Given a connected acyclic graph consisting of **V** vertices and **E** edges, a source vertex **src**, and a destination vertex **dest**, the task is to count the number of vertices between the given source and destination vertex in the graph.

**Examples**:

Input:V = 8, E = 7, src = 7, dest = 8, edges[][] ={{1 4}, {4, 5}, {4, 2}, {2, 6}, {6, 3}, {2, 7}, {3, 8}}Output:3Explanation:

The path between 7 and 8 is 7 -> 2 -> 6 -> 3 -> 8.

So, the number of nodes between 7 and 8 is 3.

Input:V = 8, E = 7, src = 5, dest = 2, edges[][] ={{1 4}, {4, 5}, {4, 2}, {2, 6}, {6, 3}, {2, 7}, {3, 8}}Output:3Explanation:

The path between 5 and 2 is 5 -> 4 -> 2.

So, the number of nodes between 5 and 2 is 1.

**Approach: **The problem can also be solved using the Disjoint Union method as stated in this article. Another approach to this problem is to solve using the Depth First Search method. Follow the steps below to solve this problem:

- Initialize a visited array
**vis[]**to mark which nodes are already visited. Mark all the nodes as 0, i.e., not visited. - Perform a DFS to find the number of nodes present in the path between
and**src****dest.** - The number of nodes between
and**src**is equal to the difference between the length of the path between them and 2, i.e.,**dest**).**(pathSrcToDest – 2** - Since the graph is acyclic and connected, there will always be a single path between
and**src****dest.**

Below is the implementation of the above algorithm.

