# Graph – Count all paths between source and destination

Objective: Given a graph, source vertex and destination vertex. Write an algorithm to count all possible paths between source and destination.

Condition: Graph does not contain any cycle.

This problem also known as “paths between two nodes”

Example:

Approach: Use Depth First Search

1. Use DFS but we cannot use visited [] to keep track of visited vertices since we need to explore all the paths. visited [] is used avoid going into cycles during iteration. (That is why we have a condition in this problem that graph does not contain cycle)
2. Start from the source vertex and make a recursive call to all it adjacent vertices.
3. During recursive call, if reach the destination vertex, increment the result (no of paths).
4. See the code for more understanding.

Code:

Output:

`No of paths between source: 0 and destination: 5 are: 3`

### 1 thought on “Graph – Count all paths between source and destination”

1. You can even do with cycles. Set visited[start] = false when returning

private static void countAllPaths(int start, int end, boolean[] visited) {

visited[start] = true;

for (int i = 0; i < adjacentList.size(); i++) {

if (destination != end && visited[destination] == false) {

countAllPaths(destination, end, visited);

} else if (destination == end) {

pathCount++;
}
}

//Remove to start again
visited[start] = false;
}