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

Challenge - 5 Problems

🧠 Conceptual

intermediate

Key Structural Difference Between Graph and Tree

Which statement best describes the key structural difference between a graph and a tree?

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

B A tree allows cycles, but a graph never allows cycles.

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

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

💡 Hint

Think about whether cycles and connectivity are allowed in each structure.

A tree is a special type of graph that is connected and has no cycles. Graphs are more general and can have cycles and disconnected parts.

❓ Predict Output

intermediate

Output of Graph vs Tree Edge Count Check

Consider the following JavaScript code that checks the number of edges in a graph and a tree. What will be the output?

DSA Javascript

const nodes = 5;
const edgesInTree = nodes - 1;
const edgesInGraph = 6;
console.log(edgesInTree === edgesInGraph);

A TypeError

B true

C undefined

D false

💡 Hint

Recall the number of edges in a tree with n nodes.

A tree with n nodes always has n-1 edges. Here, edgesInTree is 4 and edgesInGraph is 6, so the comparison is false.

🔧 Debug

advanced

Identify the Error in Tree Cycle Check Code

What error will the following JavaScript code produce when checking if a tree has cycles?

DSA Javascript

function hasCycle(graph) {
  const visited = new Set();
  function dfs(node, parent) {
    visited.add(node);
    for (const neighbor of graph[node]) {
      if (!visited.has(neighbor)) {
        if (dfs(neighbor, node)) return true;
      } else if (neighbor !== parent) {
        return true;
      }
    }
    return false;
  }
  return dfs(0, null);
}

const tree = {
  0: [1, 2],
  1: [0, 3],
  2: [0],
  3: [1]
};
console.log(hasCycle(tree));

A false

B StackOverflowError

C ReferenceError

D true

💡 Hint

Think about whether the given tree has any cycles.

The given graph is a tree with no cycles, so the function correctly returns false.

❓ Predict Output

advanced

Output of Adding Edge Creating Cycle in Graph

What will be the output after adding an edge that creates a cycle in the graph below?

DSA Javascript

const graph = {
  0: [1],
  1: [0, 2],
  2: [1]
};

// Add edge from 2 to 0
graph[2].push(0);
graph[0].push(2);

function hasCycle(graph) {
  const visited = new Set();
  function dfs(node, parent) {
    visited.add(node);
    for (const neighbor of graph[node]) {
      if (!visited.has(neighbor)) {
        if (dfs(neighbor, node)) return true;
      } else if (neighbor !== parent) {
        return true;
      }
    }
    return false;
  }
  return dfs(0, null);
}

console.log(hasCycle(graph));

A TypeError

B true

C false

D undefined

💡 Hint

Adding an edge that connects back to an earlier node creates a cycle.

After adding the edge between nodes 2 and 0, the graph contains a cycle, so the function returns true.

🧠 Conceptual

expert

Why Trees Are Always Connected but Graphs May Not Be

Why is it that trees are always connected structures but graphs may be disconnected?

A Because trees have exactly n-1 edges for n nodes ensuring connectivity, while graphs can have any number of edges including zero.

B Because graphs always have cycles that disconnect nodes, but trees never have cycles.

C Because trees allow multiple parents per node, ensuring connectivity, but graphs do not.

D Because graphs are always directed, which can cause disconnection, but trees are undirected.

💡 Hint

Think about the minimum number of edges needed to keep all nodes connected.

Trees have exactly n-1 edges for n nodes, which is the minimum needed to keep all nodes connected without cycles. Graphs can have any number of edges, so they may be disconnected.

Practice

1. Which of the following is a key structural difference between a graph and a tree?

easy

A. A tree has no cycles, but a graph can have cycles.

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

C. A tree can have multiple edges between the same nodes, but a graph cannot.

D. A graph must be connected, but a tree can be disconnected.

Solution

1. Step 1: Understand tree structure

   A tree is a special type of graph that is connected and has no cycles.

2. Step 2: Compare with graph properties

   Graphs can have cycles and may or may not be connected.

