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Summary - Backtracking

Practice backtracking with a mini N-queens style task.

Summary - Backtracking

Backtracking searches with trial and error, a state tree and pruning. N-queens, permutations and subset sum are examples.

In this mini task you will solve the subset sum problem; combine all steps.

Backtracking systematically walks the solution space; it is a powerful tool for constrained problems.

Practice Subset sum

Write subset_sum(arr, target). Use backtracking to check if any subset sums to target. Print True with print(subset_sum([3, 34, 4, 12, 5, 2], 9)).

Starter code

solution.py
def subset_sum(arr, target):
    # Subset sum exists

Sample solution

solution.py
def subset_sum(arr, target):
    # Subset sum exists
    def backtrack(i, total):
        if total == target:
            return True
        if i >= len(arr) or total > target:
            return False
        if backtrack(i + 1, total + arr[i]):
            return True
        if backtrack(i + 1, total):
            return True
        return False
    return backtrack(0, 0)
print(subset_sum([3, 34, 4, 12, 5, 2], 9))

Expected output

True

Questions and answers

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

1 Summary - Backtracking: match the terms

Term Meaning
backtrack Return
prune Prune
try Try
undo Undo

2 Undo

Question 
path.____()
Answer 
path.pop()

Explanation: pop is right.

3 When does backtracking 'undo'?

  • Never
  • Every step
  • Only at the start
  • When deepening fails Correct answer

Explanation: When deepening fails.

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