Else–if ladder in C++ - Time & Space Complexity

Time Complexity: Else-if ladder

O(n)

Understanding Time Complexity

We want to understand how the time taken by an else-if ladder changes as the input changes.

Specifically, we ask: How many steps does the program take before it finds the right condition?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int checkNumber(int n) {
    if (n == 1) {
        return 10;
    } else if (n == 2) {
        return 20;
    } else if (n == 3) {
        return 30;
    } else {
        return 40;
    }
}
    

This code checks the value of n and returns a number based on which condition matches first.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking conditions one by one in the else-if ladder.
• How many times: Up to the number of conditions until a match is found.

How Execution Grows With Input

As the input number changes, the program checks conditions from top to bottom until it finds a match.

Input Value (n)	Approx. Operations (condition checks)
1	1 check
2	2 checks
3	3 checks
4	4 checks (all conditions checked)

Pattern observation: The number of checks grows linearly with the position of the matching condition.

Final Time Complexity

Time Complexity: O(n)

This means the time grows linearly with the number of conditions checked before finding a match.

Common Mistake

[X] Wrong: "The else-if ladder always takes the same time regardless of input."

[OK] Correct: The program stops checking as soon as it finds a match, so time depends on where the match is.

Interview Connect

Understanding how condition checks add up helps you explain efficiency clearly and shows you can think about code beyond just making it work.

Self-Check

"What if we replaced the else-if ladder with a switch statement? How would the time complexity change?"

Practice

1.

What does an else-if ladder do in C++?

easy

A. Skips all conditions and runs the else block always

B. Runs all conditions regardless of their truth

C. Only runs the last condition in the ladder

D. Checks multiple conditions one by one and runs the first true block

Solution

1. Step 1: Understand the purpose of else-if ladder

   An else-if ladder is used to check multiple conditions in order, one after another.

2. Step 2: Identify how conditions are evaluated

   It runs the code block for the first condition that is true and skips the rest.

3. Final Answer:

   Checks multiple conditions one by one and runs the first true block -> Option D

4. Quick Check:

   Else-if ladder = first true condition runs [OK]

Hint: Remember: else-if stops at first true condition [OK]

Common Mistakes:

• Thinking all conditions run
• Believing else always runs
• Confusing else-if with separate ifs

2.

Which of the following is the correct syntax for an else-if ladder in C++?

int x = 10;
if (x < 5) {
  // code A
} _____ (x < 15) {
  // code B
} else {
  // code C
}

easy

A. else if

B. elseif

C. else_if

D. else if()

Solution

1. Step 1: Recall correct else-if syntax in C++

   The correct keyword is else if with a space, no underscores or parentheses after else.

2. Step 2: Check each option

   Options A, B, and C are invalid syntax in C++.

3. Final Answer:

   else if -> Option A

4. Quick Check:

   Correct syntax = else if [OK]

Hint: Use 'else if' with space, no underscores or parentheses [OK]

Common Mistakes:

• Writing 'elseif' as one word
• Using underscores like 'else_if'
• Adding parentheses after else

3.

What will be the output of this C++ code?

int num = 7;
if (num > 10) {
  std::cout << "Greater than 10";
} else if (num > 5) {
  std::cout << "Greater than 5";
} else {
  std::cout << "5 or less";
}

medium

A. Greater than 5

B. 5 or less

C. Greater than 10

D. No output

Solution

1. Step 1: Evaluate first condition (num > 10)

   7 is not greater than 10, so this block is skipped.

2. Step 2: Evaluate second condition (num > 5)

   7 is greater than 5, so this block runs and prints "Greater than 5".

3. Final Answer:

   Greater than 5 -> Option A

4. Quick Check:

   7 > 5 = true, prints "Greater than 5" [OK]

Hint: Check conditions top to bottom, first true runs [OK]

Common Mistakes:

• Choosing first condition output incorrectly
• Ignoring else-if order
• Assuming else runs always

4.

Find the error in this else-if ladder code snippet:

int score = 85;
if (score >= 90) {
  std::cout << "Grade A";
} else if score >= 80 {
  std::cout << "Grade B";
} else {
  std::cout << "Grade C";
}

medium

A. Missing semicolon after std::cout

B. Missing parentheses around condition in else-if

C. Incorrect use of else instead of else-if

D. Using >= instead of >

Solution

1. Step 1: Check syntax of else-if condition

   In C++, conditions must be inside parentheses. The else-if line lacks parentheses.

2. Step 2: Verify other parts

   Semicolons and operators are correct; only parentheses are missing.

3. Final Answer:

   Missing parentheses around condition in else-if -> Option B

4. Quick Check:

   Conditions need parentheses [OK]

Hint: Always put conditions inside parentheses [OK]

Common Mistakes:

• Forgetting parentheses in if/else-if
• Missing semicolons after statements
• Confusing else and else-if syntax

5.

Write an else-if ladder to print the day of the week given an integer day (1 to 7). What will be printed if day = 5?

int day = 5;
if (day == 1) {
  std::cout << "Monday";
} else if (day == 2) {
  std::cout << "Tuesday";
} else if (day == 3) {
  std::cout << "Wednesday";
} else if (day == 4) {
  std::cout << "Thursday";
} else if (day == 5) {
  std::cout << "Friday";
} else if (day == 6) {
  std::cout << "Saturday";
} else if (day == 7) {
  std::cout << "Sunday";
} else {
  std::cout << "Invalid day";
}

hard

A. Thursday

B. Saturday

C. Friday

D. Invalid day

Solution

1. Step 1: Match the value of day with conditions

   day is 5, so the else-if condition day == 5 is true.

2. Step 2: Identify the output for day == 5

   The code prints "Friday" for day 5.

3. Final Answer:

   Friday -> Option C

4. Quick Check:

   day 5 = Friday [OK]

Hint: Match day number to correct else-if condition [OK]

Common Mistakes:

• Mixing up day numbers and names
• Forgetting else block for invalid days
• Using wrong comparison operators