125 lines
3.1 KiB
Markdown
125 lines
3.1 KiB
Markdown
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---
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title: Breadth First Search (BFS)
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localeTitle: 广度优先搜索(BFS)
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---
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## 广度优先搜索(BFS)
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广度优先搜索是最简单的图算法之一。它首先检查当前节点,然后通过将其后继添加到下一级别来扩展它,从而遍历图形。在移动到下一级别之前,对当前级别中的所有节点重复该过程。如果找到解决方案,搜索将停止。
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### 可视化
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![](https://upload.wikimedia.org/wikipedia/commons/4/46/Animated_BFS.gif)
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### 评估
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空间复杂度:O(n)
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更糟糕的案例时间复杂性:O(n)
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广度优先搜索在有限的节点集上完成,并且如果从一个节点移动到另一个节点的成本是恒定的则是最优的。
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### BFS实现的C ++代码
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```cpp
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// Program to print BFS traversal from a given
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// source vertex. BFS(int s) traverses vertices
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// reachable from s.
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#include<iostream>
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#include <list>
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using namespace std;
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// This class represents a directed graph using
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// adjacency list representation
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class Graph
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{
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int V; // No. of vertices
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// Pointer to an array containing adjacency
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// lists
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list<int> *adj;
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public:
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Graph(int V); // Constructor
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// function to add an edge to graph
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void addEdge(int v, int w);
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// prints BFS traversal from a given source s
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void BFS(int s);
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};
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Graph::Graph(int V)
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{
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this->V = V;
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adj = new list<int>[V];
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}
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void Graph::addEdge(int v, int w)
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{
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adj[v].push_back(w); // Add w to v's list.
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}
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void Graph::BFS(int s)
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{
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// Mark all the vertices as not visited
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bool *visited = new bool[V];
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for(int i = 0; i < V; i++)
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visited[i] = false;
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// Create a queue for BFS
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list<int> queue;
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// Mark the current node as visited and enqueue it
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visited[s] = true;
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queue.push_back(s);
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// 'i' will be used to get all adjacent
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// vertices of a vertex
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list<int>::iterator i;
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while(!queue.empty())
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{
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// Dequeue a vertex from queue and print it
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s = queue.front();
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cout << s << " ";
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queue.pop_front();
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// Get all adjacent vertices of the dequeued
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// vertex s. If a adjacent has not been visited,
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// then mark it visited and enqueue it
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for (i = adj[s].begin(); i != adj[s].end(); ++i)
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{
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if (!visited[*i])
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{
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visited[*i] = true;
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queue.push_back(*i);
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}
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}
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}
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}
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// Driver program to test methods of graph class
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int main()
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{
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// Create a graph given in the above diagram
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Graph g(4);
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g.addEdge(0, 1);
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g.addEdge(0, 2);
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g.addEdge(1, 2);
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g.addEdge(2, 0);
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g.addEdge(2, 3);
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g.addEdge(3, 3);
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cout << "Following is Breadth First Traversal "
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<< "(starting from vertex 2) \n";
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g.BFS(2);
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return 0;
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}
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```
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#### 更多信息:
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[图表](https://github.com/freecodecamp/guides/computer-science/data-structures/graphs/index.md)
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[深度优先搜索(DFS)](https://github.com/freecodecamp/guides/tree/master/src/pages/algorithms/graph-algorithms/depth-first-search/index.md)
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