# Print the lexicographically smallest DFS of the graph starting from 1

Given a connected graph with N vertices and M edges. The task is to print the lexicographically smallest DFS traversal of the graph starting from 1. Note that the vertices are numbered from 1 to N.

Examples:

Input: N = 5, M = 5, edges[] = {{1, 4}, {3, 4}, {5, 4}, {3, 2}, {1, 5}}
Output: 1 4 3 2 5

Input: N = 5, M = 8, edges[] = {{1, 4}, {3, 4}, {5, 4}, {3, 2}, {1, 5}, {1, 2}, {1, 3}, {3, 5}}
Output: 1 2 3 4 5

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Instead of doing a normal DFS, first we have to sort the edges of each vertex, so that in each turn only the smallest edge is picked first. After sorting, just perform a normal DFS which will give the lexicographically smallest DFS traversal.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the lexicographically ` `// smallest traversal of a graph ` `#include ` `using` `namespace` `std; ` ` `  `// Utility function to add an ` `// edge to the graph ` `void` `insertEdges(``int` `u, ``int` `v, vector<``int``>* adj) ` `{ ` `    ``adj[u].push_back(v); ` `    ``adj[v].push_back(u); ` `} ` ` `  `// Function to perform DFS traversal ` `void` `dfs(vector<``int``>* adj, ``int` `src, ``int` `n, ` `         ``bool``* visited) ` `{ ` `    ``// Print current vertex ` `    ``cout << src << ``" "``; ` ` `  `    ``// Mark it as visited ` `    ``visited[src] = ``true``; ` ` `  `    ``// Iterate over all the edges connected ` `    ``// to this vertex ` `    ``for` `(``int` `i = 0; i < adj[src].size(); i++) { ` `        ``// If this vertex is not visited, ` `        ``/// call dfs from this node ` `        ``if` `(!visited[adj[src][i]]) ` `            ``dfs(adj, adj[src][i], n, visited); ` `    ``} ` `} ` ` `  `// Function to print the lexicographically ` `// smallest DFS ` `void` `printLexoSmall(vector<``int``>* adj, ``int` `n) ` `{ ` `    ``// A boolean array to keep track of ` `    ``// nodes visited ` `    ``bool` `visited[n + 1] = { 0 }; ` ` `  `    ``// Sort the edges of each vertex in ` `    ``// ascending order ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``sort(adj[i].begin(), adj[i].end()); ` ` `  `    ``// Call DFS ` `    ``for` `(``int` `i = 1; i < n; i++) { ` `        ``if` `(!visited[i]) ` `            ``dfs(adj, i, n, visited); ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 5, m = 5; ` `    ``vector<``int``> adj[n + 1]; ` ` `  `    ``insertEdges(1, 4, adj); ` `    ``insertEdges(3, 4, adj); ` `    ``insertEdges(5, 4, adj); ` `    ``insertEdges(3, 2, adj); ` `    ``insertEdges(1, 5, adj); ` `    ``insertEdges(1, 2, adj); ` `    ``insertEdges(3, 5, adj); ` `    ``insertEdges(1, 3, adj); ` ` `  `    ``printLexoSmall(adj, n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find the lexicographically ` `// smallest traversal of a graph ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `    ``static` `boolean` `visited[]; ` `    ``static` `Vector> adj = ``new` `Vector>(); ` `     `  `// Utility function to add an ` `// edge to the graph ` `static` `void` `insertEdges(``int` `u, ``int` `v) ` `{ ` `    ``adj.get(u).add(v); ` `    ``adj.get(v).add(u); ` `} ` ` `  `// Function to perform DFS traversal ` `static` `void` `dfs( ``int` `src, ``int` `n) ` `{ ` `    ``// Print current vertex ` `    ``System.out.print( src + ``" "``); ` ` `  `    ``// Mark it as visited ` `    ``visited[src] = ``true``; ` ` `  `    ``// Iterate over all the edges connected ` `    ``// to this vertex ` `    ``for` `(``int` `i = ``0``; i < adj.get(src).size(); i++) ` `    ``{ ` `        ``// If this vertex is not visited, ` `        ``/// call dfs from this node ` `        ``if` `(!visited[adj.get(src).get(i)]) ` `            ``dfs( adj.get(src).get(i), n); ` `    ``} ` `} ` ` `  `// Function to print the lexicographically ` `// smallest DFS ` `static` `void` `printLexoSmall( ``int` `n) ` `{ ` `    ``// A boolean array to keep track of ` `    ``// nodes visited ` `    ``visited= ``new` `boolean``[n + ``1``]; ` `     `  `    ``// Sort the edges of each vertex in ` `    ``// ascending order ` `    ``for` `(``int` `i = ``0``; i < n; i++) ` `        ``Collections.sort(adj.get(i)); ` ` `  `    ``// Call DFS ` `    ``for` `(``int` `i = ``1``; i < n; i++)  ` `    ``{ ` `        ``if` `(!visited[i]) ` `            ``dfs( i, n); ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``int` `n = ``5``, m = ``5``; ` `     `  `    ``for``(``int` `i = ``0``; i < n + ``1``; i++) ` `    ``adj.add(``new` `Vector()); ` `     `  `    ``insertEdges(``1``, ``4``); ` `    ``insertEdges(``3``, ``4``); ` `    ``insertEdges(``5``, ``4``); ` `    ``insertEdges(``3``, ``2``); ` `    ``insertEdges(``1``, ``5``); ` `    ``insertEdges(``1``, ``2``); ` `    ``insertEdges(``3``, ``5``); ` `    ``insertEdges(``1``, ``3``); ` ` `  `    ``printLexoSmall( n); ` `} ` `} ` ` `  `// This code is contributed by Arnab Kundu `

