# Route Between Nodes

Given two nodes for a given directed graph, find if there is a route between them.

Let us take a graph for example. And let the two nodes be A and C.

First let us check if there is a direct path between A and C. If yes, the problem was simple. But if not, we will try to find if there is a third node through which we can go from A to C.

We can see that there isn’t any direct path from A to C, but there is a path from A to B and from B to C. Therefore, there is a route from A to C.

To find a route from A to C, we will have to traverse all the nodes starting from A and ending at C.

For graph traversal, we can use the Depth First Search Algorithm.

The **Depth First Search** Algorithm works in the following manner -

- Take a Stack, and push the source node into it.
- Find all the neighbors of the just pushed node and push them into the stack.
- Come to the next element of the stack and push all the neighbors of this node.
- Repeat the above steps until the end of the stack.
- If during the above process at some point in time we encounter the destination node, we finally get a route from source to destination.

The below-given code is in the C programming language.

#include<stdio.h> #include<stdbool.h> int top = -1; void push(int stk[100], int x){ top = top + 1; stk[top] = x; } bool presentInStack(int stk[100], int x){ int a; for(a = 0 ; a < top+1 ; a++){ if(stk[a] == x){ return true; } } return false; } void route(int arr[100][100], int x, int m, int n){ int a, i, stk[100]; push(stk,x); for(i = 0 ; i <= top ; i++){ x = stk[i]; for(a = 0 ; a < n ; a++){ if(arr[x-1][a] == 1){ if(a + 1 == m){ printf("Yes! There's a route.\n"); return; } if(presentInStack(stk, a+1) == false){ push(stk,a+1); } } } } printf("No! There isn't any route.\n"); } void main(){ int arr[100][100] = { {0,1,0,1}, {0,0,1,0}, {1,0,0,1}, {0,0,0,0} }; route(arr,1,3,4); }

### Srajan Gupta

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