Lab 10 – Active Functions & Recursion

PSUC Lab 10 — Modular Programming & Call Stack

Active Logic: Functions & Recursion

Master modular functions in C: function signatures, pass-by-value vs pass-by-reference, recursive base cases (Euclidean GCD, Fibonacci), prime generators, and custom sorting callbacks.

Function & Recursion Rules

Concept	Rule / Formula	Key Trap / Pitfall
Function Signature	`returnType name(params)`	Return type mismatch causes implicit conversion warning
Base Case	`if (b == 0) return a;`	Missing base case causes Stack Overflow!
Euclidean GCD	`GCD(b, a % b)`	Calculates greatest common divisor recursively
Recursive Fibo	`Fibo(n-1) + Fibo(n-2)`	Base cases: `n == 0 → 0, n == 1 → 1`

🎯 Learning Philosophy: Active Logic Building

Test your function logic across 3 Interactive Learning Modes:

🧠 Tab 1 (Logic & Hints): Function call stack & recursion trees.
🧩 Tab 2 (Logic Puzzle): Complete missing recursive base cases & call trees!
💻 Tab 3 (C Solution): Reference verified C code solutions.

Solve function puzzles before inspecting C reference code!

Exercise 1 of 5

Factorial Function `Fact(n)`

Computes factorial of a number using a dedicated modular function long long Fact(int n).

Modular Function Signature

Signature: long long Fact(int n)
Return type long long prevents 32-bit integer overflow when n > 12.
Base case / Init: f = 1; for (i = 1; i <= n; i++) f *= i;

Interactive Logic Hints

💡 Hint 1: What is Fact(0)? ▼

By mathematical definition, 0! = 1! The loop for n = 0 runs 0 times and returns 1!

🧩 Complete Factorial Function

Fact(int n) {
  long long f = 1;
  for (int i = 1; i <= n; i++) f i;
   f;
}

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🔢 Factorial Function Calculator

Enter N (0-20):

Factorial result...

fact_func.cReference C Code

#include <stdio.h>

long long Fact(int n) {
    long long f = 1;
    for (int i = 1; i <= n; i++) f *= i;
    return f;
}

int main() {
    int num = 5;
    printf("%d! = %lld\n", num, Fact(num));
    return 0;
}

Exercise 2 of 5

Recursive Greatest Common Divisor `GCD(a, b)`

Computes the greatest common divisor of two integers using Euclid's recursive algorithm.

Euclidean Recursion Rule

Base Case: if (b == 0) return a;
Recursive Step: return GCD(b, a % b);
Example: GCD(48, 18) → GCD(18, 12) → GCD(12, 6) → GCD(6, 0) = 6

Interactive Logic Hints

💡 Hint 1: What is the relation between GCD and LCM? ▼

LCM(a, b) = (a × b) / GCD(a, b)!

🧩 Complete Recursive GCD Function

int GCD(int a, int b) {
if (b 0) return ;
return GCD(b, a b);
}

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🧮 Recursive GCD Visualizer

Number A:

Number B:

Recursive stack step trace...

recursive_gcd.cReference C Code

#include <stdio.h>

int GCD(int a, int b) {
    if (b == 0) return a;
    return GCD(b, a % b);
}

int main() {
    int a = 48, b = 18;
    printf("GCD(%d, %d) = %d\n", a, b, GCD(a, b));
    return 0;
}

Exercise 3 of 5

Prime Checker Function & First N Primes

Uses a modular helper function bool isPrime(int n) to print the first N prime numbers.

Modular Helper Function

Function: bool isPrime(int n)
Trial division: for (i = 2; i * i <= n; i++) if (n % i == 0) return false;
Generates N primes by calling isPrime(num) in a generator loop.

Interactive Logic Hints

💡 Hint 1: Why isolate isPrime() into a separate function? ▼

Modularity! The main loop stays clean and easily readable: if (isPrime(num)) print(num);

🧩 Complete Prime Helper Function

bool isPrime(int n) {
  if (n <= 1) return ;
  for (int i = 2; i * i <= n; i++) {
    if (n i == 0) return false;
  }
  return ;
}

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🔢 Prime Generator Engine

Generate First N Primes (N = 1 to 30):

Primes output...

prime_func.cReference C Code

#include <stdio.h>
#include <stdbool.h>

bool isPrime(int n) {
    if (n <= 1) return false;
    for (int i = 2; i * i <= n; i++) {
        if (n % i == 0) return false;
    }
    return true;
}

int main() {
    int target = 10, count = 0, num = 2;
    printf("First %d Primes: ", target);
    while (count < target) {
        if (isPrime(num)) { printf("%d ", num); count++; }
        num++;
    }
    printf("\n");
    return 0;
}

Exercise 4 of 5

Recursive Fibonacci `Fibo(n)`

Computes N-th Fibonacci term recursively: F(n) = F(n-1) + F(n-2).

