Just as your car runs more smoothly and requires less energy to go faster and farther when the wheels are in perfect alignment, you perform better when your thoughts, feelings, emotions, goals, and values are in balance.

Depth-First Search is one of the fundamental algorithms in graph theory. It's a must to know!

Nowadays it's a piece of cake, but I did struggle a bit to get my head around this and other graph theory algorithms.

## Common ways to represent graphs in a computer

The most common representations for graphs are Adjacency matrix and Adjacency list.

` ````
#include <iostream>
#include <cstdlib>
using namespace std;
// The maximum number of nodes in the graph.
// If this number is not known beforhand, dynamic allocation is a better idea.
const int N = 10;
/*
* Perform a Depth-First Search.
* Nodes are identified by integers from 0 to n - 1.
*
* graph[u][v] is true if node u and v are connected, false otherwise.
*/
void dfs(int u, bool graph[][N], bool visited[], int n) {
// Mark node u to avoid entering in an infinite loop.
visited[u] = true;
// Do something with u, e.g., print it out.
cout << u << " ";
// Visit each adjacent node of u.
for (int v = 0; v < n; v++) {
if (graph[u][v] && !visited[v]) {
dfs(v, graph, visited, n);
}
}
// This step is optional, unmark u if you want to travel all the possible
// tours, otherwise leave it marked.
//visited[u] = false;
}
int main() {
bool graph[N][N];
bool visited[N];
// A common way to express graphs is by specifiying the number for nodes n,
// and the number of edges m.
int n, m;
cin >> n >> m;
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
graph[i][j] = false;
}
}
for (int i = 0; i < m; i++) {
int u, v;
cin >> u >> v;
// An undirected graph.
graph[u][v] = true;
graph[v][u] = true;
}
for (int i = 0; i < n; i++) {
visited[i] = false;
}
for (int u = 0; u < n; u++) {
if (!visited[u]) {
dfs(u, graph, visited, n);
}
}
return 0;
}
```

` ````
5 4
0 1
0 2
2 3
2 4
```

` ````
0 1 2 3 4
```

` ````
#include <iostream>
#include <cstdlib>
#include <vector>
using namespace std;
// The maximum number of nodes in the graph.
// If this number is not known beforhand, dynamic allocation is a better idea.
const int N = 10;
/*
* Perform a Depth-First Search.
* Nodes are identified by integers from 0 to n - 1.
*
* graph[u] contains v if node v is a neighbor of u.
*/
void dfs(int u, vector<int> graph[], bool visited[]) {
// Mark node u to avoid entering in an infinite loop.
visited[u] = true;
// Do something with u, e.g., print it out.
cout << u << " ";
// Visit each adjacent node of u.
for (int v : graph[u]) {
if (!visited[v]) {
dfs(v, graph, visited);
}
}
// This step is optional, unmark u if you want to travel all the possible
// tours, otherwise leave it marked.
//visited[u] = false;
}
int main() {
vector<int> graph[N];
bool visited[N];
// A common way to express graphs is by specifiying the number for nodes n,
// and the number of edges m.
int n, m;
cin >> n >> m;
for (int i = 0; i < m; i++) {
int u, v;
cin >> u >> v;
// An undirected graph.
graph[u].push_back(v);
graph[v].push_back(u);
}
for (int i = 0; i < n; i++) {
visited[i] = false;
}
for (int u = 0; u < n; u++) {
if (!visited[u]) {
dfs(u, graph, visited);
}
}
return 0;
}
```