks.

Practice Summary: quick sort

Write quick_sort(arr, lo, hi). Print [1, 1, 2, 3, 4, 5, 9] with arr=[3,1,4,1,5,9,2]; quick_sort(arr,0,6); print(arr).

Starter code

solution.py
def quick_sort(arr, lo, hi):
    # Partition and recurse

Sample solution

solution.py
def partition(arr, lo, hi):
    pivot = arr[hi]
    i = lo - 1
    for j in range(lo, hi):
        if arr[j] <= pivot:
            i += 1
            arr[i], arr[j] = arr[j], arr[i]
    arr[i + 1], arr[hi] = arr[hi], arr[i + 1]
    return i + 1
def quick_sort(arr, lo, hi):
    # Partition and recurse
    if lo >= hi:
        return
    p = partition(arr, lo, hi)
    quick_sort(arr, lo, p - 1)
    quick_sort(arr, p + 1, hi)
arr = [3, 1, 4, 1, 5, 9, 2]
quick_sort(arr, 0, 6)
print(arr)

Expected output

[1, 1, 2, 3, 4, 5, 9]

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 Summary - Quick sort: match the terms

Term Meaning
Pivot Partition axis
Partition O(n)
Average O(n log n)
Worst case O(n^2)

2 Memory cost

Question 
Extra memory: O(____)
Answer 
Extra memory: O(log n)

Explanation: log n is right.

3 Is quick sort stable?

  • No Correct answer
  • Only on small arrays
  • Only with a good pivot
  • Yes, always

Explanation: No

All lessons in Intermediate

1 Merge sort

  1. Divide and conquer
  2. Merge operation
  3. Full merge sort
  4. Summary - Merge sort

2 Quick sort

  1. Pivot selection
  2. Partitioning
  3. Recursive quick sort
  4. Summary - Quick sort

3 Heap sort

  1. What is a heap?
  2. Heapify
  3. Build heap and sort
  4. Summary - Heap sort

4 Counting sort

  1. Counting idea
  2. Count array
  3. Output array
  4. Summary - Counting sort

5 Radix sort

  1. Radix idea
  2. Digit pass
  3. Stable sub-sort
  4. Summary - Radix sort

6 Sorting project

  1. Project: Overview
  2. Score array
  3. Apply merge sort
  4. Print statistics

7 Tree

  1. What is a tree?
  2. Node and edge
  3. Binary tree
  4. Summary - Trees

8 Binary search tree

  1. BST rule
  2. BST insert
  3. BST search
  4. Summary - BST

9 AVL tree

  1. Balanced tree
  2. Rotation
  3. Balance after insert
  4. Summary - AVL tree

10 Heap

  1. Min and max heap
  2. Insert
  3. Extract
  4. Summary - Heap

11 Priority queue

  1. What is a priority queue?
  2. Heap-based implementation
  3. Push and pop
  4. Summary - Priority queue

12 Data structures project

  1. Project: Overview
  2. Undo stack
  3. Pending queue
  4. Print the state

13 Graph basics

  1. What is a graph?
  2. Adjacency list
  3. Adjacency matrix
  4. Summary - Graph

14 Breadth-first search

  1. BFS idea
  2. Using a queue
  3. Marking visited
  4. Summary - BFS

15 Depth-first search

  1. DFS idea
  2. Stack or recursion
  3. Backtracking
  4. Summary - DFS

16 Greedy algorithms

  1. Greedy approach
  2. Coin change
  3. Greedy limits
  4. Summary - Greedy

17 Divide and conquer

  1. Three steps
  2. Recursive structure
  3. Master theorem
  4. Summary - Divide and conquer

18 Backtracking

  1. What is backtracking?
  2. State tree
  3. Pruning
  4. Summary - Backtracking

19 Graph project

  1. Project: Overview
  2. City graph
  3. BFS for reachability
  4. Print the result

20 Intermediate final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4