# Find an equal point in a string of brackets

Given a string of brackets, the task is to find an index k which decides the number of opening brackets is equal to the number of closing brackets.
String must be consists of only opening and closing brackets i.e. ‘(‘ and ‘)’.

An equal point is an index such that the number of opening brackets before it is equal to the number of closing brackets from and after.

Examples:

```Input : str = "(())))("
Output:   4
After index 4, string splits into (())
and ))(. Number of opening brackets in the
first part is equal to number of closing
brackets in the second part.

Input : str = "))"
Output: 2
As after 2nd position i.e. )) and "empty"
string will be split into these two parts:
So, in this number of opening brackets i.e.
0 in the first part is equal to number of
closing brackets in the second part i.e.
also 0.
``` ## Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

1. Store the number of opening brackets appears in the string up to every index, it must start from starting index.
2. Similarly, Store the number of closing brackets appears in the string upto each and every index but it should be done from last index.
3. Check if any index has the same value of opening and closing brackets.

## C++

 `// C++ program to find an index k which ` `// decides the number of opening brackets ` `// is equal to the number of closing brackets ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find an equal index ` `int` `findIndex(string str) ` `{ ` `    ``int` `len = str.length(); ` `    ``int` `open[len+1], close[len+1]; ` `    ``int` `index = -1; ` `    ``memset``(open, 0, ``sizeof` `(open)); ` `    ``memset``(close, 0, ``sizeof` `(close)); ` ` `  `    ``open = 0; ` `    ``close[len] = 0; ` `    ``if` `(str==``'('``) ` `        ``open = 1; ` `    ``if` `(str[len-1] == ``')'``) ` `        ``close[len-1] = 1; ` ` `  `    ``// Store the number of opening brackets ` `    ``// at each index ` `    ``for` `(``int` `i = 1; i < len; i++) ` `    ``{ ` `        ``if` `( str[i] == ``'('` `) ` `            ``open[i+1] = open[i] + 1; ` `        ``else` `            ``open[i+1] = open[i]; ` `    ``} ` ` `  `    ``// Store the number of closing brackets ` `    ``// at each index ` `    ``for` `(``int` `i = len-2; i >= 0; i--) ` `    ``{ ` `        ``if` `( str[i] == ``')'` `) ` `            ``close[i] = close[i+1] + 1; ` `        ``else` `            ``close[i] = close[i+1]; ` `    ``} ` ` `  `    ``// check if there is no opening or closing ` `    ``// brackets ` `    ``if` `(open[len] == 0) ` `        ``return` `len; ` `    ``if` `(close == 0) ` `        ``return` `0; ` ` `  `    ``// check if there is any index at which ` `    ``// both brackets are equal ` `    ``for` `(``int` `i=0; i<=len; i++) ` `        ``if` `(open[i] == close[i]) ` `            ``index = i; ` ` `  `    ``return` `index; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``string str = ``"(()))(()()())))"``; ` `    ``cout << findIndex(str); ` `    ``return` `0; ` `} `

