Problem Description

A Padovan string P(n) for a natural number n is defined as:

P(0) = ‘X’

P(1) = ‘Y’

P(2) = ‘Z’

P(n) = P(n-2) + P(n-3), n>2
where + denotes string concatenation.
For a string of the characters ‘X’ , ‘Y’ and ‘Z’ only, and given value of n, write a program that counts the number of occurrences of the string in the n-th Padovan string P(n).


An example is given below.

For n = 6 and the string ZY, the program should count the occurrences of ZY in P(6).

P(0) = ‘X’

P(1) = ‘Y’

P(2) = ‘Z’

P(n) = P(n-2) + P(n-3), n>2


P(3) = P(1)+P(0)

P(3) = YX


P(4) = P(2)+P(1)

P(4) = ZY


P(5) = P(3)+P(2)

P(5) = YXZ


P(6) = P(4)+P(3)

P(6) = ZYYX

So, the number of occurrences of the string ZY in P(6) is 1.
Instruction to work with Open PBT Client:
1. Specify the work directory path in the 'Work directory Path' field. The path should correspond to your solution Work directory.
2. Download the support files by clicking the Get Dev Files.
3. You will find the problem directories containing:
o problem.h file
o problem.c file
in your project directory.
4. Code the solution in .c file inside the problem directory
5. All required files will be downloaded to your work directory. Creating additional files is strongly discouraged.
Step 1:
In your Solution File:
• Implement your logic in function int stringOccurrences(int n, char* str)
• int n :n is an integer represents n(th) for which full main string has to formed, from which occurrence of string str has to be found.
• char* str :str is a string represents sub string whose occurrence has to be found in the main string.
• You can create more functions if required, but those functions should be in the same file.

Step 2:
In your solution keep in mind the following constraints:.
1. In this problem you have to write a program that counts the number of occurrences of the string in the n-th Padovan string P(n).
2. Padovan formula is P(n) = P(n-2) + P(n-3) where n>2 and n is the integer.
3. In the above Padovan formula + sign means string concatenation.
4. For the Padovan formula value of P(0),P(1) and P(2) is given. You have to use those value only.
5. n should not be greater than 40 otherwise return -1
6. string str should be consist of only X,Y and Z in upper case otherwise return -1
The Prototype of the function is
int stringOccurrences(int n, char* str)
This function takes following arguments.
• n is the value for which full main string has to formed, from which occurrence of string str has to be found.
• str represents sub string whose occurrence has to be found in the main string.
• This function returns a number of occurrence of string str in the main string.
The constraints are:
1. n should not be greater than 40 otherwise return -1
2. string str should be consist of only X,Y and Z in upper case otherwise return -1
Example 1
Input
________________________________________
int n = 6
string str = ZY
Output
________________________________________
1
Explanation : This question is explained in problem description.
Example 2
Input
________________________________________
int n = 6
String str = ZYmm
Output
________________________________________
-1
Explanation :
String str is containing character other than X, Z and Y.
Example 3
Input
________________________________________
int n = 8
String str = XZ
Output
________________________________________
1

public class PadovanString
 {
 
        public int stringOccurrences(int n, String str)
{
        if (n >= 40)
        return -1;
      if (str.replaceAll("X|Y|Z", "").length() > 0)
        return -1;
        String res= pad(n);
 
 
        System.out.println(res);
 
 
 
        return (res.length() - res.replaceAll(str, "").length())/(str.length());
        }
 
        public String pad(int n)
{
 
        if (n == 0) return "X";
        if (n == 1) return "Y";
        if (n == 2) return "Z";
        else return pad(n-2) + pad(n-3);
 
        }
        }