How can I use recursion instead of loops? For the functions? #include <cstdio> #

Question

How can I use recursion instead of loops? For the functions?

#include <cstdio>
#include <iostream>
using namespace std;
//======================================================================
// next(n) returns the number that follows n in the hailstonesequence.
// For example, next(7) = 22 and next(22) = 1 and next(1) = 1.
//======================================================================

int next(int n)
{
       if (n == 1)
    {
    return n;
    }
       else if (n%2==0)
    {
    return n=n/=2;
    }
       else
    {
    return n=3*n+1;
   }
}

//======================================================================
// sequence(n) takes the integer n and outputs the integer in the
// hailstorm sequence starting with the user input and ends when the
// sequence equals 1.
//======================================================================

void sequence(int n)
{
cout << n << " ";
if(n!=1)
{
n=next(n);
sequence(n);
}
}

//======================================================================
// lenght(n) takes the integer n and counts all the numbers that are in
// the hailstorm sequence and adds them up.
//======================================================================

int length(int n)
{
     if ( n == 1) return 1;
     else return 1 + length(next(n));
}

//======================================================================
// large(n) takes the integer n and checks to see if the number islarger
// than n and then returns the largest number in the hailstormsequence
//======================================================================

int largest(int n)
{
int maxint=1;
while(n!=1)
{
if(maxint < n) maxint = n;
n = next(n);
}
return maxint;
}

int main(int argc, char** argv)
{
int n;
printf("What number shall I start with? ");
scanf("%i", &n);
printf("The hailstone sequence is starting with %i is ", n);
sequence(n);
printf(" ");
printf("The lenght of the sequence is %i ", length(n));
printf("The largest number in the sequence is %i ", largest(n));
printf("The longest hailstone sequence starting with a number up to %i has length %i. ", n, length(n));
printf("The longest hailstone sequence starting with a number up to %i begins with %i. ", n, largest(n));
return 0;
}

Explanation / Answer

int largest(int n) is the only function where we are using loops , the following is the recurssive version of it

code with loop:

int largest(int n)
{
int maxint=1;
while(n!=1)
{
if(maxint < n) maxint = n;
n = next(n);
}
return maxint;
}

code:

int largest1(int n) //largest of the sequence that start with n
{
if(n==1) // if n ==1 , then it have only one element 1, return it
return 1;
// else, largest of the sequence = maximum(n, largest of the sequence that start with next(n))

int maxint = largest1(next(n)); // largest of the sequenc that start with next(n) and store it in maxint
return maxint>n? maxint:n; // return maximum of n, maxint
}

Total code with both recursion and loops :

#include <cstdio>
#include <iostream>
using namespace std;
//======================================================================
// next(n) returns the number that follows n in the hailstonesequence.
// For example, next(7) = 22 and next(22) = 1 and next(1) = 1.
//======================================================================
int next(int n)
{
if (n == 1)
{
return n;
}
else if (n%2==0)
{
return n=n/=2;
}
else
{
return n=3*n+1;
}
}
//======================================================================
// sequence(n) takes the integer n and outputs the integer in the
// hailstorm sequence starting with the user input and ends when the
// sequence equals 1.
//======================================================================
void sequence(int n)
{
cout << n << " ";
if(n!=1)
{
n=next(n);
sequence(n);
}
}
//======================================================================
// lenght(n) takes the integer n and counts all the numbers that are in
// the hailstorm sequence and adds them up.
//======================================================================
int length(int n)
{
if ( n == 1) return 1;
else return 1 + length(next(n));
}
//======================================================================
// large(n) takes the integer n and checks to see if the number islarger
// than n and then returns the largest number in the hailstormsequence
//======================================================================

//code with loop

int largest(int n)
{
int maxint=1;
while(n!=1)
{
if(maxint < n) maxint = n;
n = next(n);
}
return maxint;
}

//code with recursion
int largest1(int n) //largest of the sequence that start with n
{
if(n==1) // if n ==1 , then it have only one element 1, return it
return 1;
// else, largest of the sequence = maximum(n, largest of the sequence that start with next(n))

int maxint = largest1(next(n)); // largest of the sequenc that start with next(n) and store it in maxint
return maxint>n? maxint:n; // return maximum of n, maxint
}
int main(int argc, char** argv)
{
int n;
printf("What number shall I start with? ");
scanf("%i", &n);
printf("The hailstone sequence is starting with %i is ", n);
sequence(n);
printf(" ");
printf("The lenght of the sequence is %i ", length(n));
printf("The largest number in the sequence is %i ", largest(n));
printf("The largest number in the sequence is %i ", largest1(n));
printf("The longest hailstone sequence starting with a number up to %i has length %i. ", n, length(n));
printf("The longest hailstone sequence starting with a number up to %i begins with %i. ", n, largest(n));
return 0;
}

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