# Transpose graph

Transpose of a directed graph G is another directed graph on the same set of vertices with all of the edges reversed compared to the orientation of the corresponding edges in G. That is, if G contains an edge (u, v) then the converse/transpose/reverse of G contains an edge (v, u) and vice versa.
Given a graph (represented as adjacency list), we need to find another graph which is the transpose of the given graph.

Example:

```Input : figure (i) is the input graph.
Output : figure (ii) is the transpose graph of the given graph.
```

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

We traverse the adjacency list and as we find a vertex v in the adjacency list of vertex u which indicates an edge from u to v in main graph, we just add an edge from v to u in the transpose graph i.e. add u in the adjacency list of vertex v of the new graph. Thus traversing lists of all vertices of main graph we can get the transpose graph. Thus the total time complexity of the algorithm is O(V+E) where V is number of vertices of graph and E is the number of edges of the graph.
Note : It is simple to get the transpose of a graph which is stored in adjacency matrix format, you just need to get the transpose of that matrix.

## C++

 `// CPP program to find transpose of a graph. ` `#include ` `using` `namespace` `std; ` ` `  `// function to add an edge from vertex source to vertex dest ` `void` `addEdge(vector<``int``> adj[], ``int` `src, ``int` `dest) ` `{ ` `    ``adj[src].push_back(dest);  ` `} ` ` `  `// function to print adjacency list of a graph ` `void` `displayGraph(vector<``int``> adj[], ``int` `v) ` `{ ` `    ``for` `(``int` `i = 0; i < v; i++) { ` `        ``cout << i << ``"--> "``; ` `        ``for` `(``int` `j = 0; j < adj[i].size(); j++) ` `            ``cout << adj[i][j] << ``"  "``; ` `        ``cout << ``"\n"``; ` `    ``} ` `} ` ` `  `// function to get Transpose of a graph taking adjacency ` `// list of given graph and that of Transpose graph ` `void` `transposeGraph(vector<``int``> adj[],  ` `                     ``vector<``int``> transpose[], ``int` `v) ` `{ ` `    ``// traverse the adjacency list of given graph and ` `    ``// for each edge (u, v) add an edge (v, u) in the ` `    ``// transpose graph's adjacency list ` `    ``for` `(``int` `i = 0; i < v; i++) ` `        ``for` `(``int` `j = 0; j < adj[i].size(); j++) ` `            ``addEdge(transpose, adj[i][j], i); ` `} ` ` `  `int` `main() ` `{ ` `    ``int` `v = 5; ` `    ``vector<``int``> adj[v]; ` `    ``addEdge(adj, 0, 1); ` `    ``addEdge(adj, 0, 4); ` `    ``addEdge(adj, 0, 3); ` `    ``addEdge(adj, 2, 0); ` `    ``addEdge(adj, 3, 2); ` `    ``addEdge(adj, 4, 1); ` `    ``addEdge(adj, 4, 3); ` ` `  `    ``// Finding transpose of graph represented ` `    ``// by adjacency list adj[] ` `    ``vector<``int``> transpose[v]; ` `    ``transposeGraph(adj, transpose, v); ` ` `  `    ``// displaying adjacency list of transpose  ` `    ``// graph i.e. b ` `    ``displayGraph(transpose, v); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find the transpose of a graph ` `import` `java.util.*; ` `import` `java.lang.*; ` `import` `java.io.*; ` ` `  `class` `Graph ` `{ ` `    ``// Total number of vertices ` `    ``private` `static` `int` `vertices = ``5``; ` `     `  `    ``// Find transpose of graph represented by adj ` `    ``private` `static` `ArrayList[] adj = ``new` `ArrayList[vertices]; ` `    `  `    ``// Store the transpose of graph represented by tr ` `    ``private` `static` `ArrayList[] tr = ``new` `ArrayList[vertices]; ` ` `  `    ``// Function to add an edge from source vertex u to  ` `    ``// destination vertex v, if choice is false the edge is added ` `    ``// to adj otherwise the edge is added to tr ` `    ``public` `static` `void` `addedge(``int` `u, ``int` `v, ``boolean` `choice) ` `    ``{ ` `        ``if``(!choice) ` `            ``adj[u].add(v); ` `        ``else` `            ``tr[u].add(v); ` `    ``} ` ` `  `    ``// Function to print the graph representation ` `    ``public` `static` `void` `printGraph() ` `    ``{ ` `        ``for``(``int` `i = ``0``; i < vertices; i++) ` `        ``{ ` `            ``System.out.print(i + ``"--> "``); ` `            ``for``(``int` `j = ``0``; j < tr[i].size(); j++) ` `                ``System.out.print(tr[i].get(j) + ``" "``); ` `            ``System.out.println(); ` `        ``} ` `    ``} ` ` `  `    ``// Function to print the transpose of  ` `    ``// the graph represented as adj and store it in tr ` `    ``public` `static` `void` `getTranspose() ` `    ``{ ` ` `  `        ``// Traverse the graph and for each edge u, v  ` `        ``// in graph add the edge v, u in transpose ` `        ``for``(``int` `i = ``0``; i < vertices; i++) ` `            ``for``(``int` `j = ``0``; j < adj[i].size(); j++) ` `                ``addedge(adj[i].get(j), i, ``true``); ` `    ``} ` ` `  `    ``public` `static` `void` `main (String[] args) ``throws` `java.lang.Exception ` `    ``{ ` `        ``for``(``int` `i = ``0``; i < vertices; i++) ` `        ``{ ` `            ``adj[i] = ``new` `ArrayList(); ` `            ``tr[i] = ``new` `ArrayList(); ` `        ``} ` `        ``addedge(``0``, ``1``, ``false``); ` `        ``addedge(``0``, ``4``, ``false``); ` `        ``addedge(``0``, ``3``, ``false``); ` `        ``addedge(``2``, ``0``, ``false``); ` `        ``addedge(``3``, ``2``, ``false``); ` `        ``addedge(``4``, ``1``, ``false``); ` `        ``addedge(``4``, ``3``, ``false``); ` `         `  `        ``// Finding transpose of the graph  ` `        ``getTranspose(); ` `         `  `        ``// Printing the graph representation ` `        ``printGraph(); ` `    ``} ` `} ` ` `  `// This code is contributed by code_freak `

