Question

Data Structures: Abstraction and Design Using Java Elliot B. Koffman; Paul A. T. Wolfgang ch 5 review questions 5 and 7

5. For Towers of Hanoi, show the output string that would be created by the method call showMoves(3, 'R', 'M', 'L'). Also, show the sequence of method calls.

7. Write a recursive method that will dispense change for a given amount of money. The method will display all combinations of quarters, dimes, nickels, and pennies that equal the desired amount.

Answer 1

5.

class TowersOfHanoi
{
   static void showMoves(int n, char r, char m, char l)
   {
       if(n>0)
       {
           showMoves(n-1,r,l,m);
           System.out.println("Move "+ n + " disk from " + r + " to " + m);
           showMoves(n-1,l,m,r);
       }
   }
  
   public static void main (String[] args)
   {
       showMoves(3, 'R', 'M', 'L');
}
}

Output Strings:

Move 1 disk from R to M
Move 2 disk from R to L
Move 1 disk from M to L
Move 3 disk from R to M
Move 1 disk from L to R
Move 2 disk from L to M
Move 1 disk from R to M

Sequence of method calling:

class TowersOfHanoi
{
   static void showMoves(int n, char r, char m, char l)
   {
       if(n>0)
       {   
           System.out.println("showMoves(" + (n-1) + ", " + r + ", " + l + ", " + m + ")");
           showMoves(n-1,r,l,m);
// System.out.println("Move "+ n + " disk from " + r + " to " + m);
           System.out.println("showMoves(" + (n-1) + ", " + l + ", " + m + ", " +r + ")");
           showMoves(n-1,l,m,r);
       }
   }
  
   public static void main (String[] args)
   {
       showMoves(3, 'R', 'M', 'L');
}
}

Output of method calling sequence (without the moves):

showMoves(2, r, l, m)
showMoves(1, r, m, l)
showMoves(0, r, l, m)
showMoves(0, l, m, r)
showMoves(1, m, l, r)
showMoves(0, m, r, l)
showMoves(0, r, l, m)
showMoves(2, l, m, r)
showMoves(1, l, r, m)
showMoves(0, l, m, r)
showMoves(0, m, r, l)
showMoves(1, r, m, l)
showMoves(0, r, l, m)
showMoves(0, l, m, r)

7.

import java.util.*;

class Change
{
   static ArrayList<int[]> combos = new ArrayList<int[]>();
  
   //method to genarate different combinations of changes
   static void change(int amount, int q, int d, int n, int p)
   {
// base condition
if (q * 25 + d * 10 + n * 5 + p > amount) return;

       //write the combination
writeCombo(q, d, n, p);

       /*check if penny greater than or equal to 5 then increase nickel
       * by one and decrease penny by 5 */
if (p >= 5) change(amount, q, d, n + 1, p - 5);
  
   /*check if penny greater than or equal to 10 then increase dime
       * by one and decrease penny by 10 */
if (p >= 10) change(amount, q, d + 1, n, p - 10);

/*check if penny greater than or equal to 25 then increase quarter
       * by one and decrease penny by 25 */
if (p >= 25) change(amount, q + 1, d, n, p - 25);
}
  
//method to write the combination
static void writeCombo(int q, int d, int n, int p)
{
int[] newCombo = { q, d, n, p };

for (int[] combo : combos)
{
if (Arrays.equals(newCombo, combo))
   return; // this combination already stored
}
combos.add(newCombo);
}  
      
   //main method
   public static void main (String[] args)
   {
       //create object of Scanner class
       Scanner sc = new Scanner(System.in);
      
       System.out.print("Enter any amount in cents: ");
      
       //read the amount in cents
       int amount = sc.nextInt();
      
       //call the change() method
       change(amount, 0, 0, 0, amount);
      
       System.out.println("\nAll possible combinations for " + amount + " cents:");

//display all the combinations
for (int[] a : combos)
{
System.out.println(a[0] + " Quarter\t" + a[1] + " Dime\t" + a[2] + " Nickel\t" + a[3] + " Penny");
}
}
}

Output:

Enter any amount in cents: 49

All possible combinations for 49 cents:
0 Quarter 0 Dime 0 Nickel 49 Penny
0 Quarter 0 Dime 1 Nickel 44 Penny
0 Quarter 0 Dime 2 Nickel 39 Penny
0 Quarter 0 Dime 3 Nickel 34 Penny
0 Quarter 0 Dime 4 Nickel 29 Penny
0 Quarter 0 Dime 5 Nickel 24 Penny
0 Quarter 0 Dime 6 Nickel 19 Penny
0 Quarter 0 Dime 7 Nickel 14 Penny
0 Quarter 0 Dime 8 Nickel 9 Penny
0 Quarter 0 Dime 9 Nickel 4 Penny
0 Quarter 1 Dime 7 Nickel 4 Penny
0 Quarter 1 Dime 6 Nickel 9 Penny
0 Quarter 1 Dime 5 Nickel 14 Penny
0 Quarter 2 Dime 5 Nickel 4 Penny
0 Quarter 1 Dime 4 Nickel 19 Penny
0 Quarter 2 Dime 4 Nickel 9 Penny
1 Quarter 0 Dime 4 Nickel 4 Penny
0 Quarter 1 Dime 3 Nickel 24 Penny
0 Quarter 2 Dime 3 Nickel 14 Penny
0 Quarter 3 Dime 3 Nickel 4 Penny
1 Quarter 0 Dime 3 Nickel 9 Penny
0 Quarter 1 Dime 2 Nickel 29 Penny
0 Quarter 2 Dime 2 Nickel 19 Penny
0 Quarter 3 Dime 2 Nickel 9 Penny
1 Quarter 1 Dime 2 Nickel 4 Penny
1 Quarter 0 Dime 2 Nickel 14 Penny
0 Quarter 1 Dime 1 Nickel 34 Penny
0 Quarter 2 Dime 1 Nickel 24 Penny
0 Quarter 3 Dime 1 Nickel 14 Penny
0 Quarter 4 Dime 1 Nickel 4 Penny
1 Quarter 1 Dime 1 Nickel 9 Penny
1 Quarter 0 Dime 1 Nickel 19 Penny
0 Quarter 1 Dime 0 Nickel 39 Penny
0 Quarter 2 Dime 0 Nickel 29 Penny
0 Quarter 3 Dime 0 Nickel 19 Penny
0 Quarter 4 Dime 0 Nickel 9 Penny
1 Quarter 2 Dime 0 Nickel 4 Penny
1 Quarter 1 Dime 0 Nickel 14 Penny
1 Quarter 0 Dime 0 Nickel 24 Penny