Hash Map vs Array vs Linked List for Lookup in DSA C - Complexity Comparison

Time Complexity: Hash Map vs Array vs Linked List for Lookup

O(n) for array and linked list, O(1) average for hash map

Understanding Time Complexity

We want to understand how fast we can find a value in different data structures.

The question is: How does the time to find something change as the data grows?

Scenario Under Consideration

Analyze the time complexity of the following lookup operations.

// Lookup in array
int lookup_array(int arr[], int n, int target) {
    for (int i = 0; i < n; i++) {
        if (arr[i] == target) return i;
    }
    return -1;
}

// Lookup in linked list
int lookup_linked_list(Node* head, int target) {
    Node* current = head;
    while (current != NULL) {
        if (current->value == target) return 1;
        current = current->next;
    }
    return 0;
}

// Lookup in hash map (simplified)
int lookup_hash_map(HashMap* map, int target) {
    int index = hash(target) % map->capacity;
    Entry* entry = map->buckets[index];
    while (entry != NULL) {
        if (entry->key == target) return 1;
        entry = entry->next;
    }
    return 0;
}

This code shows how to find a value in an array, a linked list, and a hash map.

Identify Repeating Operations

Look at what repeats when searching:

• Array: Loop through each element one by one.
• Linked List: Traverse nodes one by one until found or end.
• Hash Map: Check entries in one bucket's linked list after hashing.
• Dominant operation: Number of elements checked in the search.

How Execution Grows With Input

As the number of items (n) grows, how many checks happen?

Input Size (n)	Array & Linked List Checks	Hash Map Checks (average)
10	Up to 10 checks	About 1 check
100	Up to 100 checks	About 1 check
1000	Up to 1000 checks	About 1 check

Array and linked list checks grow directly with n. Hash map checks stay roughly the same if well sized.

Final Time Complexity

Time Complexity: O(n) for array and linked list, O(1) average for hash map lookup

This means array and linked list take longer as data grows, but hash map stays fast on average.

Common Mistake

[X] Wrong: "Hash map lookup is always O(1) no matter what."

[OK] Correct: If many keys collide, hash map lookup can slow down to O(n) in worst case.

Interview Connect

Knowing these differences helps you choose the right data structure and explain your choices clearly.

Self-Check

"What if the hash map uses a poor hash function causing many collisions? How would the lookup time change?"

Practice

1. Which data structure provides the fastest average lookup time for finding an element by key?

easy

A. Stack

B. Hash Map

C. Linked List

D. Array

Solution

1. Step 1: Understand lookup times for each data structure

   Hash Map uses hashing to find keys quickly, usually in constant time O(1). Arrays require scanning or index access, O(1) if index known but O(n) if searching by value. Linked Lists require scanning all nodes, O(n).

2. Step 2: Compare average lookup times

   Hash Map is fastest on average for key lookup due to direct hashing. Arrays and Linked Lists are slower for key-based search.

3. Final Answer:

   Hash Map -> Option B

4. Quick Check:

   Fastest lookup by key = Hash Map [OK]

Hint: Hash Map lookup is usually O(1), faster than arrays or lists [OK]

Common Mistakes:

• Confusing array index access with key lookup
• Thinking linked list lookup is fast
• Assuming stack is good for key lookup

2. Which of the following is the correct way to declare an array of 5 integers in C?

easy

A. int arr(5);

B. int arr = new int[5];

C. array<int> arr(5);

D. int arr[5];

Solution

1. Step 1: Recall C array declaration syntax

   In C, arrays are declared with type, name, and size in square brackets, e.g., int arr[5];

2. Step 2: Check each option

   int arr[5]; matches correct C syntax. int arr = new int[5]; uses C++ style new keyword. int arr(5); is invalid syntax. array<int> arr(5); is C++ template syntax, not C.

3. Final Answer:

   int arr[5]; -> Option D

4. Quick Check:

   C array declaration = int arr[5]; [OK]

Hint: C arrays use square brackets for size, no new keyword [OK]

Common Mistakes:

• Using C++ new keyword in C
• Using parentheses instead of brackets
• Confusing C++ templates with C arrays

3. Consider the following C code snippet using a linked list for lookup:

typedef struct Node {
  int key;
  int value;
  struct Node* next;
} Node;

int lookup(Node* head, int key) {
  Node* current = head;
  while (current != NULL) {
    if (current->key == key) {
      return current->value;
    }
    current = current->next;
  }
  return -1;
}

// List: (1,10) -> (2,20) -> (3,30) -> NULL
// Call: lookup(head, 2);

What is the output of lookup(head, 2);?

medium

A. 20

B. 10

C. 30

D. -1

Solution

1. Step 1: Trace the linked list nodes

   The list nodes have keys and values: (1,10), (2,20), (3,30). The function searches for key 2.

2. Step 2: Follow lookup function logic

   Starting at head (key=1), key != 2, move next. Next node key=2 matches, return value 20.

3. Final Answer:

   20 -> Option A

4. Quick Check:

   Found key 2 with value 20 [OK]

Hint: Linked list lookup scans nodes until key found [OK]

Common Mistakes:

• Returning value of first node always
• Confusing key and value fields
• Returning -1 when key exists

4. The following C code attempts to find a value in an array but has a bug:

int find(int arr[], int size, int target) {
  for (int i = 0; i <= size; i++) {
    if (arr[i] == target) {
      return i;
    }
  }
  return -1;
}

What is the bug in this code?

medium

A. Return value should be arr[i], not i

B. Function should return void

C. Loop condition should be i < size, not i <= size

D. Array parameter should be int* arr

Solution

1. Step 1: Analyze loop boundary

   The loop runs from i = 0 to i <= size, which means i can be equal to size. Array indices go from 0 to size-1, so arr[size] is out of bounds.

2. Step 2: Correct loop condition

   Change condition to i < size to avoid accessing out of bounds memory.

3. Final Answer:

   Loop condition should be i < size, not i <= size -> Option C

4. Quick Check:

   Array index must be less than size [OK]

Hint: Array indices go 0 to size-1, use i < size in loops [OK]

Common Mistakes:

• Using <= size causes out-of-bounds access
• Returning arr[i] instead of index
• Changing return type unnecessarily

5. You need to store a large number of unique integer keys with associated values and perform frequent lookups. Which data structure is best and why?

hard

A. Hash Map - because it provides average constant time lookup

B. Linked List - because it allows easy insertion

C. Array - because it uses contiguous memory

D. Binary Search Tree - because it keeps keys sorted

Solution

1. Step 1: Understand requirements

   We need to store many unique keys with values and do frequent lookups efficiently.

2. Step 2: Evaluate data structures

   Array is inefficient for key lookup unless keys are indices. Linked List has slow O(n) lookup. Binary Search Tree has O(log n) lookup but more complex. Hash Map offers average O(1) lookup, ideal for fast access.

3. Final Answer:

   Hash Map - because it provides average constant time lookup -> Option A

4. Quick Check:

   Fast lookup with many keys = Hash Map [OK]

Hint: For fast key lookup, choose Hash Map over arrays or lists [OK]

Common Mistakes:

• Choosing array for non-index keys
• Ignoring lookup speed in linked lists
• Preferring BST without sorting need