Array Access and Update at Index in DSA C - Time & Space Complexity

Time Complexity: Array Access and Update at Index

O(1)

Understanding Time Complexity

We want to understand how fast we can get or change a value in an array at a certain position.

The question is: How does the time to access or update an element change as the array grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int getValue(int arr[], int index) {
    return arr[index];
}

void setValue(int arr[], int index, int value) {
    arr[index] = value;
}
    

This code gets or sets a value at a specific index in an array.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Direct access to an array element by index.
• How many times: Exactly once per call, no loops or recursion involved.

How Execution Grows With Input

Accessing or updating an element takes the same amount of time no matter how big the array is.

Input Size (n)	Approx. Operations
10	1
100	1
1000	1

Pattern observation: The time stays constant even if the array size grows.

Final Time Complexity

Time Complexity: O(1)

This means accessing or updating an element takes the same short time no matter how big the array is.

Common Mistake

[X] Wrong: "Accessing an element takes longer if the array is bigger because it has to look through all elements."

[OK] Correct: Arrays allow direct access by index, so the computer jumps straight to the spot without checking others.

Interview Connect

Knowing that array access and update are very fast helps you choose the right data structure and explain your choices clearly in interviews.

Self-Check

"What if we used a linked list instead of an array? How would the time complexity for access and update change?"

Practice

1. What does the expression arr[2] do in an array named arr?

easy

A. Accesses the element at index 0 of the array

B. Accesses the element at index 2 of the array

C. Updates the element at index 2 to zero

D. Deletes the element at index 2

Solution

1. Step 1: Understand array indexing

   Arrays use zero-based indexing, so index 2 means the third element.

2. Step 2: Access element at index 2

   The expression arr[2] retrieves the value stored at the third position in the array.

3. Final Answer:

   Accesses the element at index 2 of the array -> Option B

4. Quick Check:

   arr[2] means third element access [OK]

Hint: Remember arrays start at index 0, so arr[2] is third element [OK]

Common Mistakes:

• Thinking index starts at 1 instead of 0
• Confusing access with update or delete
• Assuming arr[2] changes the array

2. Which of the following is the correct syntax to update the 4th element of an integer array arr to 10 in C?

easy

A. arr[3] = 10;

B. arr(4) = 10;

C. arr[4] == 10;

D. arr{3} = 10;

Solution

1. Step 1: Identify correct array indexing syntax

   In C, arrays use square brackets with zero-based indexing, so the 4th element is at index 3.

2. Step 2: Use assignment operator correctly

   To update, use single equals =, so arr[3] = 10; is correct.

3. Final Answer:

   arr[3] = 10; -> Option A

4. Quick Check:

   Use arr[index] = value; with zero-based index [OK]

Hint: Use square brackets and single = for update, zero-based index [OK]

Common Mistakes:

• Using parentheses or braces instead of brackets
• Using double equals (==) instead of assignment (=)
• Using wrong index number for 4th element

3. What will be the output of the following C code?

int arr[5] = {1, 2, 3, 4, 5};
arr[1] = arr[3] + 2;
printf("%d", arr[1]);

medium

A. 6

B. 4

C. 5

D. 7

Solution

1. Step 1: Evaluate the expression arr[3] + 2

   arr[3] is the 4th element, which is 4. Adding 2 gives 6.

2. Step 2: Assign and print arr[1]

   arr[1] is updated to 6, then printed, so output is 6.

3. Final Answer:

   6 -> Option A

4. Quick Check:

   arr[3]=4 + 2 = 6 printed [OK]

Hint: Remember arr[3] is 4, add 2, assign to arr[1], print arr[1] [OK]

Common Mistakes:

• Confusing index 1 with index 3 values
• Adding incorrectly or forgetting zero-based index
• Printing wrong array element

4. Identify the error in the following C code snippet:

int arr[3] = {5, 10, 15};
arr[3] = 20;
printf("%d", arr[3]);

medium

A. Syntax error in array declaration

B. Missing semicolon after assignment

C. Array index out of bounds error

D. Incorrect printf format specifier

Solution

1. Step 1: Check array size and valid indices

   Array size is 3, valid indices are 0, 1, 2. Index 3 is out of bounds.

2. Step 2: Understand consequences of out of bounds access

   Accessing or assigning arr[3] causes undefined behavior or runtime error.

3. Final Answer:

   Array index out of bounds error -> Option C

4. Quick Check:

   Index 3 invalid for size 3 array [OK]

Hint: Array indices go from 0 to size-1 only [OK]

Common Mistakes:

• Using index equal to array size
• Ignoring zero-based indexing
• Assuming no error for out of bounds

5. Given an integer array arr of size 6 initialized as {2, 4, 6, 8, 10, 12}, which code snippet correctly doubles the value at index 4 and then prints the entire array?

hard

A. arr[4] = arr[4] + 2;
for(int i=0; i<5; i++) printf("%d ", arr[i]);

B. arr[5] = arr[4] * 2;
for(int i=0; i<=6; i++) printf("%d ", arr[i]);

C. arr[4] *= 2;
for(int i=1; i<6; i++) printf("%d ", arr[i]);

D. arr[4] = arr[4] * 2;
for(int i=0; i<6; i++) printf("%d ", arr[i]);

Solution

1. Step 1: Correctly update value at index 4

   Index 4 is the 5th element. Doubling means multiply by 2. Both arr[4] = arr[4] * 2; and arr[4] *= 2; work, but check loop next.

2. Step 2: Print entire array correctly

   Array size is 6, so loop must run from 0 to 5 (i<6). arr[4] = arr[4] * 2; for(int i=0; i<6; i++) printf("%d ", arr[i]); uses correct loop range and prints all elements.

3. Final Answer:

   arr[4] = arr[4] * 2; for(int i=0; i<6; i++) printf("%d ", arr[i]); -> Option D

4. Quick Check:

   Update index 4, loop 0 to 5 to print all [OK]

Hint: Use zero-based index and loop from 0 to size-1 [OK]

Common Mistakes:

• Using wrong index for update
• Looping beyond array size causing errors
• Printing partial array missing elements