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Summary - Counting sort

Implement counting sort and print the result.

Summary - Counting sort

Counting sort: count + cumulative + place backward. Non-comparison, O(n + k), stable. k is the key range.

Fast on a small integer range; memory explodes on large ranges. Negative values need an offset.

Used as the sub-sorter in radix sort; this lets us sort larger numbers too.

Practice Summary: counting sort

Write counting_sort(arr). Print [1, 2, 2, 4, 5, 8] with print(counting_sort([5,1,4,2,8,2])).

Starter code

solution.py
def counting_sort(arr):
    # Counting sort

Sample solution

solution.py
def counting_sort(arr):
    # Counting sort
    if not arr:
        return []
    k = max(arr) + 1
    count = [0] * k
    for x in arr:
        count[x] += 1
    for i in range(1, k):
        count[i] += count[i - 1]
    output = [0] * len(arr)
    for i in range(len(arr) - 1, -1, -1):
        output[count[arr[i]] - 1] = arr[i]
        count[arr[i]] -= 1
    return output
print(counting_sort([5, 1, 4, 2, 8, 2]))

Expected output

[1, 2, 2, 4, 5, 8]

Questions and answers

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

1 Summary - Counting sort: match the terms

Term Meaning
Cost O(n+k)
Memory O(k)
Stable Yes
Range Must be narrow

2 Cumulative

Question 
count[i] ____count[i-1]
Answer 
count[i] +=count[i-1]

Explanation: += is right.

3 Does counting sort compare elements?

  • No Correct answer
  • Only on small arrays
  • Only on large arrays
  • 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