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Determine whether an undirected graph is a tree using depth-first search. An undirected graph is a tree if and only if the graph contains no cycles. For example, this is a tree because it contains no cycles:

While this graph contains cycles and therefore is not a tree:

C program: Write a depth-first search through a graph to determine whether the graph contains cycle. A cycle is detected when depth-first search find a graph node that was already visited.

Input format: Program should take a single command line argument specifying the path to an input file. Test cases for this program are in the tests/ directory. In each test case, the first line records the number of nodes N in the graph. Then, the adjacency matrix is recorded in the subsequent N rows of the file.

Output format: Should print "yes" if the graph is a tree, "no" if the graph is not a tree.

Edit the given code below:

#include "../graphutils.h" // header for functions to load and free adjacencyList

// A program to determine whether an undirected graph is a tree

// A recursive function that returns true if no cycles found

bool isTreeDFS (

size_t graphNodeCount,

AdjacencyListNode* adjacencyList,

bool* visited,

graphNode_t parent,

graphNode_t current

) {

// First see if current node has already been visited, indicating a cycle found

/* ... */

// Current node was not already visited, so now mark it as visited

/* ... */

// Now iterate through each of the neighboring graph nodes

AdjacencyListNode* neighbor = adjacencyList[current].next;

while (neighbor) {

if (neighbor->graphNode!=parent) {

// If the neighbor nodes is not the parent node (the node from which we arrived at current), call DFS

/* ... */

}

neighbor = neighbor->next;

}

// All DFS searches from current node found no cycles, so graph is a tree from this node

return true;

}

int main ( int argc, char* argv[] ) {

// READ INPUT FILE TO CREATE GRAPH ADJACENCY LIST

AdjacencyListNode* adjacencyList = NULL;

/* ... */

// Array of boolean variables indicating whether graph node has been visited

bool* visited = calloc ( graphNodeCount, sizeof(bool) );

/* ... */

/* ... */

printf(isTree ? "yes" : "no");

return EXIT_SUCCESS;

}