Answer:

The base cases are:

1. equals( "", "" )     = true
2. equals( "", X )      = false if X is not the empty string
3. equals( X, "" )      = false if X is not the empty string
4. equals( x+X, y+Y )   = false if x != y

These are base cases because the result can be computed immediately.

Translation into Java

Of course there is an equals() method that is part of the class String. Let us forget this and write our own method. This should be merely a matter of translation:

  boolean equals( String strA, String strB )
  {
    // 1. equals( "", "" ) = true
    if       ( strA.length()  0 && strB.length()  0 )  
      return true;
      
    // 2. equals( "", X ) = false if X is not the empty string
    else if  ( strA.length()  0 && strB.length()  0 )  
      return false;
      
    // 3. equals( X, "" ) = false if X is not the empty string
    else if  ( strA.length()   0 && strB.length() 0 )  
      return false;
      
    // 4. equals( x+X, y+Y ) = false if x != y
    else if  ( strA.charAt(0)  strB.charAt(0) )         
      return false;
      
    // 5. equals( x+X, y+Y ) = true  if x == y and equals( X, Y )
    else
      return ( strA.substring(1), strB.substring(1) ); 
  }

To detect an empty string, check if the length is zero. Remember that an empty string is a string that contains no characters. The value null is something different.

The method call strA.substring(1) returns the substring that consists of character 1 and all characters that follow it in strA.

Answer:

Translation into Java

QUESTION 15: