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Valid String

Last Updated: 30 Sep, 2020
Difficulty: Moderate


Try Problem

You have been given a string 'S' containing only three types of characters, i.e. '(', ')' and '*'.

A Valid String is defined as follows:

1. Any left parenthesis '(' must have a corresponding right parenthesis ')'.
2. Any right parenthesis ')' must have a corresponding left parenthesis '('.
3. Left parenthesis '(' must go before the corresponding right parenthesis ')'.
4. '*' could be treated as a single right parenthesis ')' or a single left parenthesis '(' or an empty string.
5. An empty string is also valid.

Your task is to find out whether the given string is a Valid String or not.

Input Format:
The first line of input contains an integer 'T' representing the number of test cases or queries to run. Then the test case follows.

The only line of each test case contains a string 'S'.
Output Format:
For each test case print 'Yes' if the string 'S' is a valid string otherwise print 'No' otherwise.

The output of each test case will be printed in a separate line.
You are not required to print the expected output; it has already been taken care of. Just implement the function. 
1 <= T <= 100
1 <= N <= 5000

Where 'N' is the length of the string 'S'.

Time Limit: 1 sec

Approach 1

We can try each of the three possibilities for every asterisk in the string with the help of recursion. 


We will use a temporary string which will keep track of our current possible string. In the end, we can linearly check each possible string. If any of the possible string is a valid string, we print ‘Yes’, otherwise ‘No’.

Try Problem