## C++

`// C++ program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to return the count of nodes` `// in the path from source to destination` `int` `dfs(` `int` `src, ` `int` `dest, ` `int` `* vis,` ` ` `vector<` `int` `>* adj)` `{` ` ` `// Mark the node visited` ` ` `vis[src] = 1;` ` ` `// If dest is reached` ` ` `if` `(src == dest) {` ` ` `return` `1;` ` ` `}` ` ` `// Traverse all adjacent nodes` ` ` `for` `(` `int` `u : adj[src]) {` ` ` `// If not already visited` ` ` `if` `(!vis[u]) {` ` ` `int` `temp = dfs(u, dest, vis, adj);` ` ` `// If there is path, then` ` ` `// include the current node` ` ` `if` `(temp != 0) {` ` ` `return` `temp + 1;` ` ` `}` ` ` `}` ` ` `}` ` ` `// Return 0 if there is no path` ` ` `// between src and dest through` ` ` `// the current node` ` ` `return` `0;` `}` `// Function to return the` `// count of nodes between two` `// given vertices of the acyclic Graph` `int` `countNodes(` `int` `V, ` `int` `E, ` `int` `src, ` `int` `dest,` ` ` `int` `edges[][2])` `{` ` ` `// Initialize an adjacency list` ` ` `vector<` `int` `> adj[V + 1];` ` ` `// Populate the edges in the list` ` ` `for` `(` `int` `i = 0; i < E; i++) {` ` ` `adj[edges[i][0]].push_back(edges[i][1]);` ` ` `adj[edges[i][1]].push_back(edges[i][0]);` ` ` `}` ` ` `// Mark all the nodes as not visited` ` ` `int` `vis[V + 1] = { 0 };` ` ` `// Count nodes in the path from src to dest` ` ` `int` `count = dfs(src, dest, vis, adj);` ` ` `// Return the nodes between src and dest` ` ` `return` `count - 2;` `}` `// Driver Code` `int` `main()` `{` ` ` `// Given number of vertices and edges` ` ` `int` `V = 8, E = 7;` ` ` `// Given source and destination vertices` ` ` `int` `src = 5, dest = 2;` ` ` `// Given edges` ` ` `int` `edges[][2]` ` ` `= { { 1, 4 }, { 4, 5 },` ` ` `{ 4, 2 }, { 2, 6 },` ` ` `{ 6, 3 }, { 2, 7 },` ` ` `{ 3, 8 } };` ` ` `cout << countNodes(V, E, src, dest, edges);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.util.Vector;` `class` `GFG{` `// Function to return the count of nodes` `// in the path from source to destination` `static` `int` `dfs(` `int` `src, ` `int` `dest, ` `int` `[]vis,` ` ` `Vector<Integer> []adj)` `{` ` ` `// Mark the node visited` ` ` `vis[src] = ` `1` `;` ` ` `// If dest is reached` ` ` `if` `(src == dest)` ` ` `{` ` ` `return` `1` `;` ` ` `}` ` ` `// Traverse all adjacent nodes` ` ` `for` `(` `int` `u : adj[src])` ` ` `{` ` ` `// If not already visited` ` ` `if` `(vis[u] == ` `0` `)` ` ` `{` ` ` `int` `temp = dfs(u, dest,` ` ` `vis, adj);` ` ` `// If there is path, then` ` ` `// include the current node` ` ` `if` `(temp != ` `0` `)` ` ` `{` ` ` `return` `temp + ` `1` `;` ` ` `}` ` ` `}` ` ` `}` ` ` `// Return 0 if there is no path` ` ` `// between src and dest through` ` ` `// the current node` ` ` `return` `0` `;` `}` `// Function to return the` `// count of nodes between two` `// given vertices of the acyclic Graph` `static` `int` `countNodes(` `int` `V, ` `int` `E,` ` ` `int` `src, ` `int` `dest,` ` ` `int` `edges[][])` `{` ` ` `// Initialize an adjacency list` ` ` `Vector<Integer> []adj = ` `new` `Vector[V + ` `1` `];` ` ` `for` `(` `int` `i = ` `0` `; i < adj.length; i++)` ` ` `adj[i] = ` `new` `Vector<Integer>();` ` ` ` ` `// Populate the edges in the list` ` ` `for` `(` `int` `i = ` `0` `; i < E; i++)` ` ` `{` ` ` `adj[edges[i][` `0` `]].add(edges[i][` `1` `]);` ` ` `adj[edges[i][` `1` `]].add(edges[i][` `0` `]);` ` ` `}` ` ` `// Mark all the nodes as` ` ` `// not visited` ` ` `int` `vis[] = ` `new` `int` `[V + ` `1` `];` ` ` `// Count nodes in the path` ` ` `// from src to dest` ` ` `int` `count = dfs(src, dest,` ` ` `vis, adj);` ` ` `// Return the nodes` ` ` `// between src and dest` ` ` `return` `count - ` `2` `;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `// Given number of vertices and edges` ` ` `int` `V = ` `8` `, E = ` `7` `;` ` ` `// Given source and destination vertices` ` ` `int` `src = ` `5` `, dest = ` `2` `;` ` ` `// Given edges` ` ` `int` `edges[][] = {{` `1` `, ` `4` `}, {` `4` `, ` `5` `},` ` ` `{` `4` `, ` `2` `}, {` `2` `, ` `6` `},` ` ` `{` `6` `, ` `3` `}, {` `2` `, ` `7` `},` ` ` `{` `3` `, ` `8` `}};` ` ` `System.out.print(countNodes(V, E,` ` ` `src, dest,` ` ` `edges));` `}` `}` `// This code is contributed by shikhasingrajput` |

## Python3

`# Python3 program for the above approach` `# Function to return the count of nodes` `# in the path from source to destination` `def` `dfs(src, dest, vis, adj):` ` ` `# Mark the node visited` ` ` `vis[src] ` `=` `1` ` ` `# If dest is reached` ` ` `if` `(src ` `=` `=` `dest):` ` ` `return` `1` ` ` `# Traverse all adjacent nodes` ` ` `for` `u ` `in` `adj[src]:` ` ` `# If not already visited` ` ` `if` `not` `vis[u]:` ` ` `temp ` `=` `dfs(u, dest, vis, adj)` ` ` `# If there is path, then` ` ` `# include the current node` ` ` `if` `(temp !` `=` `0` `):` ` ` `return` `temp ` `+` `1` ` ` `# Return 0 if there is no path` ` ` `# between src and dest through` ` ` `# the current node` ` ` `return` `0` `# Function to return the` `# count of nodes between two` `# given vertices of the acyclic Graph` `def` `countNodes(V, E, src, dest, edges):` ` ` ` ` `# Initialize an adjacency list` ` ` `adj ` `=` `[[] ` `for` `i ` `in` `range` `(V ` `+` `1` `)]` ` ` `# Populate the edges in the list` ` ` `for` `i ` `in` `range` `(E):` ` ` `adj[edges[i][` `0` `]].append(edges[i][` `1` `])` ` ` `adj[edges[i][` `1` `]].append(edges[i][` `0` `])` ` ` `# Mark all the nodes as not visited` ` ` `vis ` `=` `[` `0` `] ` `*` `(V ` `+` `1` `)` ` ` `# Count nodes in the path from src to dest` ` ` `count ` `=` `dfs(src, dest, vis, adj)` ` ` `# Return the nodes between src and dest` ` ` `return` `count ` `-` `2` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `# Given number of vertices and edges` ` ` `V ` `=` `8` ` ` `E ` `=` `7` ` ` `# Given source and destination vertices` ` ` `src ` `=` `5` ` ` `dest ` `=` `2` ` ` `# Given edges` ` ` `edges ` `=` `[ [ ` `1` `, ` `4` `], [ ` `4` `, ` `5` `],` ` ` `[ ` `4` `, ` `2` `], [ ` `2` `, ` `6` `],` ` ` `[ ` `6` `, ` `3` `], [ ` `2` `, ` `7` `],` ` ` `[ ` `3` `, ` `8` `] ]` ` ` `print` `(countNodes(V, E, src, dest, edges))` `# This code is contributed by mohit kumar 29 ` |

