Dijkstra's Algorithm Single Source Shortest Path in DSA Javascript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Dijkstra's Algorithm on a Simple Graph

What is the output distances object after running Dijkstra's algorithm from node 'A' on the given graph?

DSA Javascript

const graph = {
  A: { B: 4, C: 1 },
  B: { A: 4, C: 2, D: 5 },
  C: { A: 1, B: 2, D: 8, E: 10 },
  D: { B: 5, C: 8, E: 2, Z: 6 },
  E: { C: 10, D: 2, Z: 3 },
  Z: { D: 6, E: 3 }
};

function dijkstra(graph, start) {
  const distances = {};
  const visited = new Set();
  const nodes = Object.keys(graph);

  nodes.forEach(node => distances[node] = Infinity);
  distances[start] = 0;

  while (visited.size !== nodes.length) {
    let closestNode = null;
    let shortestDistance = Infinity;

    nodes.forEach(node => {
      if (!visited.has(node) && distances[node] < shortestDistance) {
        shortestDistance = distances[node];
        closestNode = node;
      }
    });

    if (closestNode === null) break;

    visited.add(closestNode);

    const neighbors = graph[closestNode];
    for (const neighbor in neighbors) {
      const newDist = distances[closestNode] + neighbors[neighbor];
      if (newDist < distances[neighbor]) {
        distances[neighbor] = newDist;
      }
    }
  }

  return distances;
}

const result = dijkstra(graph, 'A');
console.log(result);

A {"A":0,"B":3,"C":1,"D":8,"E":10,"Z":13}

B {"A":0,"B":4,"C":1,"D":7,"E":9,"Z":12}

C {"A":0,"B":3,"C":1,"D":7,"E":9,"Z":12}

D {"A":0,"B":4,"C":1,"D":8,"E":10,"Z":13}

💡 Hint

Trace the shortest paths step by step from node 'A' updating distances.

Starting from 'A', the shortest path to 'B' is through 'C' with distance 3 (A->C->B). Similarly, distances to other nodes are updated accordingly.

🧠 Conceptual

intermediate

Understanding Priority in Dijkstra's Algorithm

In Dijkstra's algorithm, which data structure is best suited to efficiently select the next node with the smallest tentative distance?

A Priority Queue (Min-Heap)

B Queue

C Stack

D Hash Table

💡 Hint

Think about how to always pick the node with the smallest distance quickly.

A priority queue (min-heap) allows efficient retrieval of the node with the smallest tentative distance, which is essential for Dijkstra's algorithm.

🔧 Debug

advanced

Identify the Bug in Dijkstra's Algorithm Implementation

What error will the following code produce when running Dijkstra's algorithm on a graph with disconnected nodes?

DSA Javascript

function dijkstra(graph, start) {
  const distances = {};
  const visited = new Set();
  const nodes = Object.keys(graph);

  nodes.forEach(node => distances[node] = Infinity);
  distances[start] = 0;

  while (visited.size !== nodes.length) {
    let closestNode = null;
    let shortestDistance = Infinity;

    nodes.forEach(node => {
      if (!visited.has(node) && distances[node] < shortestDistance) {
        shortestDistance = distances[node];
        closestNode = node;
      }
    });

    if (closestNode === null) break;

    visited.add(closestNode);

    const neighbors = graph[closestNode];
    for (const neighbor in neighbors) {
      const newDist = distances[closestNode] + neighbors[neighbor];
      if (newDist < distances[neighbor]) {
        distances[neighbor] = newDist;
      }
    }
  }

  return distances;
}

A Infinite loop because closestNode never becomes null

B No error, runs correctly

C SyntaxError due to missing semicolon

D TypeError: Cannot read property of undefined when accessing neighbors

💡 Hint

Consider what happens when closestNode is null.

If the graph has disconnected nodes, closestNode can become null, then accessing graph[closestNode] causes a TypeError.

🚀 Application

advanced

Applying Dijkstra's Algorithm to Find Shortest Path Distance

Given the graph below, what is the shortest distance from node 'X' to node 'Y' using Dijkstra's algorithm? Graph edges with weights: X -> A (2), X -> B (5), A -> B (1), A -> Y (7), B -> Y (2)

A 7

B 5

C 9

D 10

💡 Hint

Consider all paths from X to Y and sum their weights.

