Graph Algorithms

Graph algorithms are a fundamental part of computer science and are widely used in various applications. A graph is a collection of nodes, also known as vertices, that are connected by edges. Graph algorithms are used to solve problems related to graphs, such as finding the shortest path between two nodes or finding a cycle in a graph.

Graph algorithms have numerous use cases in various domains. For example, in social networks, graph algorithms can be used to determine the shortest path between two users or find the most influential users. In transportation networks, graph algorithms can help find the shortest route between two locations or optimize vehicle routing.

One popular algorithm used with graphs is the Breadth-First Search (BFS) algorithm. The BFS algorithm explores all the vertices of a graph in breadth-first order, starting from a given vertex. It is often used to find the shortest path between two vertices in an unweighted graph.

Here's an example of the BFS algorithm implemented in C++:

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#include <iostream>

#include <vector>

#include <queue>

using namespace std;

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class Graph {

private:

  vector<vector<int>> adjacencyList;

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public:

  Graph(int vertices) {

    adjacencyList.resize(vertices);

  }

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  void addEdge(int u, int v) {

    adjacencyList[u].push_back(v);

    adjacencyList[v].push_back(u);

  }

​

  void BFS(int startVertex) {

    vector<bool> visited(adjacencyList.size(), false);

    queue<int> bfsQueue;

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    visited[startVertex] = true;

    bfsQueue.push(startVertex);

​

    cout << "BFS Traversal: ";

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    while (!bfsQueue.empty()) {