// Put your names here

// Complete each of the following methods to compute the
// values as indicated using a recursive algorithm
// Do not use a loop unless specifically indicated


public class Lab12 {
  
  // compute n!
  // Example:
  //   input:  4
  //   output: 24
  public static int factorial(int n) {
    if (n==0) {
       return 1;
       }
    else {
       return n*factorial(n-1);
       }
  }
  
  
  // Sum the first n positive integers
  // Example:
  //   input:  10
  //   output: 55
  public static int sum(int n) {
    return 0;
  }
  

  // Discuss this with your lab partner
  public static int upAndDown(int n) {
    System.out.println("Down: " + n);
    if (n > 0) upAndDown(n-1);
    System.out.println("Up: " + n);
    return 0;
  }


 // Compute the ith Fibonacci number
 // F(0) = 1
 // F(1) = 1
 // F(2) = 2
 // ...
 // F(n) = F(n-1) + F(n)
 // Note: Computing Fibonacci numbers this way is
 //       completely impractical as you will see
 //       Discuss with your lab partner
 public static long fibo(int n) {
   return 0;
 }


  // Return the number of spaces in a string
  // Example:
  //   input:  "This is a test."
  //   output: 3
  // Hint: Use substring and index methods of String
  public static int countSpaces(String s) {
    return 0;
  }


  // Output the number of digits in a given number
  // Example:
  //   input:  0
  //   output: 1
  //   input:  12345
  //   output  5
  // Hint: Use / operator
  public static int digits(int n) {
    return 0;
  }


  // Convert the integer value to a String representing its binary value
  // Example:
  //   input:  12022008
  //   output: 101101110111000011111000
  //   input:  10
  //   output  1010
  // Hint: Use / and % operators
  // Note: 10 is even, so rightmost bit is 0
  //       divide 10 by 2, resulting in 5
  //       5 is odd, so next bit is 1
  //       divide 5 by 2, resulting in 2
  //       2 is even, so next bit is 0
  //       divide 2 by 2, resulting in 1
  //       1 is odd, so next bit is 1
  public static String binary(int n) {
    return "";
  }


  // Multiply the input values using only addition and no loops.
  // Example:
  //   input:  5, 7
  //   output: 35
  public static int multiply(int m, int n) {
    return 0;
  }


  // Return minimal element in array a, starting at position p)
  // Example:
  //   input:  {1,23,54,653,12,-2,4}
  //   output: -2
  //   input:  {12345}
  //   output: 12345
  // Hint: 
  public static int min(int[ ] a, int p) {
    return 0;
  }


  // Reverses String s
  // Example:
  //   input:  "pi"
  //   output: "ip"
  //   input:  "computer"
  //   output: "retupmoc"
  //   input:  "oozy rat in a sanitary zoo"
  //   output: "ooz yratinas a ni tar yzoo"
  // Hint: Reverse what you have been doing
  public static String reverse(String s) {
    return "";
  }


  // Ackermann's Function
  // A(m,n) = n+1 if m=0
  // A(m,n) = A(m-1,1) if n=0
  // A(m,n) = A(m-1,A(m,n-1)) otherwise
  // Note: This is a really C-R-A-Z-Y function!
  //       See http://mathworld.wolfram.com/AckermannFunction.html
  public static int Ackermann(int m, int n) {
    return 0;
  }

  // Determine all the permutations of a given input string
  // Hint: Use a for loop and the substring method.
  // Example:
  //   input:  "abc"
  //   output: ["abc", "acb", "bac", "bca", "cab", "cba"]
  // Note: You will need a for loop and an array
  // Note: There are n! permutations of n elements.
  // Generally recursive, but you can additionally use one for loop
  public static String[] permutations(String s) {
     String[] a; a = null;
     return a;
     }


  public static void main(String args[]) {
    
     System.out.println("sum: " + factorial(4) + " should equal 24");

     System.out.println("sum: " + sum(10) + " should equal 55");

     System.out.println("Why does this print the numbers forward and backward?\n");
     upAndDown(5);

     System.out.println("Fibo "+10+": "+fibo(10));

     System.out.println("countSpaces: " + countSpaces("This is a test.") 
                          + " should equal 3");

     System.out.println("digits: " + digits(12345) + " should equal 5");

     System.out.println("binary: " + binary(5) + " should equal 101");

     System.out.println("multiply: " + multiply(5, 7) + " should equal 35");

     System.out.println("min: " + min(new int [ ] {1,23,54,653,12,-2,4}, 0) 
                          + " should equal -2");

     System.out.println("reverse: " + reverse("computer") + " should be retupmoc");

     System.out.println("Ackermann: " + Ackermann(3,3) + " should equal 61");
     // Why does Ackermann(5,5) cause a stackoverflow error?
     // Discuss this with your lab partner.
     //System.out.println(Ackermann(5,5));     

     System.out.println("\nOnly for the brave!");
     System.out.println("All 24 permutations of abcd: abcd, abdc, acbd, acdb, adbc, adcb, ..., dcba");
     String [] perms = permutations("abcd");
     if (perms != null) {
       for (int i = 0;  i < perms.length;  i++) {
         System.out.print(perms[i]);
         if (i < perms.length-1) System.out.print(", ");
         else System.out.println();
       }
     }

  }

}