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DFS idea

Follow a branch to the end before backtracking.

DFS idea

Depth-first search (DFS) follows a branch to the end, then backtracks at dead ends.

So DFS is naturally implemented with recursion or a stack; depth first is the priority.

DFS is often used for cycle detection, topological sort and pathfinding; its complexity is O(V + E).

Backtracking

Returning from a dead end to try another branch is called backtracking. This is core to DFS.

The state of returning branches is preserved; the path completes and no branch is skipped.

Thanks to backtracking, DFS safely visits every vertex even on cyclic graphs.

Practice DFS order

Write dfs_order(graph, start). Run stack-based DFS and return the visit order. Print [0, 2, 3, 1] with print(dfs_order({0: [1, 2], 1: [0, 3], 2: [0, 3], 3: [1, 2]}, 0)).

Starter code

solution.py
def dfs_order(graph, start):
    # Stack-based DFS

Sample solution

solution.py
def dfs_order(graph, start):
    # Stack-based DFS
    visited = []
    stack = [start]
    while stack:
        node = stack.pop()
        if node not in visited:
            visited.append(node)
            for nb in reversed(graph[node]):
                if nb not in visited:
                    stack.append(nb)
    return visited
print(dfs_order({0: [1, 2], 1: [0, 3], 2: [0, 3], 3: [1, 2]}, 0))

Expected output

[0, 2, 3, 1]

Questions and answers

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

1 Which structure naturally implements DFS?

  • Stack or recursion Correct answer
  • Only a queue
  • Only a heap
  • Hash table

Explanation: Stack or recursion.

2 DFS start

Question 
stack = [____]
Answer 
stack = [start]

Explanation: start is right.

3 DFS idea: match the terms

Term Meaning
DFS Deep
stack LIFO
BFS Layer
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