Adjacency List Representation in DSA C

Mental Model

We store each node's neighbors in a list so we can quickly see who it connects to.

Analogy: Imagine a group of friends where each person keeps a list of their close friends' names written in a notebook.

0: 2 -> 1 -> null
1: 3 -> 0 -> null
2: 0 -> null
3: 1 -> null

Dry Run Walkthrough

Input: Graph with 4 nodes and edges: 0-1, 0-2, 1-3

Goal: Build adjacency lists showing neighbors for each node

Step 1: Add edge from 0 to 1

0: 1 -> null
1: null
2: null
3: null

Why: We record that node 0 connects to node 1

Step 2: Add edge from 1 to 0

0: 1 -> null
1: 0 -> null
2: null
3: null

Why: Since graph is undirected, node 1 connects back to node 0

Step 3: Add edge from 0 to 2

0: 2 -> 1 -> null
1: 0 -> null
2: null
3: null

Why: Node 0 also connects to node 2

Step 4: Add edge from 2 to 0

0: 2 -> 1 -> null
1: 0 -> null
2: 0 -> null
3: null

Why: Node 2 connects back to node 0

Step 5: Add edge from 1 to 3

0: 2 -> 1 -> null
1: 3 -> 0 -> null
2: 0 -> null
3: null

Why: Node 1 connects to node 3

Step 6: Add edge from 3 to 1

0: 2 -> 1 -> null
1: 3 -> 0 -> null
2: 0 -> null
3: 1 -> null

Why: Node 3 connects back to node 1

Result:

0: 2 -> 1 -> null
1: 3 -> 0 -> null
2: 0 -> null
3: 1 -> null

Annotated Code

DSA C

#include <stdio.h>
#include <stdlib.h>

// Node for adjacency list
typedef struct Node {
    int dest;
    struct Node* next;
} Node;

// Graph structure
typedef struct Graph {
    int V;
    Node** array;
} Graph;

// Create new adjacency list node
Node* newNode(int dest) {
    Node* node = (Node*)malloc(sizeof(Node));
    node->dest = dest;
    node->next = NULL;
    return node;
}

// Create graph with V vertices
Graph* createGraph(int V) {
    Graph* graph = (Graph*)malloc(sizeof(Graph));
    graph->V = V;
    graph->array = (Node**)malloc(V * sizeof(Node*));
    for (int i = 0; i < V; i++)
        graph->array[i] = NULL;
    return graph;
}

// Add edge to undirected graph
void addEdge(Graph* graph, int src, int dest) {
    // Add node to src list
    Node* node = newNode(dest);
    node->next = graph->array[src];
    graph->array[src] = node;

    // Add node to dest list
    node = newNode(src);
    node->next = graph->array[dest];
    graph->array[dest] = node;
}

// Print adjacency list
void printGraph(Graph* graph) {
    for (int v = 0; v < graph->V; v++) {
        Node* pCrawl = graph->array[v];
        printf("%d: ", v);
        while (pCrawl) {
            printf("%d -> ", pCrawl->dest);
            pCrawl = pCrawl->next;
        }
        printf("null\n");
    }
}

int main() {
    int V = 4;
    Graph* graph = createGraph(V);

    addEdge(graph, 0, 1);
    addEdge(graph, 0, 2);
    addEdge(graph, 1, 3);

    printGraph(graph);
    return 0;
}

node->next = graph->array[src]; graph->array[src] = node;

Insert new neighbor at head of src adjacency list

node->next = graph->array[dest]; graph->array[dest] = node;

Insert new neighbor at head of dest adjacency list for undirected edge

while (pCrawl) { printf("%d -> ", pCrawl->dest); pCrawl = pCrawl->next; }

Traverse adjacency list to print all neighbors

Output

0: 2 -> 1 -> null

1: 3 -> 0 -> null

2: 0 -> null

3: 1 -> null

Complexity Analysis

Time: O(V + E) because we create and print adjacency lists for all vertices and edges

Space: O(V + E) because adjacency lists store all vertices and their edges

vs Alternative: Compared to adjacency matrix O(V^2) space, adjacency list is more efficient for sparse graphs

Edge Cases

Graph with no edges

All adjacency lists remain empty (NULL)

DSA C

for (int i = 0; i < V; i++) graph->array[i] = NULL;

Graph with single vertex and no edges

Single adjacency list is empty

DSA C

for (int i = 0; i < V; i++) graph->array[i] = NULL;

When to Use This Pattern

When you need to represent graph connections efficiently and want to quickly find neighbors, use adjacency lists because they store only existing edges.

Common Mistakes

Mistake: Forgetting to add edges in both directions for undirected graphs
Fix: Add edge from src to dest and also from dest to src

Mistake: Appending new nodes at the end of adjacency list causing O(n) insertion
Fix: Insert new nodes at the head of the list for O(1) insertion

Summary

Stores graph edges as lists of neighbors for each vertex.

Use when you want efficient storage and quick access to neighbors in sparse graphs.

Each vertex keeps a simple list of its connected nodes, like a friend list.

Practice

1. What does an adjacency list represent in graph data structures?

easy

A. A list where each vertex stores its adjacent vertices

B. A matrix showing connections between vertices

C. A list of all vertices without edges

D. A list of edges only without vertices

Solution

1. Step 1: Understand adjacency list concept

   An adjacency list stores each vertex and the vertices it connects to directly.

2. Step 2: Compare with other representations

   Unlike adjacency matrix, adjacency list focuses on neighbors per vertex, not a full matrix.