## Python3

 `# Python3 program to find the lexicographically  ` `# smallest traversal of a graph  ` ` `  `# Utility function to add an edge ` `# to the graph  ` `def` `insertEdges(u, v, adj):  ` ` `  `    ``adj[u].append(v)  ` `    ``adj[v].append(u)  ` ` `  `# Function to perform DFS traversal  ` `def` `dfs(adj, src, n, visited):  ` ` `  `    ``# Print current vertex  ` `    ``print``(src, end ``=` `" "``)  ` ` `  `    ``# Mark it as visited  ` `    ``visited[src] ``=` `True` ` `  `    ``# Iterate over all the edges  ` `    ``# connected to this vertex  ` `    ``for` `i ``in` `range``(``0``, ``len``(adj[src])):  ` `         `  `        ``# If this vertex is not visited,  ` `        ``# call dfs from this node  ` `        ``if` `not` `visited[adj[src][i]]:  ` `            ``dfs(adj, adj[src][i], n, visited)  ` ` `  `# Function to print the lexicographically  ` `# smallest DFS  ` `def` `printLexoSmall(adj, n): ` ` `  `    ``# A boolean array to keep track  ` `    ``# of nodes visited  ` `    ``visited ``=` `[``0``] ``*` `(n ``+` `1``)  ` ` `  `    ``# Sort the edges of each vertex   ` `    ``# in ascending order  ` `    ``for` `i ``in` `range``(``0``, n):  ` `        ``adj[i].sort()  ` ` `  `    ``# Call DFS  ` `    ``for` `i ``in` `range``(``1``, n):  ` `        ``if` `not` `visited[i]:  ` `            ``dfs(adj, i, n, visited)  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"``: ` ` `  `    ``n, m ``=` `5``, ``5` `    ``adj ``=` `[[] ``for` `i ``in` `range``(n ``+` `1``)]  ` ` `  `    ``insertEdges(``1``, ``4``, adj)  ` `    ``insertEdges(``3``, ``4``, adj)  ` `    ``insertEdges(``5``, ``4``, adj)  ` `    ``insertEdges(``3``, ``2``, adj)  ` `    ``insertEdges(``1``, ``5``, adj)  ` `    ``insertEdges(``1``, ``2``, adj)  ` `    ``insertEdges(``3``, ``5``, adj)  ` `    ``insertEdges(``1``, ``3``, adj)  ` ` `  `    ``printLexoSmall(adj, n)  ` ` `  `# This code is contributed by Rituraj Jain `

## C#

 `// C# program to find the lexicographically  ` `// smallest traversal of a graph  ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG ` `{ ` ` `  `    ``public` `static` `bool``[] visited; ` `    ``public` `static` `List> adj = ``new` `List>(); ` ` `  `// Utility function to add an  ` `// edge to the graph  ` `public` `static` `void` `insertEdges(``int` `u, ``int` `v) ` `{ ` `    ``adj[u].Add(v); ` `    ``adj[v].Add(u); ` `} ` ` `  `// Function to perform DFS traversal  ` `public` `static` `void` `dfs(``int` `src, ``int` `n) ` `{ ` `    ``// Print current vertex  ` `    ``Console.Write(src + ``" "``); ` ` `  `    ``// Mark it as visited  ` `    ``visited[src] = ``true``; ` ` `  `    ``// Iterate over all the edges connected  ` `    ``// to this vertex  ` `    ``for` `(``int` `i = 0; i < adj[src].Count; i++) ` `    ``{ ` `        ``// If this vertex is not visited,  ` `        ``/// call dfs from this node  ` `        ``if` `(!visited[adj[src][i]]) ` `        ``{ ` `            ``dfs(adj[src][i], n); ` `        ``} ` `    ``} ` `} ` ` `  `// Function to print the lexicographically  ` `// smallest DFS  ` `public` `static` `void` `printLexoSmall(``int` `n) ` `{ ` `    ``// A boolean array to keep track of  ` `    ``// nodes visited  ` `    ``visited = ``new` `bool``[n + 1]; ` ` `  `    ``// Sort the edges of each vertex in  ` `    ``// ascending order  ` `    ``for` `(``int` `i = 0; i < n; i++) ` `    ``{ ` `        ``adj[i].Sort(); ` `    ``} ` ` `  `    ``// Call DFS  ` `    ``for` `(``int` `i = 1; i < n; i++) ` `    ``{ ` `        ``if` `(!visited[i]) ` `        ``{ ` `            ``dfs(i, n); ` `        ``} ` `    ``} ` `} ` ` `  `// Driver code  ` `public` `static` `void` `Main(``string``[] args) ` `{ ` `    ``int` `n = 5, m = 5; ` ` `  `    ``for` `(``int` `i = 0; i < n + 1; i++) ` `    ``{ ` `        ``adj.Add(``new` `List<``int``>()); ` `    ``} ` ` `  `    ``insertEdges(1, 4); ` `    ``insertEdges(3, 4); ` `    ``insertEdges(5, 4); ` `    ``insertEdges(3, 2); ` `    ``insertEdges(1, 5); ` `    ``insertEdges(1, 2); ` `    ``insertEdges(3, 5); ` `    ``insertEdges(1, 3); ` ` `  `    ``printLexoSmall(n); ` `} ` `} ` ` `  `// This code is contributed by shrikanth13 `

Output:

```1 2 3 4 5
```

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