Constants and literals - Time & Space Complexity

Time Complexity: Constants and literals

O(1)

Understanding Time Complexity

When we use constants and literals in C code, we want to know how they affect the program's speed.

We ask: Does using constants or fixed values change how long the program takes as input grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

#include <stdio.h>

int main() {
    const int x = 5;
    int y = 10;
    int sum = x + y;
    printf("Sum is %d\n", sum);
    return 0;
}
    

This code adds two numbers where one is a constant and prints the result.

Identify Repeating Operations

Look for loops or repeated steps that happen many times.

• Primary operation: Simple addition and print statement.
• How many times: Runs only once, no loops or repetition.

How Execution Grows With Input

Since the code does not repeat or loop, the time it takes stays the same no matter the input size.

Input Size (n)	Approx. Operations
10	About 3 operations
100	About 3 operations
1000	About 3 operations

Pattern observation: The number of steps does not grow with input size; it stays constant.

Final Time Complexity

Time Complexity: O(1)

This means the program takes the same amount of time no matter how big the input is.

Common Mistake

[X] Wrong: "Using constants makes the program faster as input grows."

[OK] Correct: Constants do not change speed with input size because they are fixed values used once, not repeated operations.

Interview Connect

Understanding that constants and literals do not affect time growth helps you focus on parts of code that really change with input size.

Self-Check

"What if we replaced the constant with a loop that adds numbers repeatedly? How would the time complexity change?"

Practice

1. What is a constant in C programming?

easy

A. A function that returns a value

B. A fixed value that cannot be changed during program execution

C. A variable that can change its value anytime

D. A type of loop in C

Solution

1. Step 1: Understand the meaning of constant

   A constant is a value that remains the same throughout the program and cannot be modified.

2. Step 2: Compare options with definition

   Only A fixed value that cannot be changed during program execution describes a fixed value that does not change, which matches the definition of a constant.

3. Final Answer:

   A fixed value that cannot be changed during program execution -> Option B

4. Quick Check:

   Constant = fixed value [OK]

Hint: Constants never change value once set [OK]

Common Mistakes:

• Confusing constants with variables
• Thinking constants are functions
• Mixing constants with loops

2. Which of the following is the correct way to define a constant integer named MAX with value 100 in C?

easy

A. All of the above

B. #define MAX 100

C. const int MAX = 100;

D. int const MAX = 100;

Solution

1. Step 1: Review ways to define constants in C

   Constants can be defined using #define or using const keyword with variable declaration.

2. Step 2: Check each option

   #define MAX 100 uses #define, which is valid. int const MAX = 100; uses int const, which is valid. const int MAX = 100; uses const int, also valid. So all are correct.

3. Final Answer:

   All of the above -> Option A

4. Quick Check:

   All methods define constants [OK]

Hint: Use #define or const keyword for constants [OK]

Common Mistakes:

• Using variable without const
• Missing semicolon in const declaration
• Confusing #define with variable

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

#include <stdio.h>
#define PI 3.14
int main() {
    const int radius = 5;
    float area = PI * radius * radius;
    printf("%.2f", area);
    return 0;
}

medium

A. Syntax error

B. 31.40

C. 78.50

D. 25.00

Solution

1. Step 1: Calculate area using given formula

   Area = PI * radius * radius = 3.14 * 5 * 5 = 3.14 * 25 = 78.5

2. Step 2: Check printf formatting

   Using %.2f prints the float with 2 decimal places, so output is 78.50

3. Final Answer:

   78.50 -> Option C

4. Quick Check:

   Area = 3.14 * 25 = 78.50 [OK]

Hint: Calculate formula carefully and check decimal format [OK]

Common Mistakes:

• Using wrong formula
• Ignoring decimal places
• Confusing radius with diameter

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

const int x;
x = 10;
printf("%d", x);

medium

A. Cannot assign value to const variable after declaration

B. Missing semicolon after declaration

C. printf format specifier is wrong

D. No error, code runs fine

Solution

1. Step 1: Understand const variable rules

   A const variable must be initialized when declared and cannot be assigned a value later.

2. Step 2: Analyze the code

   Here, const int x; declares x without initialization, then tries to assign 10 later, which is not allowed.

3. Final Answer:

   Cannot assign value to const variable after declaration -> Option A

4. Quick Check:

   const variables must be initialized once [OK]

Hint: Initialize const variables when declared [OK]

Common Mistakes:

• Assigning value after declaration
• Not initializing const variables
• Ignoring const rules

5. You want to create a constant array of 3 integers in C that cannot be modified after initialization. Which of the following declarations achieves this correctly?

hard

A. int arr[3] = {1, 2, 3};

B. int const *arr = {1, 2, 3};

C. #define arr {1, 2, 3}

D. const int arr[3] = {1, 2, 3};

Solution

1. Step 1: Understand const array declaration

   Declaring an array with const int arr[3] means the elements cannot be changed after initialization.

2. Step 2: Check each option

   int arr[3] = {1, 2, 3}; declares a normal array, elements can be changed. const int arr[3] = {1, 2, 3}; declares a constant array correctly. #define arr {1, 2, 3} uses #define incorrectly for array. int const *arr = {1, 2, 3}; declares a pointer to const int, but initialization is invalid.

3. Final Answer:

   const int arr[3] = {1, 2, 3}; -> Option D

4. Quick Check:

   const array elements cannot change [OK]

Hint: Use const before type for constant arrays [OK]

Common Mistakes:

• Using #define for arrays
• Declaring non-const arrays
• Incorrect pointer initialization