3. Final Answer:

   A list where each vertex stores its adjacent vertices -> Option A

4. Quick Check:

   Adjacency list = vertex with neighbors [OK]

Hint: Adjacency list stores neighbors per vertex, not full matrix [OK]

Common Mistakes:

• Confusing adjacency list with adjacency matrix
• Thinking it stores only edges without vertices
• Assuming it lists vertices without connections

2. Which of the following is the correct C syntax to declare an adjacency list for a graph with 5 vertices using an array of pointers to linked lists?

easy

A. int* adjList[5];

B. int adjList[5][5];

C. struct Node adjList[5];

D. struct Node* adjList[5];

Solution

1. Step 1: Understand adjacency list declaration

   Adjacency list uses array of pointers to linked list nodes, so 'struct Node* adjList[5];' is correct.

2. Step 2: Check other options

   int adjList[5][5]; is adjacency matrix, C is array of structs (not pointers), A is array of int pointers (not nodes).

3. Final Answer:

   struct Node* adjList[5]; -> Option D

4. Quick Check:

   Array of pointers to nodes = correct adjacency list declaration [OK]

Hint: Adjacency list uses array of pointers to node structs [OK]

Common Mistakes:

• Using 2D array instead of array of pointers
• Declaring array of structs instead of pointers
• Using int pointers instead of node pointers

3. Given the following adjacency list representation code snippet for a graph with 3 vertices (0,1,2):

struct Node {
  int vertex;
  struct Node* next;
};

struct Node* adjList[3] = {NULL, NULL, NULL};

// Adding edge 0->1
struct Node* newNode = malloc(sizeof(struct Node));
newNode->vertex = 1;
newNode->next = adjList[0];
adjList[0] = newNode;

// Adding edge 0->2
newNode = malloc(sizeof(struct Node));
newNode->vertex = 2;
newNode->next = adjList[0];
adjList[0] = newNode;

// Adding edge 1->2
newNode = malloc(sizeof(struct Node));
newNode->vertex = 2;
newNode->next = adjList[1];
adjList[1] = newNode;

// Print adjacency list for vertex 0
struct Node* temp = adjList[0];
while(temp != NULL) {
  printf("%d -> ", temp->vertex);
  temp = temp->next;
}
printf("NULL\n");

What is the printed output?

medium

A. 1 -> 2 -> NULL

B. 0 -> 1 -> 2 -> NULL

C. 2 -> 1 -> NULL

D. NULL

Solution

1. Step 1: Trace insertion order for vertex 0

   Edges 0->1 then 0->2 are added at head, so list is 2 -> 1 -> NULL.

2. Step 2: Understand print loop

   Prints vertices in order from head: 2 then 1, then NULL.

3. Final Answer:

   2 -> 1 -> NULL -> Option C

4. Quick Check:

   Last inserted edge appears first in adjacency list [OK]

Hint: New nodes added at head, so last added appears first [OK]

Common Mistakes:

• Assuming order is insertion order instead of reversed
• Printing vertex 0 itself in adjacency list
• Confusing NULL print format

4. Consider this buggy code snippet to add an edge from vertex u to v in an adjacency list:

void addEdge(struct Node* adjList[], int u, int v) {
  struct Node* newNode = malloc(sizeof(struct Node));
  newNode->vertex = v;
  newNode->next = NULL;
  adjList[u] = newNode;
}

What is the main problem with this code?

medium

A. It overwrites existing adjacency list for vertex u, losing previous edges

B. It does not allocate memory for newNode

C. It sets newNode->next incorrectly to itself

D. It does not assign vertex v to newNode

Solution

1. Step 1: Analyze pointer assignment

   Setting adjList[u] = newNode overwrites old list head, losing previous edges.

2. Step 2: Check linked list linking

   newNode->next is NULL, so no link to old list; old edges lost.

3. Final Answer:

   It overwrites existing adjacency list for vertex u, losing previous edges -> Option A

4. Quick Check:

   Overwriting head pointer loses old adjacency list [OK]

Hint: Always link new node to old head to keep edges [OK]

Common Mistakes:

• Not linking new node to existing list
• Forgetting to allocate memory
• Incorrectly setting next pointer

5. You have a directed graph with 4 vertices (0 to 3). You want to represent it using adjacency lists and add edges:
- 0 -> 1
- 0 -> 2
- 1 -> 2
- 2 -> 0
- 2 -> 3
- 3 -> 3

Which data structure and insertion method correctly represents this graph in C?

hard

A. Use 2D int array; set 1 for edges and 0 otherwise

B. Use array of pointers to Node structs; insert new nodes at head linking to old list

C. Use array of Node structs; overwrite each vertex's list on insertion

D. Use array of int pointers; store vertex numbers without linking

Solution

1. Step 1: Choose correct data structure

   Adjacency list uses array of pointers to linked nodes for each vertex.

2. Step 2: Insert edges properly

   Insert new nodes at head, linking to previous list to keep all edges.

3. Step 3: Check other options

   Use 2D int array; set 1 for edges and 0 otherwise is adjacency matrix, C overwrites lists losing edges, D lacks linking.

4. Final Answer:

   Use array of pointers to Node structs; insert new nodes at head linking to old list -> Option B

5. Quick Check:

   Array of pointers + head insertion = correct adjacency list [OK]

Hint: Use pointers array and link new nodes at head to keep edges [OK]

Common Mistakes:

• Using adjacency matrix instead of list
• Overwriting adjacency list on insertion
• Not linking nodes properly