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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the graph adjacency list.

DSA C

int graph[[1]][[1]] = {0};

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

A10

B5

C50

D100

Attempts:

3 left

💡 Hint

Common Mistakes

Using a size too small for the graph nodes.

Confusing the size with the number of edges.

The graph is initialized as a 10x10 adjacency matrix to represent up to 10 nodes.

2fill in blank

medium

Complete the code to update the distance array for shortest path calculation.

DSA C

dist[i] = [1];

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

A0

B1

C-1

DINT_MAX

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing distances to 0, which is incorrect.

Using negative values which don't make sense for distances.

Distances are initialized to INT_MAX to represent infinity before starting the shortest path algorithm.

3fill in blank

hard

Fix the error in the loop condition to correctly iterate over graph nodes.

DSA C

for (int i = 0; i [1] n; i++) {

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

A<

B>

C>=

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using <= instead of < causing index errors.

Using > or >= which never enter the loop.

The loop should run while i is less than n to avoid out-of-bounds errors.

4fill in blank

hard

Fill both blanks to correctly check and update the shortest path distance.

DSA C

if (graph[u][v] != 0 && dist[u] != INT_MAX && dist[u] [1] dist[v] - graph[u][v]) {
    dist[v] = dist[u] [2] graph[u][v];
}

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

A<

B+

C>

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using > instead of < in the condition.

Subtracting edge weight instead of adding.

The condition checks if the new path is shorter (dist[u] + graph[u][v] < dist[v]) and updates dist[v] accordingly.

5fill in blank

hard

Fill all three blanks to correctly implement the relaxation step in Dijkstra's algorithm.

DSA C

for (int v = 0; v [1] n; v++) {
    if (!visited[v] && graph[u][v] != 0 && dist[u] [2] graph[u][v] [3] dist[v]) {
        dist[v] = dist[u] + graph[u][v];
    }
}

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

A<=

B<

C+

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using <= instead of < in loop condition.

Using wrong comparison operators in if condition.

The loop iterates while v < n. The condition checks if dist[u] + graph[u][v] < dist[v] to update dist[v].

Practice

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

easy

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

B. Because trees always have weighted edges

C. Because shortest path algorithms only work on trees

D. Because trees do not have nodes

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 A

4. Quick Check:

   Graphs allow multiple paths, trees do not [OK]

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

Common Mistakes:

• Thinking trees can have cycles
• Assuming shortest path only applies to trees
• Confusing nodes with edges

2. Which of the following is the correct way to represent a graph for shortest path algorithms in C?

easy

A. Using an adjacency list with arrays of linked lists

B. Using a single integer variable

C. Using a string to store nodes

D. Using a stack only

Solution

1. Step 1: Identify common graph representations

   Graphs are commonly represented using adjacency lists or adjacency matrices for efficient traversal.

2. Step 2: Match representation to shortest path needs

   Adjacency lists with arrays of linked lists efficiently store neighbors for each node, suitable for shortest path algorithms.

3. Final Answer:

   Using an adjacency list with arrays of linked lists -> Option A

4. Quick Check:

   Adjacency list is standard graph representation [OK]

Hint: Use adjacency lists for graph representation in C [OK]

Common Mistakes:

• Using a single variable to represent graph
• Using strings instead of data structures
• Confusing stack with graph storage

3. Consider the following C code snippet for a graph with 3 nodes and edges:

int graph[3][3] = {
  {0, 1, 4},
  {1, 0, 2},
  {4, 2, 0}
};
// Find shortest path from node 0 to 2 using Dijkstra's algorithm
// What is the shortest distance?

medium

A. 6

B. 4

C. 5

D. 3

Solution

1. Step 1: Understand the graph matrix

   The matrix shows distances: 0->1=1, 0->2=4, 1->2=2.

2. Step 2: Calculate shortest path from 0 to 2

   Path 0->1->2 distance = 1 + 2 = 3, which is less than direct 0->2 distance 4.

3. Final Answer:

   3 -> Option D

4. Quick Check:

   0->1->2 = 3 is shortest [OK]

Hint: Check all paths, sum edges, pick smallest [OK]

Common Mistakes:

• Choosing direct edge without checking alternatives
• Adding edges incorrectly
• Ignoring intermediate nodes

4. The following code attempts to find the shortest path in a graph but has a bug:

int dist[5];
for(int i=0; i<=5; i++) {
  dist[i] = INT_MAX;
}

What is the bug?

medium

A. dist array is not initialized to zero

B. Loop goes out of array bounds causing undefined behavior

C. INT_MAX is not defined in C

D. Loop should start from 1 instead of 0

Solution

1. Step 1: Analyze the loop range and array size

   Array dist has size 5, valid indices are 0 to 4, but loop runs i=0 to 5 inclusive.

2. Step 2: Identify consequences of out-of-bounds access

   Accessing dist[5] is outside array bounds, causing undefined behavior or crash.

3. Final Answer:

   Loop goes out of array bounds causing undefined behavior -> Option B

4. Quick Check:

   Array index must be less than size [OK]

Hint: Loop index must be less than array size [OK]

Common Mistakes:

• Ignoring array bounds
• Confusing INT_MAX availability
• Changing loop start unnecessarily

5. You have a weighted graph with cycles and multiple paths between nodes. Why can't you use a tree-based shortest path approach here?

hard

A. Because trees are slower than graphs for shortest path

B. Because trees require all edges to have the same weight

C. Because trees do not handle cycles or multiple paths, so shortest path may be missed

D. Because trees do not have nodes

Solution

1. Step 1: Understand tree limitations

   Trees have no cycles and only one unique path between nodes, so they cannot represent multiple paths or cycles.

2. Step 2: Analyze impact on shortest path

   In graphs with cycles and multiple paths, shortest path algorithms must consider all paths; trees cannot represent this complexity.

3. Final Answer:

   Because trees do not handle cycles or multiple paths, so shortest path may be missed -> Option C

4. Quick Check:

   Cycles and multiple paths need graphs, not trees [OK]

Hint: Cycles and multiple paths require graph structures [OK]

Common Mistakes:

• Assuming trees can represent cycles
• Thinking trees are faster always
• Confusing edge weights requirements