4. Context Free Grammar

A context-free grammar (CFG) is a set of recursive rewriting rules (or productions) used to generate patterns of strings.
A CFG consists of the following components:

• a set of terminal symbols, which are the characters of the alphabet that appear in the strings generated by the grammar.
• a set of non-terminal symbols, which are placeholders for patterns of terminal symbols that can be generated by the non-terminal symbols.
• a set of productions, which are rules for replacing (or rewriting) non-terminal symbols (on the left side of the production) in a string with other non-terminal or terminal symbols (on the right side of the production).
• a seed, which is a special non-terminal symbol that appears in the initial string generated by the grammar.

To generate a string of terminal symbols from a CFG, we:

• Begin with a string consisting of the start symbol;
• Apply one of the productions with the start symbol on the left hand side, replacing the start symbol with the right hand side of the production;
• Repeat the process of selecting non-terminal symbols in the string, and replacing them with the right hand side of some corresponding production, until all non-terminals have been replaced by terminal symbols.

For example, this specification:
A = BD
B = bB | b | Bb
D = dD
D = d

with A as the seed represents the set of words that have one or more b's followed by one or more d's (bd, bbd, bddd, bbbddd, etc.).
Above production grammar contains string “bbd”. So your task is to find out the given string can be formed by given grammar or not. If that string can formed by the given grammar then return true otherwise false.

Instructions to use 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 Support Files

.

3. You will find the problem directories containing:
   • problem.h file
   • problem.c file

in your work directory.

4. Write your solution in .c file

Step 1:

In your Solution File:

• Add method int checkString(char** production, char seed, char* str)

Step 2:

Pass the following parameter to the method checkString()

1. production is a character pointer array represents the available productions for the CFG as mentioned in the problem description.
2. seed

is a character,which is a special non-terminal symbol that appears in the initial string generated by the grammar.

3. str is a String which can be created by the given productions.

Step 3:

Write the appropriate code as mentioned in the problem description by following the below given Constraints.

4. The first input should be the String Array which specify the production to the given grammer in the format given below:

{"S=aSa" , "S = bSb" , "S=aa" , "S =bb"}

5. The second input is the seed character,which is a special non-terminal symbol that appears in the initial string generated by the grammar.
6. The third input is the string itself, which you have to determine whether it is generated by the above given production
7. You need to figure out whether the string (the third input) can be generated by the given production (the first input) by using the seed (second input) as a initial non-terminal symbol.
8. Your method should return true if it can be generated else return false
9. If the given production string is null then return false.

The prototype of the function is:

int checkString(char** production, char seed, char* str)
Where production is the string array.
             seed is the character.
             str is the string .

Constraint:

• If the given production string is null then return false.

Example 1

Input:

Output:
         true

Explanation:The string "abaaba" can formed by using production
S=aSa---->S=a(bSb)a------->S=ab(aa)ba---------->S=abaaba

Example 2

Input:

Output:
         false

For C++ solutions

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