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12.7. Trace Practice

Consider the following recursive method:

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public static int mystery(int n)
{
    if (n == 0)
        return 1;
    else
        return 3 * mystery (n - 1);
}

The trace of this code for mystery(4) is shown below.

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mystery(4) returns 3 * mystery(3)
mystery(3) returns 3 * mystery(2)
mystery(2) returns 3 * mystery(1)
mystery(1) returns 3 * mystery(0)
mystery(0) returns A

Once mystery(0) returns 1 the value for each call to mystery can now be calculated and returned.

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mystery(4) returns 3 * mystery(3) = 3 * X = Y
mystery(3) returns 3 * mystery(2) = 3 * 9 = 27
mystery(2) returns 3 * mystery(1) = 3 * 3 = 9
mystery(1) returns 3 * mystery(0) = 3 * 1 = 3
mystery(0) returns 1

Consider the following recursive method:

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public static int strMethod(String str)
{
   if (str.length() == 1) return 0;
   else
   {
      if (str.substring(0,1).equals("e")) return 1 +
                           strMethod(str.substring(1));
      else return strMethod(str.substring(1));
   }
}

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strMethod("every") returns 1 + strMethod("very")
strMethod("very") returns strMethod("ery")
strMethod("ery") returns 1 + strMethod("ry")
strMethod("ry") returns strMethod("y")
strMethod("y") returns B

Once strMethod(“y”) returns, the value from each recursive call on the stack can be calculated and returned.

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strMethod("every") returns 1 + strMethod("very") = Z
strMethod("very") returns strMethod("ery") = Y
strMethod("ery") returns 1 + strMethod("ry") = 1 + X
strMethod("ry") returns strMethod("y") = 0
strMethod("y") returns 0

12.8. Try Writing a Recursive Method

If you would like to try writing recursive methods check out the recursion problems at CodingBat at http://codingbat.com/java/Recursion-1.

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