## C#

`// C# program for` `// the above approach` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG{` `// Function to return the count of nodes` `// in the path from source to destination` `static` `int` `dfs(` `int` `src, ` `int` `dest,` ` ` `int` `[]vis, List<` `int` `> []adj)` `{` ` ` `// Mark the node visited` ` ` `vis[src] = 1;` ` ` `// If dest is reached` ` ` `if` `(src == dest)` ` ` `{` ` ` `return` `1;` ` ` `}` ` ` `// Traverse all adjacent nodes` ` ` `foreach` `(` `int` `u ` `in` `adj[src])` ` ` `{` ` ` `// If not already visited` ` ` `if` `(vis[u] == 0)` ` ` `{` ` ` `int` `temp = dfs(u, dest,` ` ` `vis, adj);` ` ` `// If there is path, then` ` ` `// include the current node` ` ` `if` `(temp != 0)` ` ` `{` ` ` `return` `temp + 1;` ` ` `}` ` ` `}` ` ` `}` ` ` `// Return 0 if there is no path` ` ` `// between src and dest through` ` ` `// the current node` ` ` `return` `0;` `}` `// Function to return the` `// count of nodes between two` `// given vertices of the acyclic Graph` `static` `int` `countNodes(` `int` `V, ` `int` `E,` ` ` `int` `src, ` `int` `dest,` ` ` `int` `[,]edges)` `{` ` ` `// Initialize an adjacency list` ` ` `List<` `int` `> []adj = ` `new` `List<` `int` `>[V + 1];` ` ` ` ` `for` `(` `int` `i = 0; i < adj.Length; i++)` ` ` `adj[i] = ` `new` `List<` `int` `>();` ` ` ` ` `// Populate the edges in the list` ` ` `for` `(` `int` `i = 0; i < E; i++)` ` ` `{` ` ` `adj[edges[i, 0]].Add(edges[i, 1]);` ` ` `adj[edges[i, 1]].Add(edges[i, 0]);` ` ` `}` ` ` `// Mark all the nodes as` ` ` `// not visited` ` ` `int` `[]vis = ` `new` `int` `[V + 1];` ` ` `// Count nodes in the path` ` ` `// from src to dest` ` ` `int` `count = dfs(src, dest,` ` ` `vis, adj);` ` ` `// Return the nodes` ` ` `// between src and dest` ` ` `return` `count - 2;` `}` `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` ` ` `// Given number of vertices and edges` ` ` `int` `V = 8, E = 7;` ` ` `// Given source and destination vertices` ` ` `int` `src = 5, dest = 2;` ` ` `// Given edges` ` ` `int` `[,]edges = {{1, 4}, {4, 5},` ` ` `{4, 2}, {2, 6},` ` ` `{6, 3}, {2, 7},` ` ` `{3, 8}};` ` ` `Console.Write(countNodes(V, E, src,` ` ` `dest, edges));` `}` `}` `// This code is contributed by 29AjayKumar` |

**Output:**

1

**Time Complexity: **O(V+E)**Auxiliary Space: **O(V)