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Summary - Divide and conquer

Solve a problem by dividing it in a mini task.

Summary - Divide and conquer

Divide and conquer solves problems by dividing, conquering recursively and combining. Merge sort, quick sort and binary search use it.

In this mini task you will count using divide and conquer; combine all steps.

The approach also runs well on parallel hardware; subproblems are independent.

Practice Divide and count

Write dc_count(arr, target). Split in half, count target recursively in each half, add. Print 3 with print(dc_count([1, 2, 1, 3, 1], 1)).

Starter code

solution.py
def dc_count(arr, target):
    # Divide and count

Sample solution

solution.py
def dc_count(arr, target):
    # Divide and count
    if len(arr) == 0:
        return 0
    if len(arr) == 1:
        return 1 if arr[0] == target else 0
    mid = len(arr) // 2
    return dc_count(arr[:mid], target) + dc_count(arr[mid:], target)
print(dc_count([1, 2, 1, 3, 1], 1))

Expected output

3

Questions and answers

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

1 Summary - Divide and conquer: match the terms

Term Meaning
divide Split
conquer Solve
combine Merge
base case Stop

2 Find mid

Question 
mid = len(arr) ____ 2
Answer 
mid = len(arr) // 2

Explanation: // is right.

3 Where is divide and conquer used?

  • Linear search
  • Merge sort, quick sort Correct answer
  • Bubble sort
  • Heap only

Explanation: Merge sort, quick sort.

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