Shortest path is X->A->B->Y with distances 2 + 1 + 2 = 5.

❓ Predict Output

expert

Output of Dijkstra's Algorithm with Negative Edge Weight

What will be the output or error when running Dijkstra's algorithm on the following graph with a negative edge weight?

DSA Javascript

const graph = {
  A: { B: 1, C: 4 },
  B: { C: -3, D: 2 },
  C: { D: 3 },
  D: {}
};

function dijkstra(graph, start) {
  const distances = {};
  const visited = new Set();
  const nodes = Object.keys(graph);

  nodes.forEach(node => distances[node] = Infinity);
  distances[start] = 0;

  while (visited.size !== nodes.length) {
    let closestNode = null;
    let shortestDistance = Infinity;

    nodes.forEach(node => {
      if (!visited.has(node) && distances[node] < shortestDistance) {
        shortestDistance = distances[node];
        closestNode = node;
      }
    });

    if (closestNode === null) break;

    visited.add(closestNode);

    const neighbors = graph[closestNode];
    for (const neighbor in neighbors) {
      const newDist = distances[closestNode] + neighbors[neighbor];
      if (newDist < distances[neighbor]) {
        distances[neighbor] = newDist;
      }
    }
  }

  return distances;
}

const result = dijkstra(graph, 'A');
console.log(result);

A {"A":0,"B":1,"C":4,"D":7}

B {"A":0,"B":1,"C":-2,"D":0}

C {"A":0,"B":1,"C":-2,"D":1}

D Algorithm produces incorrect distances due to negative edge weight

💡 Hint

Dijkstra's algorithm does not work correctly with negative edge weights.

Dijkstra's algorithm assumes all edge weights are non-negative. Negative weights can cause incorrect shortest path calculations.

Practice

1. What is the main purpose of Dijkstra's Algorithm in graph theory?

easy

A. To sort vertices in topological order

B. To find the maximum flow in a network

C. To detect cycles in a graph

D. To find the shortest path from a single source to all other vertices

Solution

1. Step 1: Understand the algorithm's goal

   Dijkstra's Algorithm is designed to find the shortest paths from one starting point (source) to all other points in a graph with non-negative edge weights.

2. Step 2: Compare with other graph algorithms

   Other algorithms like max flow or cycle detection serve different purposes, so they do not match Dijkstra's goal.

3. Final Answer:

   To find the shortest path from a single source to all other vertices -> Option D

4. Quick Check:

   Shortest path from one source = To find the shortest path from a single source to all other vertices [OK]

Hint: Dijkstra finds shortest paths from one start point [OK]

Common Mistakes:

• Confusing Dijkstra with max flow algorithms
• Thinking it detects cycles
• Assuming it sorts vertices

2. Which of the following is the correct way to initialize the distance array in Dijkstra's Algorithm in JavaScript?

easy

A. const dist = new Array(n).fill(Infinity); dist[source] = 0;

B. const dist = Array(n).fill(0); dist[source] = Infinity;

C. const dist = new Array(n).fill(null); dist[source] = 0;

D. const dist = new Array(n).fill(-1); dist[source] = 0;

Solution

1. Step 1: Understand distance initialization

   Distances to all nodes except the source should start as Infinity to represent unknown paths, and the source distance is 0.

2. Step 2: Check each option

   const dist = new Array(n).fill(Infinity); dist[source] = 0; correctly sets all distances to Infinity and source to 0. Others either set wrong initial values or invert source distance.

3. Final Answer:

   const dist = new Array(n).fill(Infinity); dist[source] = 0; -> Option A

4. Quick Check:

   Distance array starts with Infinity except source = const dist = new Array(n).fill(Infinity); dist[source] = 0; [OK]

Hint: Start distances as Infinity, source as 0 [OK]

Common Mistakes:

• Setting source distance to Infinity
• Using 0 for all distances initially
• Using null or -1 incorrectly

3. Consider the following JavaScript code snippet implementing part of Dijkstra's Algorithm. What will be the output of the distance array after running this code?