3. Final Answer:

   A tree has no cycles, but a graph can have cycles. -> Option A

4. Quick Check:

   No cycles in tree = key difference [OK]

Hint: Trees never loop back; graphs can have loops [OK]

Common Mistakes:

• Thinking graphs always have a root node
• Believing trees can have cycles
• Confusing connectivity rules between graphs and trees

2. Which syntax correctly represents a tree structure in JavaScript using adjacency lists?

easy

A. const tree = [ [1, 2], [2, 3], [3, 4] ];

B. const tree = { 1: 2, 2: 3, 3: 4 };

C. const tree = { 1: [2, 3], 2: [4], 3: [], 4: [] };

D. const tree = [1, 2, 3, 4];

Solution

1. Step 1: Identify adjacency list format

   An adjacency list uses an object with keys as nodes and values as arrays of connected nodes.

2. Step 2: Check each option

   const tree = { 1: [2, 3], 2: [4], 3: [], 4: [] }; matches adjacency list format for a tree; others do not represent adjacency lists properly.

3. Final Answer:

   const tree = { 1: [2, 3], 2: [4], 3: [], 4: [] }; -> Option C

4. Quick Check:

   Adjacency list uses object with arrays [OK]

Hint: Adjacency list = object keys with array values [OK]

Common Mistakes:

• Using arrays of pairs instead of adjacency lists
• Assigning single values instead of arrays for neighbors
• Confusing array of nodes with adjacency list

3. What will be the output of the following code snippet representing a graph with a cycle?

const graph = { 1: [2], 2: [3], 3: [1] };
function hasCycle(node, visited, stack) {
  if (!visited[node]) {
    visited[node] = true;
    stack[node] = true;
    for (const neighbor of graph[node]) {
      if (!visited[neighbor] && hasCycle(neighbor, visited, stack)) {
        return true;
      } else if (stack[neighbor]) {
        return true;
      }
    }
  }
  stack[node] = false;
  return false;
}
console.log(hasCycle(1, {}, {}));

medium

A. false

B. true

C. undefined

D. TypeError

Solution

1. Step 1: Understand the graph structure

   The graph has edges 1->2, 2->3, and 3->1, forming a cycle.

2. Step 2: Trace the hasCycle function

   Starting at node 1, the function detects the cycle when it revisits node 1 in the recursion stack.

3. Final Answer:

   true -> Option B

4. Quick Check:

   Cycle detected = true [OK]

Hint: Cycle detection returns true if node revisited in recursion [OK]

Common Mistakes:

• Assuming no cycle because of simple code
• Confusing visited and recursion stack usage
• Expecting false without tracing recursion

4. Find the error in the following code that tries to check if a tree has cycles:

const tree = { 1: [2], 2: [3], 3: [] };
function hasCycle(node, visited) {
  if (visited[node]) return true;
  visited[node] = true;
  for (const neighbor of tree[node]) {
    if (hasCycle(neighbor, visited)) return true;
  }
  return false;
}
console.log(hasCycle(1, {}));

medium

A. The function does not track recursion stack, so false positives occur.

B. The visited object is not initialized properly.

C. The tree object keys should be numbers, not strings.

D. The function should return false immediately after visiting a node.

Solution

1. Step 1: Analyze cycle detection logic

   The function uses only visited to detect cycles but misses recursion stack tracking.

2. Step 2: Explain why this causes errors

   Without recursion stack, revisiting a node from a different branch may cause false cycle detection.

3. Final Answer:

   The function does not track recursion stack, so false positives occur. -> Option A

4. Quick Check:

   Missing recursion stack causes wrong cycle detection [OK]

Hint: Track recursion stack to avoid false cycle detection [OK]

Common Mistakes:

• Ignoring recursion stack importance
• Assuming visited alone detects cycles correctly
• Confusing object key types

5. Given a graph represented as adjacency lists, how can you verify if it is a tree? Choose the best approach.

hard

A. Check if the graph has cycles and is disconnected.

B. Check if the graph has no cycles regardless of connectivity.

C. Check if the graph has a root node and all nodes have at most two children.

D. Check if the graph is connected and has exactly n-1 edges for n nodes.

Solution

1. Step 1: Recall tree properties

   A tree with n nodes must be connected and have exactly n-1 edges, with no cycles.

2. Step 2: Analyze options

   Check if the graph is connected and has exactly n-1 edges for n nodes. correctly combines connectivity and edge count to verify a tree. Others miss key conditions.

3. Final Answer:

   Check if the graph is connected and has exactly n-1 edges for n nodes. -> Option D

4. Quick Check:

   Connectivity + edges = tree check [OK]

Hint: Tree = connected + edges = nodes minus one [OK]

Common Mistakes:

• Ignoring connectivity requirement
• Only checking for cycles without edges count
• Assuming root or children count defines tree