Recursive Fibonacci Tree

Base cases: if (n == 0) return 0; if (n == 1) return 1;
Recurrence: return Fibo(n - 1) + Fibo(n - 2);

Interactive Logic Hints

💡 Hint 1: What is the time complexity of naive recursive Fibonacci? ▼

Exponential O(2ⁿ) time! Because it recalculates duplicate subproblems multiple times!

🧩 Complete Recursive Fibonacci Base Cases

int Fibo(int n) {
  if (n 0) return 0;
  if (n == 1) return ;
  return Fibo(n - 1) Fibo(n - 2);
}

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🌀 Recursive Fibonacci Tree Visualizer

N-th Term (0-15):

Fibonacci tree status...

recursive_fibo.cReference C Code

#include <stdio.h>

int Fibo(int n) {
    if (n == 0) return 0;
    if (n == 1) return 1;
    return Fibo(n - 1) + Fibo(n - 2);
}

int main() {
    int n = 7;
    printf("Fibonacci(%d) = %d\n", n, Fibo(n));
    return 0;
}

Exercise 5 of 5

Custom Name Sorting using `Sort()` & `Compare()`

Sorts an array of strings alphabetically using custom modular functions Sort() and Compare().

Callback / Helper Logic

Compare(s1, s2) wraps strcmp(s1, s2). Returns > 0 if s1 > s2.
Sort(names, n) uses Bubble Sort with strcpy() for string swaps.

Interactive Logic Hints

💡 Hint 1: Can we swap strings using assignment = ? ▼

No! In C, array assignment s1 = s2 is invalid! You MUST use strcpy(temp, s1); strcpy(s1, s2); strcpy(s2, temp);!

🧩 Complete Name Swap Logic

if (Compare(names[j], names[j + 1]) 0) {
  char temp[50];
  (temp, names[j]);
  strcpy(names[j], names[j + 1]);
  strcpy(names[j + 1], temp);
}

Select functions above and click Check!

🔤 Alphabetical Name Sorting Engine

Names (comma separated):

Sorted names output...

name_sort.cReference C Code

#include <stdio.h>
#include <string.h>

int Compare(char s1[], char s2[]) { return strcmp(s1, s2); }

void Sort(char names[][50], int n) {
    char temp[50];
    for (int i = 0; i < n - 1; i++) {
        for (int j = 0; j < n - i - 1; j++) {
            if (Compare(names[j], names[j + 1]) > 0) {
                strcpy(temp, names[j]);
                strcpy(names[j], names[j + 1]);
                strcpy(names[j + 1], temp);
            }
        }
    }
}

int main() {
    char names[5][50] = {"Rahul", "Abhay", "Priya", "Rohan", "Ananya"};
    Sort(names, 5);
    printf("Sorted Names:\n");
    for (int i = 0; i < 5; i++) printf("%s\n", names[i]);
    return 0;
}

Knowledge Check

Test Your Functions & Recursion Mastery

Question 1 of 5

Loading question...

Active Logic: Functions & Recursion

Function & Recursion Rules

🎯 Learning Philosophy: Active Logic Building

Factorial Function Fact(n)

Modular Function Signature

Interactive Logic Hints

🧩 Complete Factorial Function

🔢 Factorial Function Calculator

Recursive Greatest Common Divisor GCD(a, b)

Euclidean Recursion Rule

Interactive Logic Hints

🧩 Complete Recursive GCD Function

🧮 Recursive GCD Visualizer

Prime Checker Function & First N Primes

Modular Helper Function

Interactive Logic Hints

🧩 Complete Prime Helper Function

🔢 Prime Generator Engine

Recursive Fibonacci Fibo(n)

Recursive Fibonacci Tree

Interactive Logic Hints

🧩 Complete Recursive Fibonacci Base Cases

🌀 Recursive Fibonacci Tree Visualizer

Custom Name Sorting using Sort() & Compare()

Callback / Helper Logic

Interactive Logic Hints

🧩 Complete Name Swap Logic

🔤 Alphabetical Name Sorting Engine

Test Your Functions & Recursion Mastery

Factorial Function `Fact(n)`

Recursive Greatest Common Divisor `GCD(a, b)`

Recursive Fibonacci `Fibo(n)`

Custom Name Sorting using `Sort()` & `Compare()`