The document provides C programming examples for various tasks including calculating factorial, power of a number, counting digits, summing natural numbers, calculating the GCD, and finding Fibonacci numbers using both recursion and iteration. Each task is accompanied by explanations and sample codes demonstrating the implementation of recursive and iterative approaches. The document serves as a comprehensive guide for learning algorithms in C programming.

1. Q) C program to findfactorial of number usingrecursionas well as iteration
𝑓𝑎𝑐𝑡𝑜𝑟𝑖𝑎𝑙(𝑛) = {
𝑟𝑒𝑡𝑢𝑟𝑛 1 ; 𝑖𝑓 𝑛 == 0 𝑜𝑟 𝑛 == 1
𝑛
𝑟𝑒𝑡𝑢𝑟𝑛 𝑛 ∗ 𝑓𝑎𝑐𝑡𝑜𝑟𝑖𝑎𝑙( 𝑛 − 1); 𝑖𝑓 𝑛 > 1
Using loops:
factorial=1;
while(n>1)
{
factorial=factorial*n;
n=n-1;
}
Q) Calculate power of a number program in c usingRecursion and Iteration
𝑝𝑜𝑤𝑒𝑟(𝑏, 𝑒) = {
𝑟𝑒𝑡𝑢𝑟𝑛 1; 𝑖𝑓 𝑒 == 0
𝑛
𝑟𝑒𝑡𝑢𝑟𝑛 𝑏 ∗ 𝑝𝑜𝑤𝑒𝑟( 𝑏, 𝑒 − 1); 𝑖𝑓 𝑒 > 0
Explanationwithexample:
53 = 5 ∗ 52 power(5,3) = 5*power(5,2)
power(5,3) = 5 * power(5,3-1) = 5 * power(5,2) = 5*25 = 125
power(5,2) = 5 * power(5,2-1) = 5 * power(5,1) = 5*5 =25
power(5,1) = 5 * power(5,1-1) = 5 * power(5,0) = 5*1 = 5
power(5,0) = 1
Using loops:
power=1;
while(e>0)
{
power=power*b;
e=e-1;
}
Q) Write a C program to count digitsof a number usingRecursion and Iteration.
𝑐𝑜𝑢𝑛𝑡(𝑛) = {
𝑟𝑒𝑡𝑢𝑟𝑛 0; 𝑖𝑓 𝑛 == 0
𝑛
𝑟𝑒𝑡𝑢𝑟𝑛 1 + 𝑐𝑜𝑢𝑛𝑡( 𝑛/10); 𝑖𝑓 𝑛 > 0
Explanationwithexample:
count(872) = 1+count(872/10) = 1+count(87) = 1+2=3
count(87) = 1+count(87/10) = 1+count(8) =1+1 = 2
count(8) = 1+count(8/10) = 1+count(0) =1+0 =1
count(0) = 0
Using loops:
count = 0;
while(n>0)
{
count = count+1;
n=n/10;
}
Q) Write a C program to find sum of firstn natural numbers using Recursion.
𝑠𝑢𝑚(𝑛) = {
𝑟𝑒𝑡𝑢𝑟𝑛 1; 𝑖𝑓 𝑛 == 1
𝑛
𝑟𝑒𝑡𝑢𝑟𝑛 𝑛 + 𝑠𝑢𝑚( 𝑛 − 1); 𝑖𝑓 𝑛 > 1
Explanationwithexample:
sumof first5 natural numbers=
1+2+3+4+5