const graph = {
  0: [{node:1, weight:4}, {node:2, weight:1}],
  1: [{node:3, weight:1}],
  2: [{node:1, weight:2}, {node:3, weight:5}],
  3: []
};
const dist = [0, Infinity, Infinity, Infinity];
const visited = new Set();

function dijkstra() {
  while (visited.size < 4) {
    let u = -1;
    let minDist = Infinity;
    for (let i = 0; i < 4; i++) {
      if (!visited.has(i) && dist[i] < minDist) {
        minDist = dist[i];
        u = i;
      }
    }
    visited.add(u);
    for (const neighbor of graph[u]) {
      if (dist[u] + neighbor.weight < dist[neighbor.node]) {
        dist[neighbor.node] = dist[u] + neighbor.weight;
      }
    }
  }
}
dijkstra();
console.log(dist);

medium

A. [0, 4, 1, 6]

B. [0, 3, 1, 4]

C. [0, 2, 1, 3]

D. [0, 5, 1, 7]

Solution

1. Step 1: Trace initial distances and first iteration

   Start dist = [0, Infinity, Infinity, Infinity]. Pick node 0 (dist=0). Update neighbors: node 1 = 4, node 2 = 1.

2. Step 2: Next iterations and updates

   Pick node 2 (dist=1). Update node 1: min(4, 1+2=3) = 3; node 3: min(Infinity, 1+5=6) = 6. Pick node 1 (dist=3). Update node 3: min(6, 3+1=4) = 4. Pick node 3 (dist=4). No neighbors.

3. Final Answer:

   [0, 3, 1, 4] -> Option B

4. Quick Check:

   Distances after updates = [0, 3, 1, 4] [OK]

Hint: Pick unvisited node with smallest dist, update neighbors [OK]

Common Mistakes:

• Not updating distances correctly
• Choosing wrong next node
• Ignoring neighbor updates

4. The following code snippet is intended to implement Dijkstra's Algorithm but contains a bug. What is the bug?

const dist = new Array(n).fill(Infinity);
dist[source] = 0;
const visited = new Set();

while (visited.size < n) {
  let u = -1;
  let minDist = Infinity;
  for (let i = 0; i < n; i++) {
    if (dist[i] < minDist) {
      minDist = dist[i];
      u = i;
    }
  }
  visited.add(u);
  for (const neighbor of graph[u]) {
    if (dist[u] + neighbor.weight < dist[neighbor.node]) {
      dist[neighbor.node] = dist[u] + neighbor.weight;
    }
  }
}

medium

A. The visited set is not updated inside the loop

B. The distance array is not initialized correctly

C. The code does not check if node i is already visited before selecting u

D. The neighbor weights are not added to dist[u]

Solution

1. Step 1: Analyze node selection loop

   The loop selects node u with smallest dist[i] but does not check if i is already visited, so it may pick visited nodes again.

2. Step 2: Understand impact of missing visited check

   Without skipping visited nodes, the algorithm can loop incorrectly or update distances wrongly, breaking correctness.

3. Final Answer:

   The code does not check if node i is already visited before selecting u -> Option C

4. Quick Check:

   Must skip visited nodes when picking u = The code does not check if node i is already visited before selecting u [OK]

Hint: Always skip visited nodes when choosing next node [OK]

Common Mistakes:

• Forgetting to check visited nodes in selection
• Incorrect distance initialization
• Not updating visited set

5. You have a weighted graph with 5 nodes (0 to 4). The edges are:

• 0 -> 1 (2)
• 0 -> 2 (4)
• 1 -> 2 (1)
• 1 -> 3 (7)
• 2 -> 4 (3)
• 3 -> 4 (1)

Using Dijkstra's Algorithm from source node 0, what is the shortest distance to node 4?

hard

A. 6

B. 7

C. 8

D. 5

Solution

1. Step 1: Trace shortest paths from node 0

   Start dist: 0=0, others=Infinity. From 0: dist[1]=2, dist[2]=4.

2. Step 2: Update distances via neighbors

   From 1: dist[2]=min(4,2+1=3)=3, dist[3]=2+7=9. From 2: dist[4]=3+3=6. From 3: dist[4]=min(6,9+1=10)=6.

3. Final Answer:

   6 -> Option A

4. Quick Check:

   Shortest distance to node 4 = 6 [OK]

Hint: Check all paths, pick minimum sum of weights [OK]

Common Mistakes:

• Ignoring shorter path through node 2
• Adding wrong edge weights
• Not updating distances properly