# Insert minimum parantheses to make string balanced

Given a string of digits S. The task is to insert a minimum number of opening and closing parentheses into the string S such that the resulting string is balanced and each digit d must be inside d pairs of matching parentheses.

Examples:

Input: S = 221
Output: ((22)1)
Explanation:
The string ((2))((2))(1) is not valid solutions because it is not of minimum length.

Input: S = 3102
Output: (((3))1)0((2))

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

1. First, we will insert the required opening parentheses for the first element and store its value in p.
2. Then we iterate over the string from 1 to length of string and

• Subtract current element from the previous element (int(S[i-1]) – int(S[i])) and store its value in a variable w.
• If w >= 0 then insert w closing parentheses and update p to (p – w). Otherwise,
• Insert current value minus p (int(S[i]) – p) opening parentheses and update p to equals to the current value.
• At the end of the loop, we balance parentheses by inserting the required closing parentheses.

Below is the implementation of the above approach:

 `# Python 3 implementation to balance  ` `# the string ` ` `  `# Function to insert matching parantheses ` `def` `ParanthesesNesting(S): ` ` `  `    ``# To check first element if 0 or not ` `    ``if` `S[``0``]``=``=``'0'``: ` `        ``out ``=``'0'` `        ``p ``=` `0` ` `  `    ``else``: ` `        ``out ``=``'('``*``(``int``(S[``0``])) ``+` `S[``0``] ` `        ``p ``=` `int``(S[``0``]) ` ` `  `    ``# Loop from 1 to length of input_string ` `    ``for` `i ``in` `range``(``1``, (``len``(S))): ` `        ``w ``=` `int``(S[i ``-` `1``]) ``-` `int``(S[i]) ` ` `  `        ``# To check w is greater than or  ` `        ``# equal to zero or not ` `        ``if``(w >``=` `0``): ` `            ``out ``=` `out ``+` `')'` `*` `int``(w) ``+` `S[i] ` `            ``p ``=` `p ``-` `w ` ` `  `        ``else``: ` `            ``out ``=` `out ``+` `'('` `*` `(``int``(S[i]) ``-` `p) ``+` `S[i] ` `            ``p ``=` `int``(S[i]) ` ` `  `    ``y ``=` `out.count(``'('``) ``-` `out.count(``')'``) ` `    ``out ``+``=` `')'` `*` `int``(y) ` `    ``return``(out) ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `'__main__'``:  ` `    ``string ``=``'221'` `    ``print``(ParanthesesNesting(string)) `

Output:

```((22)1)
``` My Personal Notes arrow_drop_up Check out this Author's contributed articles.

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