Graph vs Tree Key Structural Difference in DSA C - Compare & Choose

Challenge - 5 Problems

🧠 Conceptual

intermediate

Key Structural Difference Between Graph and Tree

Which of the following statements correctly describes the key structural difference between a graph and a tree?

A A tree can have cycles, but a graph cannot have cycles.

B A tree is a connected graph with no cycles, while a graph can have cycles and may be disconnected.

C A graph always has a root node, but a tree does not have a root.

D A graph is always directed, while a tree is always undirected.

💡 Hint

Think about connectivity and cycles in both structures.

A tree is a special type of graph that is connected and has no cycles. Graphs can be disconnected and may contain cycles.

❓ Predict Output

intermediate

Output of Graph and Tree Edge Count

Consider a tree with 5 nodes and a graph with 5 nodes and 6 edges. What is the number of edges in the tree?

DSA C

int tree_nodes = 5;
int tree_edges = tree_nodes - 1;
printf("%d", tree_edges);

A 4

B 5

C 6

D 3

💡 Hint

Remember the property of edges in a tree.

A tree with n nodes always has n-1 edges.

❓ Predict Output

advanced

Detecting Cycle in Graph vs Tree

What will be the output of the following C code snippet that checks if a graph with edges has a cycle?

int edges[][2] = {{0,1}, {1,2}, {2,0}};
int n = 3;
int hasCycle = 0;
// Simplified check: if edges >= nodes, cycle likely
if (sizeof(edges)/sizeof(edges[0]) >= n) hasCycle = 1;
printf("%d", hasCycle);

A 1

B 0

C Compilation error

D Undefined behavior

💡 Hint

Think about the minimum edges needed to form a cycle.

If the number of edges is equal or more than the number of nodes, a cycle is possible in a graph.

🧠 Conceptual

advanced

Why Trees Cannot Have Cycles

Why is it impossible for a tree to have cycles?

A Because trees are disconnected graphs.

B Because trees always have directed edges that prevent cycles.

C Because trees are defined as connected graphs with exactly n-1 edges for n nodes, which prevents cycles.

D Because trees have multiple roots that block cycles.

💡 Hint

Consider the relationship between nodes and edges in a tree.

A tree with n nodes must have exactly n-1 edges to be connected without cycles. Adding any edge creates a cycle.

🚀 Application

expert

Identify Structure from Properties

You have a data structure with 7 nodes and 7 edges. It is connected and has no cycles. What is this structure?

A Cannot determine from given information

B Graph

C Tree

D Neither graph nor tree

💡 Hint

Recall the edge count property of trees.

A tree with 7 nodes must have exactly 6 edges. Since this structure has 7 edges, it cannot be a tree. It is a connected graph without cycles, which is contradictory, so it must be a graph with a cycle or error in data.