Graph Terminology Vertices Edges Directed Undirected Weighted in DSA Typescript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of adjacency list for directed weighted graph

What is the printed adjacency list after running this TypeScript code for a directed weighted graph?

DSA Typescript

type Edge = { to: number; weight: number };
const graph: Map<number, Edge[]> = new Map();

function addEdge(from: number, to: number, weight: number) {
  if (!graph.has(from)) graph.set(from, []);
  graph.get(from)!.push({ to, weight });
}

addEdge(1, 2, 5);
addEdge(1, 3, 10);
addEdge(2, 3, 2);
addEdge(3, 1, 7);

for (const [node, edges] of graph.entries()) {
  console.log(`${node} -> ${edges.map(e => `${e.to}(${e.weight})`).join(', ')}`);
}

A 1 -> 2(5), 3(10)\n2 -> 3(2)\n3 -> 1(0)

B 1 -> 2(5), 3(10)\n2 -> 3(2)\n3 -> 1(7)

C 1 -> 2(5)\n2 -> 3(2), 1(7)\n3 -> 3(10)

D 1 -> 3(10)\n2 -> 1(5), 3(2)\n3 -> 1(7)

💡 Hint

Check how edges are added and printed for each node in the directed graph.

The code adds edges from one node to another with weights. It prints each node's edges exactly as added. Option B matches the exact output.

🧠 Conceptual

intermediate

Identify the type of graph from description

Which type of graph is described by: "Edges have no direction and each edge has a number representing cost or distance"?

A Directed Weighted Graph

B Directed Unweighted Graph

C Undirected Weighted Graph

D Undirected Unweighted Graph

💡 Hint

Edges without direction mean connections go both ways.

Edges without direction are undirected. Having a number for cost means weighted. So it is an undirected weighted graph.

🔧 Debug

advanced

Find the error in this undirected graph edge addition

What error will occur when running this TypeScript code to add edges in an undirected graph?

DSA Typescript

const graph: Map<number, number[]> = new Map();

function addEdge(u: number, v: number) {
  if (!graph.has(u)) graph.set(u, []);
  graph.get(u)!.push(v);
  graph.get(v)!.push(u);
}

addEdge(1, 2);
addEdge(2, 3);
console.log(graph);

A TypeError: Cannot read property 'push' of undefined

B No error, graph prints correctly

C ReferenceError: graph is not defined

D SyntaxError: Unexpected token

💡 Hint

Check if both nodes have arrays initialized before pushing.

When adding edge from v to u, graph.get(v) may be undefined if v was not initialized, causing a TypeError.

❓ Predict Output

advanced

Output of BFS traversal on undirected graph

What is the order of nodes printed by this BFS traversal on the undirected graph?

DSA Typescript

const graph: Map<number, number[]> = new Map();

function addEdge(u: number, v: number) {
  if (!graph.has(u)) graph.set(u, []);
  if (!graph.has(v)) graph.set(v, []);
  graph.get(u)!.push(v);
  graph.get(v)!.push(u);
}

addEdge(1, 2);
addEdge(1, 3);
addEdge(2, 4);
addEdge(3, 5);

function bfs(start: number) {
  const visited = new Set<number>();
  const queue: number[] = [];
  queue.push(start);
  visited.add(start);
  const order: number[] = [];

  while (queue.length > 0) {
    const node = queue.shift()!;
    order.push(node);
    for (const neighbor of graph.get(node)!) {
      if (!visited.has(neighbor)) {
        visited.add(neighbor);
        queue.push(neighbor);
      }
    }
  }
  return order;
}

console.log(bfs(1).join(' -> '));

A 1 -> 2 -> 3 -> 4 -> 5

B 1 -> 3 -> 2 -> 5 -> 4

C 1 -> 2 -> 4 -> 3 -> 5

D 1 -> 3 -> 5 -> 2 -> 4

💡 Hint

BFS visits neighbors level by level in the order they appear in adjacency list.

BFS starts at 1, visits neighbors 2 and 3 in order, then visits neighbors of 2 (4), then neighbors of 3 (5).

🧠 Conceptual

expert

Which graph type allows cycles and weighted edges but no direction?

Select the graph type that can have cycles, edges with weights, and edges without direction.

A Directed Acyclic Weighted Graph

B Undirected Unweighted Graph without cycles

C Directed Weighted Graph without cycles

D Undirected Weighted Graph

💡 Hint

Edges without direction and with weights allow cycles.

Undirected weighted graphs can have cycles and weighted edges without direction.