Lifetime and scope comparison - Time & Space Complexity

Time Complexity: Lifetime and scope comparison

O(1)

Understanding Time Complexity

When we look at lifetime and scope in C, we want to understand how long variables exist and where they can be used.

We ask: How does the program's work change as we use variables with different lifetimes and scopes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

#include <stdio.h>

void func() {
    int x = 0; // local variable
    for (int i = 0; i < 1000; i++) {
        x += i;
    }
    printf("%d\n", x);
}

int main() {
    static int y = 0; // static variable
    y++;
    func();
    return 0;
}
    

This code shows a local variable inside a function and a static variable in main, then runs a loop inside func.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop inside func that runs 1000 times.
• How many times: Exactly 1000 times each time func is called.

How Execution Grows With Input

Here, the loop runs a fixed 1000 times, so the work does not grow with input size.

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

Pattern observation: The number of operations stays the same no matter the input size.

Final Time Complexity

Time Complexity: O(1)

This means the program does a fixed amount of work regardless of input size.

Common Mistake

[X] Wrong: "Because there is a loop, the time complexity must grow with input size."

[OK] Correct: The loop runs a fixed number of times (1000), so it does not depend on input size and stays constant.

Interview Connect

Understanding how variable lifetime and scope affect program behavior helps you explain code clearly and reason about performance in real projects.

Self-Check

"What if the loop count in func was based on a function parameter n? How would the time complexity change?"

Practice

1. Which of the following best describes the scope of a variable in C?

easy

A. The time duration the variable exists in memory

B. The amount of memory the variable uses

C. The part of the program where the variable can be accessed

D. The data type of the variable

Solution

1. Step 1: Understand the meaning of scope

   Scope means where in the code a variable can be used or accessed.

2. Step 2: Differentiate scope from lifetime

   Lifetime is about how long the variable exists in memory, not where it can be used.

3. Final Answer:

   The part of the program where the variable can be accessed -> Option C

4. Quick Check:

   Scope = where variable is accessible [OK]

Hint: Scope means where variable is visible in code [OK]

Common Mistakes:

• Confusing scope with lifetime
• Thinking scope is about memory size
• Mixing scope with data type

2. Which declaration correctly creates a variable with local scope and static lifetime inside a function?

easy

A. static int count = 0;

B. int static count = 0;

C. auto static int count = 0;

D. register static int count = 0;

Solution

1. Step 1: Recall correct syntax for static local variable

   The keyword static comes before the type: static int count = 0;.

2. Step 2: Identify invalid syntax options

   int static count = 0; has incorrect order. auto static int count = 0; and register static int count = 0; use invalid combinations of storage class specifiers.

3. Final Answer:

   static int count = 0; -> Option A

4. Quick Check:

   Static local variable syntax = static before type [OK]

Hint: Put 'static' before type for static local variable [OK]

Common Mistakes:

• Placing 'static' after type
• Combining 'auto' and 'static' incorrectly
• Using 'register' with 'static'

3. What is the output of this C code?

void func() {
    static int x = 0;
    x++;
    printf("%d ", x);
}

int main() {
    for(int i = 0; i < 3; i++) {
        func();
    }
    return 0;
}

medium

A. 1 2 3

B. 1 1 1

C. 0 1 2

D. 3 3 3

Solution

1. Step 1: Understand static variable behavior inside function

   Static variable x keeps its value between function calls and starts at 0.

2. Step 2: Trace the loop and function calls

   Each call increments x by 1 and prints it: first 1, then 2, then 3.

3. Final Answer:

   1 2 3 -> Option A

4. Quick Check:

   Static variable increments across calls = 1 2 3 [OK]

Hint: Static variables keep value between calls [OK]

Common Mistakes:

• Assuming static resets each call
• Confusing initial value of static variable
• Ignoring the loop effect

4. Identify the error in this code snippet related to variable scope:

int main() {
    if (1) {
        int a = 5;
    }
    printf("%d", a);
    return 0;
}

medium

A. Variable 'a' should be declared static

B. Missing semicolon after variable declaration

C. printf format specifier is incorrect

D. Variable 'a' is used outside its scope

Solution

1. Step 1: Check where 'a' is declared and used

   'a' is declared inside the if-block and cannot be accessed outside it.

2. Step 2: Understand scope rules

   Variables declared inside braces have local scope limited to those braces, so 'a' is out of scope in printf.

3. Final Answer:

   Variable 'a' is used outside its scope -> Option D

4. Quick Check:

   Using variable outside its block scope causes error [OK]

Hint: Variables only visible inside their braces [OK]

Common Mistakes:

• Trying to use variable outside its block
• Thinking static fixes scope errors
• Ignoring variable lifetime vs scope

5. Consider this code:

void counter() {
    static int count = 0;
    int temp = 0;
    count++;
    temp++;
    printf("%d %d\n", count, temp);
}

int main() {
    for (int i = 0; i < 3; i++) {
        counter();
    }
    return 0;
}

What will be the output and why?

hard

A. 1 1
2 2
3 3
Because both variables keep their values between calls

B. 1 1
2 1
3 1
Because 'count' is static and 'temp' is local each call

C. 1 0
1 0
1 0
Because 'temp' is never incremented properly

D. 0 0
0 0
0 0
Because variables are not initialized

Solution

1. Step 1: Analyze 'count' variable behavior

   'count' is static, so it keeps incrementing across calls: 1, 2, 3.

2. Step 2: Analyze 'temp' variable behavior

   'temp' is local and reinitialized to 0 each call, so it increments to 1 every time.

3. Step 3: Understand output pattern

   Output lines are: "1 1", "2 1", "3 1" matching the behavior above.

4. Final Answer:

   1 1 2 1 3 1 Because 'count' is static and 'temp' is local each call -> Option B

5. Quick Check:

   Static keeps value; local resets each call [OK]

Hint: Static persists, local resets each function call [OK]

Common Mistakes:

• Assuming local variable keeps value between calls
• Confusing initialization of static vs local
• Ignoring that temp resets every call