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Three steps

Divide, conquer, combine.

Three steps

Divide and conquer has three steps: divide, conquer, combine.

The problem is split into subproblems, each solved recursively, then results are combined.

This approach is used in classic algorithms like merge sort, quick sort and binary search.

Example: merge sort

Merge sort follows these three steps: split the array in half, sort each half, merge the sorted halves.

This approach gives O(n log n) time; it scales well on large data.

Merge sort is a typical example of divide and conquer; the array splits in two at each level.

Practice Divide and sum

Write dc_sum(arr). Split the array in half, sum each recursively, then add. Print 10 with print(dc_sum([1, 2, 3, 4])).

Starter code

solution.py
def dc_sum(arr):
    # Divide and sum

Sample solution

solution.py
def dc_sum(arr):
    # Divide and sum
    if len(arr) <= 1:
        return sum(arr)
    mid = len(arr) // 2
    left = dc_sum(arr[:mid])
    right = dc_sum(arr[mid:])
    return left + right
print(dc_sum([1, 2, 3, 4]))

Expected output

10

Questions and answers

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

1 What is the order of divide and conquer steps?

  • Divide, conquer, combine Correct answer
  • Divide, combine, conquer
  • Conquer, divide, combine
  • Combine, divide, conquer

Explanation: Divide, conquer, combine.

2 Subproblem

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

Explanation: // is right.

3 Three steps: match the terms

Term Meaning
divide Split
conquer Solve
combine Merge
recursion Self-call

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