# Check if the Depth of Parentheses is correct in the given String

Last Updated : 27 Dec, 2022

Given a string S consisting of opening parentheses, closing parentheses and integers, the task is to print Yes if, in this string, the integers correctly indicates its depth. Depth refers to the number of nested sets of parentheses surrounding that integer. Print No otherwise.
Examples:

Input: S = “((2)((3)))”
Output: Yes
Explanation:
No of Opening & Closing Parentheses around 2 = 2
No of Opening & Closing Parentheses around 3 = 3
Input: S = “((35)(2))”
Output: No
Explanation:
No of Opening & Closing Parentheses around 35 = 2
No of Opening & Closing Parentheses around 2 = 2

Approach:

1. Iterate the string character by character
2. If it is opening or closing parenthesis then append into an array arr[]
3. If the character is digit, then iterate till the entire number is read and then append into the arr[]
4. Iterate the array arr[] element by element
• If the element is ‘(‘ increment depth and open by 1
• If the element is ‘)’ decrement depth by 1 and increment close by 1
• If the element is an Integer, check if “Integer != depth”, if true
set flag to 0 and break the loop
5. After iterating the entire string, check if open not equals to close, if true set flag = 0

Below is the implementation of the above approach

## C++

 `// Function to check if the Depth` `// of Parentheses is correct` `// in the given String`   `#include ` `using` `namespace` `std;`   `bool` `Formatted(string s)` `{` `    ``vector<``char``> k;` `    ``int` `i = 0;`   `    ``while` `(i < s.size())` `    ``{` `        ``// Appending if the` `        ``// Character is not integer` `        ``if` `(s[i]==``')'` `or s[i]==``'('``)` `        ``{` `            ``k.push_back(s[i]);` `            ``i += 1;` `        ``}` `        ``else` `        ``{` `            ``// Iterating till the entire` `            ``// Digit is read` `            ``char` `st;` `            ``while` `(s[i]!=``')'` `and s[i]!=``')'``)` `            ``{` `                ``st = s[i];` `                ``i = i + 1;` `            ``}` `            ``k.push_back(st);` `        ``}` `    ``}`   `    ``int` `depth = 0, flag = 1;` `    ``int` `open = 0, close = 0;`   `    ``for` `(``char` `i:k)` `    ``{`   `        ``// Check if character is '('` `        ``if` `(i == ``'('``)` `        ``{` `            ``// Increment depth by 1` `            ``depth += 1;`   `            ``// Increment open by 1` `            ``open += 1;`   `        ``// Check if character is ')'` `    ``}``else` `if` `(i == ``')'``){`   `            ``// Decrement depth by 1` `            ``depth -= 1;`   `            ``// Increment close by 1` `            ``close += 1;` `        ``}` `        ``else``{` `            ``if` `(i-``'0'` `!= depth){` `                ``flag = 0;` `                ``break``;` `            ``}` `        ``}` `    ``}`   `    ``// Check if open parentheses` `    ``// NOT equals close parentheses` `    ``if` `(open != close)` `        ``flag = 0;`   `    ``return` `(flag == 1)?``true``:``false``;` `}`   `// Driver Code` `int` `main()` `{` `    ``string s = ``"((2)((3)))"``;` `    ``bool` `k = Formatted(s);` `    ``if` `(k == ``true``)` `        ``printf``(``"Yes"``);` `    ``else` `        ``printf``(``"No"``);` `    ``return` `0;` `}`   `// This code is contributed by mohit kumar 29`

## Java

 `// Function to check if the Depth` `// of Parentheses is correct` `// in the given String` `import` `java.util.*;`   `class` `GFG{`   `static` `boolean` `Formatted(String s)` `{` `    ``Vector k = ``new` `Vector();` `    ``int` `i = ``0``;`   `    ``while` `(i < s.length())` `    ``{` `        ``// Appending if the` `        ``// Character is not integer` `        ``if` `(s.charAt(i)==``')'` `|| s.charAt(i)==``'('``)` `        ``{` `            ``k.add(s.charAt(i));` `            ``i += ``1``;` `        ``}` `        ``else` `        ``{` `            ``// Iterating till the entire` `            ``// Digit is read` `            ``char` `st = ``0``;` `            ``while` `(s.charAt(i)!=``')'` `&& s.charAt(i)!=``')'``)` `            ``{` `                ``st = s.charAt(i);` `                ``i = i + ``1``;` `            ``}` `            ``k.add(st);` `        ``}` `    ``}`   `    ``int` `depth = ``0``, flag = ``1``;` `    ``int` `open = ``0``, close = ``0``;`   `    ``for` `(``char` `i2 : k)` `    ``{`   `        ``// Check if character is '('` `        ``if` `(i2 == ``'('``)` `        ``{` `            ``// Increment depth by 1` `            ``depth += ``1``;`   `            ``// Increment open by 1` `            ``open += ``1``;`   `        ``// Check if character is ')'` `    ``}``else` `if` `(i2 == ``')'``){`   `            ``// Decrement depth by 1` `            ``depth -= ``1``;`   `            ``// Increment close by 1` `            ``close += ``1``;` `        ``}` `        ``else``{` `            ``if` `(i2-``'0'` `!= depth){` `                ``flag = ``0``;` `                ``break``;` `            ``}` `        ``}` `    ``}`   `    ``// Check if open parentheses` `    ``// NOT equals close parentheses` `    ``if` `(open != close)` `        ``flag = ``0``;`   `    ``return` `(flag == ``1``)?``true``:``false``;` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``String s = ``"((2)((3)))"``;` `    ``boolean` `k = Formatted(s);` `    ``if` `(k == ``true``)` `        ``System.out.printf(``"Yes"``);` `    ``else` `        ``System.out.printf(``"No"``);` `}` `}`   `// This code is contributed by Rajput-Ji`

