4.2 KiB
4.2 KiB
title, localeTitle
| title | localeTitle |
|---|---|
| Depth First Search (DFS) | Primeira pesquisa de profundidade (DFS) |
Primeira pesquisa de profundidade (DFS)
Profundidade A primeira pesquisa é um dos algoritmos gráficos mais simples. Ele percorre o gráfico verificando primeiro o nó atual e, em seguida, movendo-se para um de seus sucessores para repetir o processo. Se o nó atual não tiver um sucessor para verificar, retornamos ao predecessor e o processo continua (mudando para outro sucessor). Se a solução for encontrada, a pesquisa será interrompida.
Visualização
Implementation (C++14)
#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
using namespace std;
class Graph{
int v; // number of vertices
// pointer to a vector containing adjacency lists
vector < int > *adj;
public:
Graph(int v); // Constructor
// function to add an edge to graph
void add_edge(int v, int w);
// prints dfs traversal from a given source `s`
void dfs();
void dfs_util(int s, vector < bool> &visited);
};
Graph::Graph(int v){
this -> v = v;
adj = new vector < int >[v];
}
void Graph::add_edge(int u, int v){
adj[u].push_back(v); // add v to u’s list
adj[v].push_back(v); // add u to v's list (remove this statement if the graph is directed!)
}
void Graph::dfs(){
// visited vector - to keep track of nodes visited during DFS
vector < bool > visited(v, false); // marking all nodes/vertices as not visited
for(int i = 0; i < v; i++)
if(!visited[i])
dfs_util(i, visited);
}
// notice the usage of call-by-reference here!
void Graph::dfs_util(int s, vector < bool > &visited){
// mark the current node/vertex as visited
visited[s] = true;
// output it to the standard output (screen)
cout << s << " ";
// traverse its adjacency list and recursively call dfs_util for all of its neighbours!
// (only if the neighbour has not been visited yet!)
for(vector < int > :: iterator itr = adj[s].begin(); itr != adj[s].end(); itr++)
if(!visited[*itr])
dfs_util(*itr, visited);
}
int main()
{
// create a graph using the Graph class we defined above
Graph g(4);
g.add_edge(0, 1);
g.add_edge(0, 2);
g.add_edge(1, 2);
g.add_edge(2, 0);
g.add_edge(2, 3);
g.add_edge(3, 3);
cout << "Following is the Depth First Traversal of the provided graph"
<< "(starting from vertex 0): ";
g.dfs();
// output would be: 0 1 2 3
return 0;
}
Evaluation
Complexidade Espacial: O(n)
Complexidade Temporal no pior caso: O(n) A DFS é completa num numero finito de nós. Trabalhando melhor em arvores esparssas.
Implementation of DFS in C++
#include<iostream>
#include<vector>
#include<queue>
using namespace std;
struct Graph{
int v;
bool **adj;
public:
Graph(int vcount);
void addEdge(int u,int v);
void deleteEdge(int u,int v);
vector<int> DFS(int s);
void DFSUtil(int s,vector<int> &dfs,vector<bool> &visited);
};
Graph::Graph(int vcount){
this->v = vcount;
this->adj=new bool*[vcount];
for(int i=0;i<vcount;i++)
this->adj[i]=new bool[vcount];
for(int i=0;i<vcount;i++)
for(int j=0;j<vcount;j++)
adj[i][j]=false;
}
void Graph::addEdge(int u,int w){
this->adj[u][w]=true;
this->adj[w][u]=true;
}
void Graph::deleteEdge(int u,int w){
this->adj[u][w]=false;
this->adj[w][u]=false;
}
void Graph::DFSUtil(int s, vector<int> &dfs, vector<bool> &visited){
visited[s]=true;
dfs.push_back(s);
for(int i=0;i<this->v;i++){
if(this->adj[s][i]==true && visited[i]==false)
DFSUtil(i,dfs,visited);
}
}
vector<int> Graph::DFS(int s){
vector<bool> visited(this->v);
vector<int> dfs;
DFSUtil(s,dfs,visited);
return dfs;
}