## Python3

 `# Python3 program to find transpose of a graph.  ` ` `  `# function to add an edge from vertex  ` `# source to vertex dest  ` `def` `addEdge(adj, src, dest): ` `    ``adj[src].append(dest) ` ` `  `# function to pradjacency list  ` `# of a graph  ` `def` `displayGraph(adj, v): ` `    ``for` `i ``in` `range``(v): ` `        ``print``(i, ``"--> "``, end ``=` `"") ` `        ``for` `j ``in` `range``(``len``(adj[i])): ` `            ``print``(adj[i][j], end ``=` `" "``)  ` `        ``print``() ` ` `  `# function to get Transpose of a graph  ` `# taking adjacency list of given graph ` `# and that of Transpose graph  ` `def` `transposeGraph(adj, transpose, v): ` `     `  `    ``# traverse the adjacency list of given  ` `    ``# graph and for each edge (u, v) add  ` `    ``# an edge (v, u) in the transpose graph's ` `    ``# adjacency list ` `    ``for` `i ``in` `range``(v): ` `        ``for` `j ``in` `range``(``len``(adj[i])): ` `            ``addEdge(transpose, adj[i][j], i) ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` ` `  `    ``v ``=` `5` `    ``adj ``=` `[[] ``for` `i ``in` `range``(v)]  ` `    ``addEdge(adj, ``0``, ``1``)  ` `    ``addEdge(adj, ``0``, ``4``)  ` `    ``addEdge(adj, ``0``, ``3``)  ` `    ``addEdge(adj, ``2``, ``0``)  ` `    ``addEdge(adj, ``3``, ``2``)  ` `    ``addEdge(adj, ``4``, ``1``)  ` `    ``addEdge(adj, ``4``, ``3``)  ` ` `  `    ``# Finding transpose of graph represented  ` `    ``# by adjacency list adj[]  ` `    ``transpose ``=` `[[]``for` `i ``in` `range``(v)] ` `    ``transposeGraph(adj, transpose, v)  ` ` `  `    ``# displaying adjacency list of  ` `    ``# transpose graph i.e. b  ` `    ``displayGraph(transpose, v) ` ` `  `# This code is contributed by PranchalK `

Output:

```0--> 2
1--> 0  4
2--> 3
3--> 0  4
4--> 0
```

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