---
title: Depth First Search (DFS)
localeTitle: 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

![](https://upload.wikimedia.org/wikipedia/commons/7/7f/Depth-First-Search.gif)

### Implementation (C++14)

 ```c++
#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++ 
```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;
}
```


#### Mais Informações:

[Gráficos](https://github.com/freecodecamp/guides/computer-science/data-structures/graphs/index.md)

[Largura da Primeira Pesquisa (BFS)](https://github.com/freecodecamp/guides/tree/master/src/pages/algorithms/graph-algorithms/breadth-first-search/index.md)

[Primeira pesquisa de profundidade (DFS) - Wikipedia](https://en.wikipedia.org/wiki/Depth-first_search)