Why Shortest Path Is a Graph Problem Not a Tree Problem in DSA Typescript - Test Your Knowledge

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize an adjacency list for a graph with 3 nodes.

DSA Typescript

const graph: number[][] = [[], [], []];
graph[0].push([1]);

Drag options to blanks, or click blank then click option'

A2

B1

C0

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Using node numbers outside the graph range.

Confusing node indices with edge weights.

We add node 1 as a neighbor to node 0 to represent an edge from 0 to 1.

2fill in blank

medium

Complete the code to check if a node has been visited in a graph traversal.

DSA Typescript

const visited: boolean[] = [false, false, false];
if (!visited[[1]]) {
  visited[1] = true;
}

Drag options to blanks, or click blank then click option'

A1

B0

C2

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Using an index outside the visited array.

Checking the wrong node index.

We check if node 1 is visited before marking it true.

3fill in blank

hard

Fix the error in the code that tries to find the shortest path in a graph using BFS.

DSA Typescript

const queue: number[] = [];
queue.push(0);
while (queue.length > 0) {
  const node = queue.shift()[1];
  // process node
}

Drag options to blanks, or click blank then click option'

A();

B[0]

C()

D;

Attempts:

3 left

💡 Hint

Common Mistakes

Forgetting parentheses after shift.

Using incorrect syntax for method calls.

shift() is a function and must be called with parentheses to remove the first element.

4fill in blank

hard

Fill both blanks to update distances and enqueue neighbors during BFS shortest path search.

DSA Typescript

for (const neighbor of graph[node]) {
  if (distances[neighbor] === [1]) {
    distances[neighbor] = distances[node] [2] 1;
    queue.push(neighbor);
  }
}

Drag options to blanks, or click blank then click option'

A-1

B+

C0

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0 instead of -1 for unvisited check.

Subtracting 1 instead of adding 1 to distance.

Distances start at -1 meaning unvisited. We add 1 to the current node's distance to update neighbor's distance.

5fill in blank

hard

Fill all three blanks to create a function that returns the shortest path length from start to end in a graph.

DSA Typescript

function shortestPath(graph: number[][], start: number, end: number): number {
  const distances = Array(graph.length).fill([1]);
  const queue: number[] = [];
  distances[start] = 0;
  queue.push(start);
  while (queue.length > 0) {
    const node = queue.shift()[2];
    if (node === end) return distances[node];
    for (const neighbor of graph[node]) {
      if (distances[neighbor] === [3]) {
        distances[neighbor] = distances[node] + 1;
        queue.push(neighbor);
      }
    }
  }
  return -1;
}

Drag options to blanks, or click blank then click option'

A-1

B()

C0

D;

Attempts:

3 left

💡 Hint

Common Mistakes

Not initializing distances with -1.

Forgetting parentheses on shift.

Checking for 0 instead of -1 for unvisited.

Initialize distances with -1 for unvisited nodes, call shift() with parentheses, and check for -1 to find unvisited neighbors.

Practice

1. Why is finding the shortest path usually considered a graph problem rather than a tree problem?

easy

A. Because shortest path algorithms only work on trees.

B. Because trees do not have nodes or edges.

C. Because trees always have negative edge weights.

D. Because graphs can have cycles and multiple paths between nodes, unlike trees.

Solution

1. Step 1: Understand the structure of trees and graphs

   Trees are a special type of graph with no cycles and exactly one path between any two nodes.

2. Step 2: Analyze shortest path requirements

   Shortest path problems require handling multiple paths and cycles, which only general graphs can have.

3. Final Answer:

   Because graphs can have cycles and multiple paths between nodes, unlike trees. -> Option D

4. Quick Check:

   Graphs allow multiple paths [OK]

Hint: Shortest path needs multiple paths; trees have only one [OK]

Common Mistakes:

• Thinking trees have cycles
• Assuming shortest path only applies to trees
• Confusing nodes and edges in trees

2. Which of the following TypeScript code snippets correctly declares a graph adjacency list for shortest path calculation?

easy

A. const graph: Map = new Map();

B. const graph: number[][] = []; graph[0] = 1;

C. const graph: string = 'adjacency list';

D. const graph: number = 0;

Solution

1. Step 1: Identify correct graph adjacency list type

   An adjacency list for a graph is best represented as a Map from node to array of connected nodes.

