recursive functions

recursion.c

@@ -14,12 +14,30 @@
 #include<stdio.h>
 
 
-// n! = 0               if n = 0  (base case)
+// n! = 1               if n = 0  (base case)
 // n! = n * (n-1)!      otherwise (recursive case)
 
 // Function to calculate factorial of n.
 int factorial(int n) {
+    if (n == 0)
+        return 1;
+    else
+        return n * factorial(n - 1);
 }
+// Factorial using recursion is calculated like so:
+// 6! = 6 * factorial(5)
+//    = 6 * 5 * factorial(4)
+//    = 6 * 5 * 4 * factorial(3)
+//    = 6 * 5 * 4 * 3 * factorial(2)
+//    = 6 * 5 * 4 * 3 * 2 * factorial(1)
+//    = 6 * 5 * 4 * 3 * 2 * 1 * factorial(0)
+//    = 6 * 5 * 4 * 3 * 2 * 1 * 1
+//    = 6 * 5 * 4 * 3 * 2 * 1
+//    = 6 * 5 * 4 * 3 * 2
+//    = 6 * 5 * 4 * 6
+//    = 6 * 5 * 24
+//    = 6 * 120
+// 6! = 720
 
 
 // Finbonacci series -> 1, 1, 2, 3, 5, 8, 13, 21...
@@ -30,15 +48,43 @@ int factorial(int n) {
 // Function to calculate nth fibonacci number
 // using recursion
 int fibonacci(int n) {
+    if (n <= 2)
+        return 1;
+    return fibonacci(n - 2) + fibonacci(n - 1);
 }
 
 // Function to calculate nth fibonacci number
 // without using recursion
 int fibonacci_loop(int n) {
+    if (n <= 2)
+        return 1;
+    int i;
+    // Initialize second_last variable with the 
+    // first element of the fibonacci series and 
+    // last variable with second element of the
+    // series.
+    int last = 1;
+    int second_last = 1;
+    // Current variable to keep track of n-th
+    // fibonacci number.
+    int current;
+
+    // Update last and second_last variable in 
+    // each iteration of loop.
+    // Set second_last variable equal to last and 
+    // last equal to current variable.
+    for (i = 3; i <= n; i++) {
+        current = second_last + last;
+        second_last = last;
+        last = current;
+    }
+
+    // current element is n-th fibonacci number
+    return current;
 }
 
 int main(void) {
     printf("Factorial of 5 -> %d\n", factorial(5));
-    printf("Fibonacci of 7 -> %d\n", fibonacci(7));
-    printf("Fibonacci of 7 -> %d\n", fibonacci_loop(7));
+    printf("7th number in Fibonacci series -> %d\n", fibonacci(7));
+    printf("8th number in Fibonacci series -> %d\n", fibonacci_loop(8));
 }