## Python3

 `# Function to check if the Depth ` `# of Parentheses is correct` `# in the given String`   `def` `Formatted(s):` `    ``k ``=` `[]` `    ``i ``=` `0`   `    ``while` `i < ``len``(s):`   `        ``# Appending if the ` `        ``# Character is not integer` `        ``if` `s[i].isdigit() ``=``=` `False``:`   `            ``k.append(s[i])` `            ``i ``+``=` `1` `        ``else``:`   `            ``# Iterating till the entire` `            ``# Digit is read` `            ``st ``=` `""` `            ``while` `s[i].isdigit():` `                ``st ``+``=` `s[i]` `                ``i ``=` `i ``+` `1` `            ``k.append(``int``(st))`   `    ``depth, flag ``=` `0``, ``1` `    ``open``, close ``=` `0``, ``0`   `    ``for` `i ``in` `k:`   `        ``# Check if character is '('` `        ``if` `i ``=``=` `'('``:`   `            ``# Increment depth by 1` `            ``depth ``+``=` `1`   `            ``# Increment open by 1` `            ``open` `+``=` `1`   `        ``# Check if character is ')'` `        ``elif` `i ``=``=` `')'``:`   `            ``# Decrement depth by 1` `            ``depth ``-``=` `1`   `            ``# Increment close by 1` `            ``close ``+``=` `1` `        ``else``:` `            ``if` `i !``=` `depth:` `                ``flag ``=` `0` `                ``break`   `    ``# Check if open parentheses` `    ``# NOT equals close parentheses` `    ``if` `open` `!``=` `close:` `        ``flag ``=` `0`   `    ``return` `True` `if` `flag ``=``=` `1` `else` `False`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    ``s ``=` `'((2)((3)))'` `    ``k ``=` `Formatted(s)` `    ``if` `k ``=``=` `True``:` `        ``print``(``"Yes"``)` `    ``else``:` `        ``print``(``"No"``)`

## C#

 `// Function to check if the Depth` `// of Parentheses is correct` `// in the given String` `using` `System;` `using` `System.Collections.Generic;`   `class` `GFG` `{`   `static` `bool` `Formatted(String s)` `{` `    ``List<``char``> k = ``new` `List<``char``>();` `    ``int` `i = 0;`   `    ``while` `(i < s.Length)` `    ``{` `        ``// Appending if the` `        ``// char is not integer` `        ``if` `(s[i]==``')'` `|| s[i]==``'('``)` `        ``{` `            ``k.Add(s[i]);` `            ``i += 1;` `        ``}` `        ``else` `        ``{` `            ``// Iterating till the entire` `            ``// Digit is read` `            ``char` `st = ``'\x0000'``;` `            ``while` `(s[i] != ``')'` `&& s[i] != ``')'``)` `            ``{` `                ``st = s[i];` `                ``i = i + 1;` `            ``}` `            ``k.Add(st);` `        ``}` `    ``}`   `    ``int` `depth = 0, flag = 1;` `    ``int` `open = 0, close = 0;`   `    ``foreach` `(``char` `i2 ``in` `k)` `    ``{`   `        ``// Check if character is '('` `        ``if` `(i2 == ``'('``)` `        ``{` `            ``// Increment depth by 1` `            ``depth += 1;`   `            ``// Increment open by 1` `            ``open += 1;`   `        ``// Check if character is ')'` `    ``}``else` `if` `(i2 == ``')'``){`   `            ``// Decrement depth by 1` `            ``depth -= 1;`   `            ``// Increment close by 1` `            ``close += 1;` `        ``}` `        ``else``{` `            ``if` `(i2-``'0'` `!= depth){` `                ``flag = 0;` `                ``break``;` `            ``}` `        ``}` `    ``}`   `    ``// Check if open parentheses` `    ``// NOT equals close parentheses` `    ``if` `(open != close)` `        ``flag = 0;`   `    ``return` `(flag == 1)?``true``:``false``;` `}`   `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` `    ``String s = ``"((2)((3)))"``;` `    ``bool` `k = Formatted(s);` `    ``if` `(k == ``true``)` `        ``Console.Write(``"Yes"``);` `    ``else` `        ``Console.Write(``"No"``);` `}` `}`   `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output:

`Yes`

Time Complexity: O(n)
Auxiliary Space: O(n), where n is the length of the given string.