2. Step 2: Check code correctness

   const graph: Map = new Map(); uses Map which is correct. const graph: number[][] = []; graph[0] = 1; assigns a number to an array index incorrectly. Options C and D use wrong types.

3. Final Answer:

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

4. Quick Check:

   Map with arrays [OK]

Hint: Use Map for adjacency lists [OK]

Common Mistakes:

• Using wrong data types for graph
• Assigning values directly to array index without initialization
• Confusing string or number types for graph

3. Given the following graph represented as adjacency list, what is the shortest path distance from node 0 to node 3?

const graph = new Map([
  [0, [1, 2]],
  [1, [2, 3]],
  [2, [3]],
  [3, []]
]);

// Assume each edge has weight 1
// Use BFS to find shortest path distance

medium

A. 1

B. 2

C. 3

D. 4

Solution

1. Step 1: Trace BFS from node 0 to node 3

   From 0, neighbors are 1 and 2 (distance 1). From 1, neighbors include 3 (distance 2). From 2, neighbor is 3 (distance 2).

2. Step 2: Determine shortest distance

   Shortest path is 0 -> 1 -> 3 or 0 -> 2 -> 3, both length 2.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   Shortest path length = 2 [OK]

Hint: BFS finds shortest path in unweighted graph [OK]

Common Mistakes:

• Counting edges incorrectly
• Confusing path length with number of nodes
• Ignoring multiple paths

4. Identify the bug in this TypeScript code snippet for shortest path in a graph and select the fix:

function shortestPath(graph: Map, start: number, end: number): number {
  const queue: number[] = [start];
  const distances: Map = new Map();
  distances.set(start, 0);

  while (queue.length > 0) {
    const node = queue.shift();
    for (const neighbor of graph.get(node)!) {
      if (!distances.has(neighbor)) {
        distances.set(neighbor, distances.get(node)! + 1);
        queue.push(neighbor);
      }
    }
  }
  return distances.get(end)!;
}

medium

A. Change queue.shift() to queue.pop() to get correct order.

B. Remove the exclamation marks (!) to avoid errors.

C. Add check if node is undefined after shift before using it.

D. Initialize distances with Infinity for all nodes before starting.

Solution

1. Step 1: Analyze queue.shift() usage

   queue.shift() can return undefined if queue is empty, but loop condition prevents that. However, TypeScript needs explicit check for undefined.

2. Step 2: Fix by checking node is not undefined

   Adding a check after shift ensures safe usage of node in graph.get(node).

3. Final Answer:

   Add check if node is undefined after shift before using it. -> Option C

4. Quick Check:

   Check for undefined after shift [OK]

Hint: Always check shift() result before use in TypeScript [OK]

Common Mistakes:

• Using pop() breaks BFS order
• Ignoring possible undefined from shift()
• Misunderstanding exclamation mark usage

5. You want to find the shortest path in a network where some edges have negative weights but no negative cycles. Why is this a graph problem and which algorithm suits best?

hard

A. Because graphs can have cycles and negative edges; use Bellman-Ford algorithm.

B. Because trees cannot have negative weights; use Dijkstra's algorithm.

C. Because trees always have positive weights; use BFS.

D. Because graphs with negative edges are invalid; no algorithm applies.

Solution

1. Step 1: Understand edge weights and graph structure

   Negative edge weights and cycles can only appear in graphs, not trees.

2. Step 2: Choose suitable algorithm

   Dijkstra's algorithm fails with negative edges; Bellman-Ford handles negative weights and detects negative cycles.

3. Final Answer:

   Because graphs can have cycles and negative edges; use Bellman-Ford algorithm. -> Option A

4. Quick Check:

   Negative edges + cycles = Bellman-Ford [OK]

Hint: Negative edges? Use Bellman-Ford on graphs [OK]

Common Mistakes:

• Using Dijkstra with negative edges
• Thinking trees can have negative edges
• Assuming no algorithm works with negative edges