Dijkstra's Algorithm Single Source Shortest Path in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the distance to the source node as zero.

DSA C#

distances[source] = [1];

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

Aint.MaxValue

B-1

C0

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Setting the distance to int.MaxValue instead of zero.

Using a negative value for the source distance.

The distance from the source node to itself is always zero.

2fill in blank

medium

Complete the code to select the next node with the smallest tentative distance.

DSA C#

int u = [1];

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

Aunvisited.Last()

Bunvisited.Max()

Cunvisited.Min()

Dunvisited.OrderBy(node => distances[node]).FirstOrDefault()

Attempts:

3 left

💡 Hint

Common Mistakes

Selecting the maximum distance node instead of minimum.

Using Last() which does not guarantee smallest distance.

We pick the unvisited node with the smallest distance to explore next.

3fill in blank

hard

Fix the error in updating the distance if a shorter path is found.

DSA C#

if (distances[u] + graph[u][v] < distances[v])
{
    distances[v] = distances[u] [1] graph[u][v];
    previous[v] = u;
}

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

A+

B-

C/

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction instead of addition.

Multiplying distances which is incorrect for path sums.

We add the edge weight to the current distance to update the neighbor's distance.

4fill in blank

hard

Fill both blanks to correctly remove the visited node and check if all nodes are visited.

DSA C#

unvisited.[1](u);
while (unvisited.[2] > 0)

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

ARemove

BCount

CAdd

DLength

Attempts:

3 left

💡 Hint

Common Mistakes

Using Add instead of Remove to delete nodes.

Using Length which is not a property of collections like HashSet.

Remove the visited node from unvisited set and continue while unvisited nodes remain.

5fill in blank

hard

Fill all three blanks to correctly build the shortest path from source to target.

DSA C#

List<int> path = new List<int>();
int current = target;
while (current != [1])
{
    path.[2](current);
    current = previous[[3]];
}
path.[2](current);
path.Reverse();

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

Asource

BAdd

Ccurrent

DRemove

Attempts:

3 left

💡 Hint

Common Mistakes

Using Remove instead of Add to build the path.

Using target instead of current when accessing previous nodes.

We trace back from target to source using previous nodes, adding each to the path list, then reverse it.

Practice

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

easy

A. To find the minimum spanning tree of a graph

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

C. To detect cycles in a graph

D. To sort the vertices in topological order

Solution

1. Step 1: Understand the goal of Dijkstra's Algorithm

   Dijkstra's Algorithm is designed to find the shortest paths from one starting point (source) to all other points in a weighted graph.

2. Step 2: Compare with other graph algorithms

   Minimum spanning tree algorithms find a tree connecting all vertices with minimum total edge weight, cycle detection finds loops, and topological sort orders vertices in a DAG. These are different goals.

3. Final Answer:

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

4. Quick Check:

   Dijkstra's Algorithm = shortest path from source [OK]

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

Common Mistakes:

• Confusing shortest path with minimum spanning tree
• Thinking it detects cycles
• Mixing it with topological sorting

2. Which of the following C# code snippets correctly initializes the distance array for Dijkstra's Algorithm for a graph with 5 vertices?

easy

A. int[] dist = new int[5]; for(int i = 0; i < 5; i++) dist[i] = -1;

B. int[] dist = new int[5] {0, 0, 0, 0, 0};

C. int[] dist = new int[5]; dist.Fill(0);

D. int[] dist = new int[5]; for(int i = 0; i < 5; i++) dist[i] = int.MaxValue;

Solution

1. Step 1: Understand initialization for Dijkstra's distances

   Distances are set to a very large number (infinity) initially, except the source vertex which is set to 0 later.

2. Step 2: Check each option

   int[] dist = new int[5]; for(int i = 0; i < 5; i++) dist[i] = int.MaxValue; sets all distances to int.MaxValue, which is correct. int[] dist = new int[5] {0, 0, 0, 0, 0}; sets all to 0, which is wrong. int[] dist = new int[5]; dist.Fill(0); uses a non-existent Fill method. int[] dist = new int[5]; for(int i = 0; i < 5; i++) dist[i] = -1; sets distances to -1, which is invalid for distances.