2. 5+4+3+2+1
5+sum of first4 natural numbers
sumof first4 natural numbers=
4+sum of first3 natural numbers
sumof first3 natural numbers=
3+sum of first2 natural numbers
sumof first2 natural numbers =
2+sum of first1 natural numbers
sumof first1 natural numbers= 1
sum(5) = 5+sum(5-1) = 5+ sum(4) = 10+5 = 15
sum(4) = 4+sum(4-1) = 4+ sum(3) = 6+4 = 10
sum(3) = 3+sum(3-1) = 3+ sum(2) = 3+3 = 6
sum(2) = 2+sum(2-1) = 2+ sum(1) = 2+1 = 3
sum(1) = 1
Using loops:
sum=0
while(n>0)
{
sum=sum+n;
n=n-1;
}
Q. C program to print sum of digitsof a given numberusing recursion
𝑠𝑢𝑚(𝑛) = {
𝑟𝑒𝑡𝑢𝑟𝑛 0; 𝑖𝑓 𝑛 == 0
𝑛
𝑟𝑒𝑡𝑢𝑟𝑛 𝑛%10 + 𝑠𝑢𝑚( 𝑛/10); 𝑖𝑓 𝑛 > 0
Explanationwithexample:
sum(872) = 872%10 + sum(872/10) = 2+sum(87) = 2+15= 17
sum(87) = 87%10 + sum (87/10) = 7+sum(8) = 7+8 = 15
sum(8) = 8%10 + sum (8/10) = 8+sum(0) = 8+0 = 8
sum(0) = 0
Q. Write a C program to findnth term in Fibonacci Seriesusing Recursion.
𝑓𝑖𝑏(𝑛) = {
𝑟𝑒𝑡𝑢𝑟𝑛 0; 𝑖𝑓 𝑛 == 1
𝑟𝑒𝑡𝑢𝑟𝑛 1; 𝑖𝑓 𝑛 == 2
𝑟𝑒𝑡𝑢𝑟𝑛 𝑓𝑖𝑏( 𝑛 − 1) + 𝑓𝑖𝑏( 𝑛 − 2); 𝑖𝑓 𝑛 > 2
Q. C program to find out the GCD (GreatestCommonDivisor )ofthe two numbers usingrecursion
𝑔𝑐𝑑 (𝑎, 𝑏) = {
𝑟𝑒𝑡𝑢𝑟𝑛 𝑎; 𝑖𝑓 𝑏%𝑎 == 0
𝑛
𝑟𝑒𝑡𝑢𝑟𝑛 gcd( 𝑏%𝑎, 𝑎) ; 𝑖𝑓 𝑏%𝑎 ! = 0
Explanationwithexample:
Sample Input:8 12
Sample Output:4
8 ) 12 ( 1
8
---------
4 ) 8 ( 2
8
-------
0

3. --------
gcd(8,12) =gcd(12%8 , 8) = gcd( 4, 8) = 4
gcd(4,8) = 4
Full Program:
#include <stdio.h>
intprint(intn)
{
if(n<= 2)
printf("%d",n%2);
else
{
print(n/2);
printf("%d",n%2);
}
}
intmain()
{
int n;
printf("enteranumber");
scanf("%d",&n);
print(n);
}
Q. Write a C program to findthe first uppercase letterin the givenstring usingrecursion.Sample
Input : kl University
Sample Output: U
𝑠𝑒𝑎𝑟𝑐ℎ(𝑠𝑡𝑟, 𝑖) = {
𝑟𝑒𝑡𝑢𝑟𝑛 − 1; 𝑖𝑓 𝑠𝑡𝑟[𝑖] == ′0′
𝑟𝑒𝑡𝑢𝑟𝑛 𝑖; 𝑖𝑓 𝑠𝑡𝑟[𝑖] == ′𝑈′
𝑟𝑒𝑡𝑢𝑟𝑛 𝑠𝑒𝑎𝑟𝑐ℎ( 𝑠𝑡𝑟, 𝑖 + 1); 𝑖𝑓 𝑠𝑡𝑟[𝑖] ! = ′𝑈′
Q) write C program to calculate lengthof the string usingRecursion
𝑙𝑒𝑛(𝑠𝑡𝑟) = {
0 𝑖𝑓 𝑠𝑡𝑟[0] == ′0′
𝑛
1 + len(string left after removing first character) 𝑖𝑓 𝑠𝑡𝑟[0] ! = ′0′
Explanationwithexample:
lengthof string“abc” = 1+ lengthof string“bc”
lengthof string“bc” = 1+ lengthof string“c”
lengthof string“c” = 1+ lengthof string“0”
lengthof string“0” = 0
Q) Write a program in C to count numberof divisorsof a givennumberusing recursion
𝑐𝑜𝑢𝑛𝑡(𝑛, 𝑖) = {
𝑟𝑒𝑡𝑢𝑟𝑛 1; 𝑖𝑓 𝑖 == 𝑛
𝑟𝑒𝑡𝑢𝑟𝑛 1 + 𝑐𝑜𝑢𝑛𝑡( 𝑛, 𝑖 + 1) ; 𝑖𝑓 (𝑛%𝑖 == 0)
𝑟𝑒𝑡𝑢𝑟𝑛 𝑐𝑜𝑢𝑛𝑡( 𝑛, 𝑖 + 1); 𝑖𝑓(𝑛%𝑖 ! = 1)
Using loops:
for(i=1;i<=n;i++)
{
If(n%i ==0)
{
count=count+1;
}
}

