Loops & Nested Loops: Types, Patterns, and Real-World Applications

TAKEAWAYS:

• Three loop types: for (count-controlled), while (condition-controlled), do-while (post-test) differ in initialization, condition, and update placement.
• Nested loops enable multi-dimensional tasks (e.g., matrix traversal, pattern printing) by embedding loops inside loops.
• Pattern generation uses nested loops to print structured outputs (e.g., pyramids, number sequences) by controlling row/column logic.
• Prime checks leverage loops to test divisibility iteratively, optimizing with sqrt(n) for efficiency.
• Real-world ties: Loops power transaction validation (e.g., eSewa’s payment retries), inventory systems (Daraz’s stock checks), and loan calculations (bank interest).
• Exam focus: Write correct loop conditions, avoid infinite loops, and trace variable changes step-by-step for full marks.

1. Introduction to Loops

Loops in C repeat code blocks until a condition is met, reducing redundancy. They are essential for:

• Processing arrays/lists.
• Generating patterns.
• Validating inputs (e.g., retries in eSewa).
• Simulating real-world cycles (e.g., Daraz’s order fulfillment).

Types of Loops

graph LR
    A["Loops in C"] --> B["for"]
    A --> C["while"]
    A --> D["do-while"]
    B -->|"count-controlled"| E["Initialization; Condition; Update"]
    C -->|"condition-controlled"| F["Test before execution"]
    D -->|"post-test"| G["Execute then test"]

2. for Loop: Count-Controlled Repetition

Syntax:

for (initialization; condition; update) {
    // Code to repeat
}

How it works:

1. Initialization: Runs once (e.g., int i=0).
2. Condition: Checked before each iteration (e.g., i<5).
3. Update: Executed after each iteration (e.g., i++).

Example: Print Numbers 1 to 5

for (int i=1; i<=5; i++) {
    printf("%d ", i);
}

Trace Table:

Visualization: Real-World Tie:

• eSewa’s Payment Retry Logic:

  for (int attempts=0; attempts<3; attempts++) {
      if (processPayment()) break;
  }
  

  Uses for to retry failed transactions up to 3 times.

3. while Loop: Condition-Controlled Repetition

Syntax:

while (condition) {
    // Code to repeat
}

Key Points:

• Test before execution: May never run if condition is false initially.
• Infinite loop risk: If condition never becomes false (e.g., missing i++).

Example: Sum of Digits

int num = 1234, sum = 0;
while (num != 0) {
    sum += num % 10;  // Extract last digit
    num /= 10;        // Remove last digit
}
printf("Sum = %d", sum);  // Output: 10

Trace Table:

Visualization:

Real-World Tie:

• Daraz’s Order Fulfillment Queue:

  while (ordersInQueue > 0) {
      processOrder();
      ordersInQueue--;
  }
  

  Uses while to handle orders until the queue is empty.

4. do-while Loop: Post-Test Repetition

Syntax:

do {
    // Code to repeat
} while (condition);

Key Difference:

• Guarantees at least one execution (test happens after).
• Useful for menus or input validation.

Example: Simple Menu

int choice;
do {
    printf("\n1. Deposit\n2. Withdraw\n3. Exit\n");
    scanf("%d", &choice);
    // Process choice...
} while (choice != 3);

Trace Table:

Visualization:

flowchart TD
    A["Start"] --> B["Show Menu"]
    B --> C{"choice == 3?"}
    C -->|"No"| D["Process Choice"]
    D --> B
    C -->|"Yes"| E["Exit"]

Real-World Tie:

• Ncell’s Top-Up Retry:

  do {
      if (validatePin()) break;
      printf("Invalid PIN. Retry.\n");
  } while (1);  // Infinite until valid
  

  Uses do-while to ensure PIN validation runs at least once.

5. Nested Loops: Multi-Layered Repetition

Definition: A loop inside another loop. The inner loop completes all iterations for each outer loop iteration.

Example: Multiplication Table

for (int i=1; i<=3; i++) {          // Outer loop (rows)
    for (int j=1; j<=3; j++) {      // Inner loop (columns)
        printf("%d ", i*j);
    }
    printf("\n");
}

Output:

1 2 3
2 4 6
3 6 9

Trace Table:

Visualization:

Real-World Tie:

• Bank Loan Interest Calculation:

  for (int year=1; year<=5; year++) {      // Outer: years
      float interest = principal * rate;
      principal += interest;
      printf("Year %d: %.2f\n", year, interest);
  }
  

  Nested loops could extend this to calculate monthly interest within each year.