3. Final Answer:

   int[] dist = new int[5]; for(int i = 0; i < 5; i++) dist[i] = int.MaxValue; -> Option D

4. Quick Check:

   Initialize distances to max value [OK]

Hint: Use int.MaxValue to represent infinity distances [OK]

Common Mistakes:

• Setting all distances to zero initially
• Using negative values for distances
• Using non-existent array methods

3. Consider the following C# code snippet implementing Dijkstra's Algorithm on a graph with 4 vertices (0 to 3). What is the shortest distance from vertex 0 to vertex 3?

int[,] graph = {
  {0, 1, 4, 0},
  {1, 0, 2, 6},
  {4, 2, 0, 3},
  {0, 6, 3, 0}
};

int V = 4;
int[] dist = new int[V];
bool[] sptSet = new bool[V];

for (int i = 0; i < V; i++) dist[i] = int.MaxValue;
dist[0] = 0;

for (int count = 0; count < V - 1; count++) {
  int u = -1;
  int minDist = int.MaxValue;
  for (int v = 0; v < V; v++) {
    if (!sptSet[v] && dist[v] < minDist) {
      minDist = dist[v];
      u = v;
    }
  }
  sptSet[u] = true;

  for (int v = 0; v < V; v++) {
    if (!sptSet[v] && graph[u, v] != 0 && dist[u] != int.MaxValue && dist[u] + graph[u, v] < dist[v]) {
      dist[v] = dist[u] + graph[u, v];
    }
  }
}

Console.WriteLine(dist[3]);

medium

A. 6

B. 7

C. 9

D. 10

Solution

1. Step 1: Trace the algorithm's distance updates

   Start dist = [0, ∞, ∞, ∞]. - Pick vertex 0: update dist[1] = 1, dist[2] = 4. - Pick vertex 1 (dist=1): update dist[2] = min(4, 1+2=3) = 3, dist[3] = 1+6=7. - Pick vertex 2 (dist=3): update dist[3] = min(7, 3+3=6) = 6. - Pick vertex 3 (dist=6): done.

2. Step 2: Final shortest distance to vertex 3

   After all updates, dist[3] = 6.

3. Final Answer:

   6 -> Option A

4. Quick Check:

   Shortest distance to vertex 3 = 6 [OK]

Hint: Update distances only if new path is shorter [OK]

Common Mistakes:

• Not updating distances when a shorter path is found
• Confusing vertex indices
• Ignoring zero-weight edges as no edge

4. The following C# code snippet for Dijkstra's Algorithm has a bug. What is the error?

int V = 3;
int[] dist = new int[V];
bool[] visited = new bool[V];

for (int i = 0; i < V; i++)
  dist[i] = int.MaxValue;
dist[0] = 0;

for (int count = 0; count < V; count++) {
  int u = 0;
  for (int v = 0; v < V; v++) {
    if (!visited[v] && dist[v] < dist[u])
      u = v;
  }
  visited[u] = true;
  // Update distances here (omitted)
}

medium

A. Variable u is initialized to 0 causing incorrect minimum selection

B. dist array is not initialized properly

C. visited array is not updated

D. Loop runs one time too many

Solution

1. Step 1: Analyze initialization of u in inner loop

   Variable u is set to 0 before checking for minimum dist among unvisited vertices. If dist[0] is int.MaxValue, comparison fails and minimum may not be found correctly.

2. Step 2: Correct approach for minimum selection

   u should be initialized to -1 or a sentinel, and updated only when a better candidate is found to avoid wrong minimum selection.

3. Final Answer:

   Variable u is initialized to 0 causing incorrect minimum selection -> Option A

4. Quick Check:

   Initialize u properly to find minimum dist [OK]

Hint: Initialize min index to -1 before searching minimum [OK]

Common Mistakes:

• Initializing min index to 0 without checking if visited
• Not updating visited array
• Incorrect loop count

5. You have a weighted graph with 5 vertices and edges:

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

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

hard

A. 7

B. 8

C. 6

D. 9

Solution

1. Step 1: Trace shortest paths from vertex 0

   Start dist = [0, ∞, ∞, ∞, ∞]. - From 0: dist[1] = 2, dist[2] = 4. - 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.

2. Step 2: Final shortest distance to vertex 4

   The shortest distance to vertex 4 is 6 via path 0->1->2->4.

3. Final Answer:

   6 -> Option C

4. Quick Check:

   Shortest path distance to 4 = 6 [OK]

Hint: Check all paths and pick minimum sum of edges [OK]

Common Mistakes:

• Ignoring shorter indirect paths
• Adding edge weights incorrectly
• Assuming direct edge is always shortest