Array Traversal Patterns in DSA C - Time & Space Complexity

Time Complexity: Array Traversal Patterns

O(n)

Understanding Time Complexity

When we go through an array to check or change its items, we want to know how long it takes as the array grows.

We ask: How does the work increase when the array gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void printArray(int arr[], int n) {
    for (int i = 0; i < n; i++) {
        printf("%d ", arr[i]);
    }
    printf("\n");
}
    

This code goes through each item in the array once and prints it.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that visits each array element once.
• How many times: Exactly n times, where n is the array size.

How Execution Grows With Input

As the array size grows, the number of steps grows the same way.

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

Pattern observation: Doubling the array size doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to finish grows directly with the number of items in the array.

Common Mistake

[X] Wrong: "Since the loop is simple, it must be constant time O(1)."

[OK] Correct: The loop runs once for each item, so time grows with array size, not fixed.

Interview Connect

Understanding how simple loops scale helps you explain your code clearly and shows you know how programs behave with bigger data.

Self-Check

"What if we nested another loop inside to compare each element with every other? How would the time complexity change?"

Practice

1. What does the following code snippet do?
for (int i = 0; i < n; i++) { printf("%d ", arr[i]); }

easy

A. Prints only the last element of the array

B. Prints all elements of the array from end to start

C. Prints only the first element of the array

D. Prints all elements of the array from start to end

Solution

1. Step 1: Understand the loop range

   The loop starts at 0 and runs while i is less than n, incrementing i by 1 each time.

2. Step 2: Analyze the print statement inside the loop

   Each iteration prints the element at index i, so it prints elements from arr[0] to arr[n-1].

3. Final Answer:

   Prints all elements of the array from start to end -> Option D

4. Quick Check:

   Loop from 0 to n-1 prints all elements [OK]

Hint: Loop from 0 to n-1 prints array forward [OK]

Common Mistakes:

• Confusing loop direction and thinking it prints backward
• Assuming it prints only one element
• Misreading the loop condition

2. Which of the following is the correct syntax to traverse an array arr of size n backwards in C?

easy

A. for (int i = 0; i < n; i++) { printf("%d", arr[i]); }

B. for (int i = n; i > 0; i++) { printf("%d", arr[i]); }

C. for (int i = n-1; i >= 0; i--) { printf("%d", arr[i]); }

D. for (int i = 1; i <= n; i++) { printf("%d", arr[i]); }

Solution

1. Step 1: Identify correct loop start and end for backward traversal

   Backward traversal starts from index n-1 down to 0.

2. Step 2: Check loop syntax correctness

   for (int i = n-1; i >= 0; i--) { printf("%d", arr[i]); } uses i = n-1; i >= 0; i-- which correctly traverses backward.

3. Final Answer:

   for (int i = n-1; i >= 0; i--) { printf("%d", arr[i]); } -> Option C

4. Quick Check:

   Backward loop uses i = n-1 to 0 with decrement [OK]

Hint: Backward loop starts at n-1 and decrements to 0 [OK]

Common Mistakes:

• Starting loop at n instead of n-1
• Using i++ instead of i-- for backward traversal
• Accessing arr[i] with out-of-range indices

3. What is the output of the following code?

int arr[] = {5, 10, 15, 20};
int sum = 0;
for (int i = 1; i < 4; i++) {
    sum += arr[i];
}
printf("%d", sum);

medium

A. 50

B. 45

C. 30

D. Syntax Error

Solution

1. Step 1: Identify loop indices and elements summed

   The loop runs i from 1 to 3, summing arr[1], arr[2], arr[3] which are 10, 15, and 20.

2. Step 2: Calculate sum of selected elements

   sum = 10 + 15 + 20 = 45

3. Final Answer:

   45 -> Option B

4. Quick Check:

   Sum of arr[1..3] = 45 [OK]

Hint: Sum elements from index 1 to 3 inclusive [OK]

Common Mistakes:

• Starting sum from arr[0] mistakenly
• Adding wrong indices or missing last element
• Confusing loop range boundaries

4. Find the error in the following code that attempts to print all elements of an array arr of size n:

for (int i = 0; i <= n; i++) {
    printf("%d ", arr[i]);
}

medium

A. Loop condition should be i < n, not i <= n

B. Array indexing should start from 1, not 0

C. printf statement syntax is incorrect

D. No error, code is correct

Solution

1. Step 1: Analyze loop condition and array indexing

   Loop runs from i = 0 to i = n inclusive, accessing arr[n] which is out of bounds.

2. Step 2: Correct loop condition to avoid out-of-bounds access

   Change condition to i < n so indices go from 0 to n-1, valid for array of size n.

3. Final Answer:

   Loop condition should be i < n, not i <= n -> Option A

4. Quick Check:

   Array indices valid from 0 to n-1 [OK]

Hint: Use i < n to avoid out-of-bounds errors [OK]

Common Mistakes:

• Using <= instead of < in loop condition
• Starting index at 1 instead of 0
• Ignoring array size limits

5. Given an integer array arr of size n, which code snippet correctly prints every second element starting from the first element?

hard

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

B. for (int i = 1; i < n; i += 2) { printf("%d ", arr[i]); }

C. for (int i = 0; i <= n; i += 2) { printf("%d ", arr[i]); }

D. for (int i = n-1; i >= 0; i -= 2) { printf("%d ", arr[i]); }

Solution

1. Step 1: Understand requirement to print every second element starting at first

   Start at index 0 and increment index by 2 each time to skip every other element.

2. Step 2: Check loop correctness and bounds

   for (int i = 0; i < n; i += 2) { printf("%d ", arr[i]); } uses i = 0; i < n; i += 2 which correctly prints arr[0], arr[2], arr[4], etc.

3. Final Answer:

   for (int i = 0; i < n; i += 2) { printf("%d ", arr[i]); } -> Option A

4. Quick Check:

   Increment by 2 starting at 0 prints every second element [OK]

Hint: Increment index by 2 starting at 0 for every second element [OK]

Common Mistakes:

• Starting at index 1 instead of 0
• Using <= n causing out-of-bounds
• Looping backward when forward is needed