// Next(n) returns the number that follows n in a hailstone sequence.
// For example, next(7) = 22 and next(8) = 4.
//
// Next requires n > 1, since there is no number that follows 1.
   int next(int n)
   {  if(n > 1)
      {
         if((n%2)==0)
         {
            n = n/2;
         }

         else
         {
            n = 3*n+1;
         }
      }
      return n;
   }

   //writeHailstoneSequence returns the
   void writeHailstoneSequence(int n)
   {
      int m = n;
      if(m == 1)
      {
         printf("%i", m);
      }
      else
      {
         printf("%i ", m);
         writeHailstoneSequence(next(n));
      }

   }

   //reads int n from the 'next' function
   //counts every time we calculate in
   //'next' and returns that value
   int lengthHailstone(int n)
   {
      int l = n;
      if(l == 1)
      {
         return 1;
      }
      else
      {

         return lengthHailstone(next(n))+1;
      }

   }

   //calculates every int n and compares
   //it to the int largestValue and if n
   //is larger then largestValue takes
   //same value as n
   int largestHailstoneValue(int n)
   {
      int v = n;
      if(v == 1)
      {
         return 1;
      }
      else
      {
         return max(largestHailstoneValue(next(n)), v);
      }

   }

   //if int n is 1 then returns 1
   //calculates the longest length
   //seqeunce from 1 to n
   int longestLength(int n)
   {
      if(n > 1)
      {
         return max(lengthHailstone(n), longestLength(n-1));
      }
      else
      {
         return 1;
      }
   }

   //uses lengthHailstone function to
   //compare each int up to int n to find
   //the first value of the longest sequence
   int firstValueBiggestSequence(int n)
   {
      int firstValue = 1;
      for(int i = 2; i <= n; i++)
      {
         if(lengthHailstone(i) > lengthHailstone(firstValue))
            firstValue = i;

      }
      return firstValue;
   }

   //uses largestHailstoneValue function
   //to find the largest value from 1
   // to n using a loop from i(1) to n
   int biggestOverallValue(int n)
   {
      int biggestValue = 0;
      for(int i = 1; i <= n; i++)
      {
         if(biggestValue < largestHailstoneValue(i))
         {
            biggestValue = largestHailstoneValue(i);
         }
      }
      return biggestValue;


   }

   int main()
   {
      int n;
      printf("What number shall I start with?\n");
      scanf("%i", &n);
      printf("The hailstone sequence starting at %i is: \n", n);
      writeHailstoneSequence(n);
      printf("\nThe length of the sequence is %i.\n", lengthHailstone(n));
      printf("The largest number in the sequence is %i.\n", largestHailstoneValue(n));
      printf("The longest hailstone sequence starting with a number up to ");
      printf("%i has length %i.\n", n, longestLength(n));
      printf("The longest hailstone sequence starting with a number up to ");
      printf("%i begins with %i.\n", n, firstValueBiggestSequence(n));
      printf("The largest value in any hailstone sequence starting with ");
      printf("a number up to %i is %i.\n", n, biggestOverallValue(n));
      return 0;
   }