6. Pattern Generation with Nested Loops

Common Patterns:

1. Right-Angled Triangle:

   for (int i=1; i<=4; i++) {
       for (int j=1; j<=i; j++) {
           printf("* ");
       }
       printf("\n");
   }
   

   Output:

   *
   * *
   * * *
   * * * *
   

2. Pyramid:

   for (int i=1; i<=5; i++) {
       for (int j=1; j<=5-i; j++) printf(" ");
       for (int j=1; j<=2*i-1; j++) printf("*");
       printf("\n");
   }
   

   Output:

      *
     ***
    *****
   *******
   

Exam Tip: For pattern questions, identify the logic for rows and columns separately. Use printf(" ") for spaces and printf("*") for stars.

7. Prime Number Check with Loops

Algorithm:

1. Test divisibility from 2 to sqrt(n).
2. If any divisor divides n, it’s not prime.

#include <math.h>
int isPrime(int n) {
    if (n <= 1) return 0;
    for (int i=2; i<=sqrt(n); i++) {
        if (n % i == 0) return 0;
    }
    return 1;
}

Trace for n=17:

Output: 1 (prime).

Real-World Tie:

• NEPSE’s Stock Validity Check:

  if (!isPrime(stockCode)) {
      printf("Invalid stock code!\n");
  }
  

  Uses prime checks to validate unique stock identifiers.

8. Loop Control Statements

Example with break:

for (int i=1; i<=5; i++) {
    if (i == 3) break;  // Exit at i=3
    printf("%d ", i);
}
// Output: 1 2

9. Common Pitfalls & How to Avoid Them

10. Comparison of Loop Types

11. Exam Tip: How to Score Full Marks

1. Loop Structure:

   • Always include initialization, condition, and update (for for).
   • For while/do-while, clearly state the termination condition.

2. Pattern Questions:

   • Break down rows/columns: Ask, “How many stars/spaces per row?”
   • Use nested loops: Outer loop for rows, inner for columns.
   • Example Trace: Show the first 2–3 iterations in your answer.

3. Prime Checks:

   • Optimize: Test up to sqrt(n), not n/2.
   • Edge Cases: Handle n <= 1 separately.

4. Avoid Common Mistakes:

   • Infinite loops: Ensure the loop variable changes.
   • Off-by-one: Test with n=1 and n=2.

5. Real-World Connection:

   • Link loops to transaction retries (eSewa), inventory checks (Daraz), or interest calculations (banks).
   • Example: “This for loop retries a failed payment like eSewa does.”

12. Practice Questions (Exam-Style)

1. Write a program to print:

   1
   1 2
   1 2 3
   1 2 3 4
   

   Hint: Use nested loops with printf("%d ", j) inside the inner loop.

2. Check if a number is a palindrome (e.g., 121) using loops. Hint: Reverse the number and compare.

3. Calculate the sum of even numbers from 1 to n using a while loop.

4. Print the following pattern:

   10101
   0101
   101
   01
   1
   

   Hint: Use a counter to alternate 1 and 0.

13. Model Answer: Prime Number Check

Question: Write a C program to check if a number is prime or composite.

#include <stdio.h>
#include <math.h>

int main() {
    int n, is_prime = 1;
    printf("Enter a number: ");
    scanf("%d", &n);

    if (n <= 1) {
        is_prime = 0;
    } else {
        for (int i = 2; i <= sqrt(n); i++) {
            if (n % i == 0) {
                is_prime = 0;
                break;
            }
        }
    }

    if (is_prime) {
        printf("%d is a prime number.\n", n);
    } else {
        printf("%d is a composite number.\n", n);
    }
    return 0;
}

Trace for n=17:

Output: 17 is a prime number.

14. In the Real World

1. eSewa’s Payment Retry System:

   • Loop Type: for or while
   • How: Retries failed transactions up to 3 times before notifying the user.
   • Code Snippet:

     for (int retry=0; retry<3; retry++) {
         if (processPayment()) break;
         printf("Retry %d...\n", retry+1);
     }
     

2. Daraz’s Inventory Management:

   • Loop Type: Nested for loops
   • How: Checks stock levels across all product categories daily.
   • Example:

     for (int category=0; category<10; category++) {
         for (int product=0; product<100; product++) {
             if (stock[category][product] < 5) reorder();
         }
     }
     

3. Ncell’s Top-Up Validation:

   • Loop Type: do-while
   • How: Ensures the user enters a valid PIN before processing.
   • Example:

     do {
         printf("Enter PIN: ");
         scanf("%d", &pin);
     } while (!validatePIN(pin));
     

4. Bank Loan Interest Calculation:

   • Loop Type: Nested loops
   • How: Calculates monthly interest for each year of the loan term.
   • Example:

     for (int year=0; year<loanTerm; year++) {
         for (int month=0; month<12; month++) {
             monthlyInterest = principal * rate / 12;
             principal += monthlyInterest;
         }
     }
     

15. Summary Checklist for Exams

• Can you differentiate for, while, and do-while loops?
• Can you write nested loops to generate patterns?
• Can you trace a loop’s execution step-by-step?
• Can you optimize a prime check using sqrt(n)?
• Can you connect loops to real-world systems (e.g., eSewa, Daraz)?