4. Recursive programtocheck whetheragivennumberisprime orcomposite.
#include <stdio.h>
intcount(intn,inti)
{
if(i == n)
return1;
else if(n%i==0)
return1+count(n,i+1); //1+count of divisorsfromi+1 to n if i isdivisor
else if(n%i!=0)
returncount(n,i+1); // count of divisorswontchange if i isnot divisor
}
intmain()
{
int n;
printf("enteranumber");
scanf("%d",&n);
int c=count(n,1);//count of divisorsfrom1 to n
if(c== 2)
printf("prime");
else
printf("composite");
}
Q. C program to displays integers100 through 1 usingRecursion and Iteration
𝑑𝑖𝑠𝑝𝑙𝑎𝑦(𝑛) = {
𝑝𝑟𝑖𝑛𝑡𝑓(%d, 𝑛); 𝑖𝑓 𝑛 == 1
𝑛
𝑝𝑟𝑖𝑛𝑡𝑓(%d, 𝑛); 𝑑𝑖𝑠𝑝𝑙𝑎𝑦( 𝑛 − 1); 𝑖𝑓 𝑛 > 1
Q. Write a program in C to converta decimal number to binary usingrecursion.
Sample Input : 66
Sample Output: 1000010
𝑑𝑒𝑐𝑡𝑜𝑏𝑖𝑛(𝑛) = {
𝑝𝑟𝑖𝑛𝑡𝑓("%d", 𝑛%2); 𝑖𝑓 𝑛 ≤ 2
𝑛
𝑑𝑒𝑐𝑡𝑜𝑏𝑖𝑛( 𝑛/2); 𝑝𝑟𝑖𝑛𝑡𝑓("%d", 𝑛%2); 𝑖𝑓 𝑛 > 2
Full program
#include <stdio.h>
intdectobin(intn)
{
if(n<= 2)
printf("%d",n%2);
else
{
dectobin(n/2);
printf("%d",n%2);
}
}
intmain()
{
int n;
printf("enteranumber");
scanf("%d",&n);
dectobin(n);
}

5. RecursionStackof factorial of 3
intfactorial(1)
{
if(1== 0 || 1==1)
return1;
else if(n>1)
returnn*factorial(n-1);
}
intfactorial(2)
{
if(2== 0 || 2 ==1)
return1;
else if(2>1)
return2*factorial(2-1);
}
intfactorial(3)
{
if(3== 0 || 3==1)
return1;
else if(3>1)
return3*factorial(3-1);
}
intmain()
{
int n,fact;
printf("enteranumber");
scanf("%d",&n);
fact=factorial(n);//factorial(3)
printf("factorialof %dis%d",n,fact);
}

6. Recursionstackof 4 th term of Fibonacci
intfib(2)
{
if( 2 == 1)
return0;
else if(2== 2)
return1;
else
returnfib(n -1)+fib(n-2);
}
intfib(1)
{
if( n == 1)
return0;
else if(n==2)
return1;
else
returnfib(n -1)+fib(n-2);}
intfib(2)
{
if( 2 == 1)
return0;
else if(2== 2)
return1;
else
returnfib(n -1)+fib(n-2);
}
intfib(3)
{
if( 3 == 1)
return0;
else if(3== 2)
return1;
else
returnfib(3-1)+fib(3-2);
}
intfib(4)
{
if( 4 == 1)
return0;
else if(4== 2)
return1;
else
returnfib(4-1)+fib(4-2);
}
intmain()
{
int n,term;
printf("entern value");
scanf("%d",&n);
term=fib(n); //fib(4)
printf("%dthtermis%d",n,term);
}

7. C program to findfactorial of number usingrecursion as well as iteration ,
Calculate power of a number program in c usingRecursion and Iteration,Write a C program to
count digitsof a numberusing Recursionand Iteration, Write a C program to find sum of firstn
natural numbers usingRecursion, C program to printsum of digits ofa givennumber using
recursion,Write a C program to findnth term in Fibonacci SeriesusingRecursion, C program to
findout the GCD (GreatestCommonDivisor )ofthe two numbersusing recursion,
Write a C program to find the first upper case letterin the givenstring using recursion, write C
program to calculate lengthof the string using Recursion,
Write a program in C to count number of divisorsof a givennumber usingrecursion, Recursive
program to checkwhetheragivennumberisprime orcomposite,
C program to displaysintegers100 through 1 using Recursionand Iteration,Write a program in C
to convert a decimal numberto binary usingrecursion,
RecursionStackof factorial of 3 Recursionstackof 4th term of Fibonacci