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Algorithms Analysis & Design
  • Algorithm Analysis & Design
  • 🚢Searching and Sorting
    • Introduction-Search
    • Linear Search
    • Binary Search
    • Interpolation Search
    • Introduction-Sorting
    • Bubble Sort
    • Selection Sort
    • Counting Sort
  • 💸Greedy Method
    • Introduction
    • Activity Selection
    • Fractional Knapsack Problem
    • Graph Colouring
  • 🚠Backtracking
    • Introduction
    • Hamiltonian Path/Cycle Problem
    • N Queen Problem
    • Rat in a Maze
    • Knight's Tour Problem
  • ⚔️Divide and Conquer
    • Introduction
    • Strassen's Matrix multiplication
    • Karatsuba algorithm
    • Tower of Hanoi
    • Closest Pair
  • 💣Dynamic Programming
    • Introduction
    • Longest Common Subsequence
    • Floyd-Warshall Algorithm
    • 0-1 Knapsack problem
    • Dice Throw
  • 📈Graph
    • Introduction
    • DFS
    • Dictionary Game
    • BFS
    • Flood Fill Algorithm
    • Minesweeper Lite
  • 🔢Number Theory
    • Introduction
    • GCD
    • Factorial
    • IsPrime | School Method
    • IsPrime | Fermat's Little Theorem
    • IsPrime | Miller-Rabin Method
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  • BFS algorithm
  • BFS example
  • BFS pseudocode
  • BFS Algorithm Complexity

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BFS

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Last updated 3 years ago

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BFS algorithm

A standard BFS implementation puts each vertex of the graph into one of two categories:

  1. Visited

  2. Not Visited

The purpose of the algorithm is to mark each vertex as visited while avoiding cycles.

The algorithm works as follows:

  1. Start by putting any one of the graph's vertices at the back of a queue.

  2. Take the front item of the queue and add it to the visited list.

  3. Create a list of that vertex's adjacent nodes. Add the ones which aren't in the visited list to the back of the queue.

  4. Keep repeating steps 2 and 3 until the queue is empty.

The graph might have two different disconnected parts so to make sure that we cover every vertex, we can also run the BFS algorithm on every node

BFS example

Let's see how the Breadth First Search algorithm works with an example. We use an undirected graph with 5 vertices.

Undirected graph with 5 vertices

We start from vertex 0, the BFS algorithm starts by putting it in the Visited list and putting all its adjacent vertices in the stack.

Next, we visit the element at the front of queue i.e. 1 and go to its adjacent nodes. Since 0 has already been visited, we visit 2 instead.

Vertex 2 has an unvisited adjacent vertex in 4, so we add that to the back of the queue and visit 3, which is at the front of the queue.

Only 4 remains in the queue since the only adjacent node of 3 i.e. 0 is already visited. We visit it.

Since the queue is empty, we have completed the Breadth First Traversal of the graph.

BFS pseudocode

create a queue Q 
mark v as visited and put v into Q 
while Q is non-empty 
    remove the head u of Q 
    mark and enqueue all (unvisited) neighbours of u

BFS Algorithm Complexity

The time complexity of the BFS algorithm is represented in the form of O(V + E), where V is the number of nodes and E is the number of edges.

The space complexity of the algorithm is O(V).

Visit start vertex and add its adjacent vertices to queue

Visit the first neighbour of start node 0, which is 1

Visit 2 which was added to queue earlier to add its neighbours4 remains in the queue

Visit last remaining item in the stack to check if it has unvisited neighbors

📈
visit last remaining item in stack to check if it has unvisited neighbours
undirected graph with 5 vertices
visit the first neighbour of start node 0, which is 1
visit start vertex and add its adjacent vertices to queue
visit 2 which was added to queue earlier to add its neighbours
visit