## Java

 `// Java program to find an index k which ` `// decides the number of opening brackets ` `// is equal to the number of closing brackets ` ` `  `public` `class` `GFG  ` `{ ` `    ``// Method to find an equal index ` `    ``static` `int` `findIndex(String str) ` `    ``{ ` `        ``int` `len = str.length(); ` `        ``int` `open[] = ``new` `int``[len+``1``]; ` `        ``int`    `close[] = ``new` `int``[len+``1``]; ` `        ``int` `index = -``1``; ` `      `  `        ``open[``0``] = ``0``; ` `        ``close[len] = ``0``; ` `        ``if` `(str.charAt(``0``)==``'('``) ` `            ``open[``1``] = ``1``; ` `        ``if` `(str.charAt(len-``1``) == ``')'``) ` `            ``close[len-``1``] = ``1``; ` `      `  `        ``// Store the number of opening brackets ` `        ``// at each index ` `        ``for` `(``int` `i = ``1``; i < len; i++) ` `        ``{ ` `            ``if` `( str.charAt(i) == ``'('` `) ` `                ``open[i+``1``] = open[i] + ``1``; ` `            ``else` `                ``open[i+``1``] = open[i]; ` `        ``} ` `      `  `        ``// Store the number of closing brackets ` `        ``// at each index ` `        ``for` `(``int` `i = len-``2``; i >= ``0``; i--) ` `        ``{ ` `            ``if` `( str.charAt(i) == ``')'` `) ` `                ``close[i] = close[i+``1``] + ``1``; ` `            ``else` `                ``close[i] = close[i+``1``]; ` `        ``} ` `      `  `        ``// check if there is no opening or closing ` `        ``// brackets ` `        ``if` `(open[len] == ``0``) ` `            ``return` `len; ` `        ``if` `(close[``0``] == ``0``) ` `            ``return` `0``; ` `     `  `        ``// check if there is any index at which ` `        ``// both brackets are equal ` `        ``for` `(``int` `i=``0``; i<=len; i++) ` `            ``if` `(open[i] == close[i]) ` `                ``index = i; ` `      `  `        ``return` `index; ` `    ``} ` `     `  `    ``// Driver Method ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``String str = ``"(()))(()()())))"``; ` `        ``System.out.println(findIndex(str)); ` `    ``} ` `} `

## Python 3

 `# Method to find an equal index ` `def` `findIndex(``str``): ` `    ``l ``=` `len``(``str``) ` `    ``open` `=` `[``0``] ``*` `(l ``+` `1``) ` `    ``close ``=` `[``0``] ``*` `(l ``+` `1``) ` `    ``index ``=` `-``1` `     `  `    ``open``[``0``] ``=` `0` `    ``close[l] ``=` `0` `    ``if` `(``str``[``0``]``=``=``'('``): ` `        ``open``[``1``] ``=` `1` `    ``if` `(``str``[l ``-` `1``] ``=``=` `')'``): ` `        ``close[l ``-` `1``] ``=` `1` `     `  `    ``# Store the number of ` `    ``# opening brackets ` `    ``# at each index ` `    ``for` `i ``in` `range``(``1``, l): ` `        ``if` `(``str``[i] ``=``=` `'('``): ` `            ``open``[i ``+` `1``] ``=` `open``[i] ``+` `1` `        ``else``: ` `            ``open``[i ``+` `1``] ``=` `open``[i] ` `     `  `    ``# Store the number ` `    ``# of closing brackets ` `    ``# at each index ` `    ``for` `i ``in` `range``(l ``-` `2``, ``-``1``, ``-``1``): ` `        ``if` `( ``str``[i] ``=``=` `')'``): ` `            ``close[i] ``=` `close[i ``+` `1``] ``+` `1` `        ``else``: ` `            ``close[i] ``=` `close[i ``+` `1``] ` `     `  `    ``# check if there is no  ` `    ``# opening or closing brackets ` `    ``if` `(``open``[l] ``=``=` `0``): ` `        ``return` `len` `    ``if` `(close[``0``] ``=``=` `0``): ` `        ``return` `0` `     `  `    ``# check if there is any  ` `    ``# index at which both ` `    ``# brackets are equal ` `    ``for` `i ``in` `range``(l ``+` `1``): ` `        ``if` `(``open``[i] ``=``=` `close[i]): ` `            ``index ``=` `i ` `     `  `    ``return` `index ` `     `  `# Driver Code ` `str` `=` `"(()))(()()())))"` `print``(findIndex(``str``)) ` ` `  `# This code is contributed  ` `# by ChitraNayal `

## C#

 `// C# program to find an index  ` `// k which decides the number ` `// of opening brackets is equal  ` `// to the number of closing brackets ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `// Method to find an equal index ` `static` `int` `findIndex(``string` `str) ` `{ ` `    ``int` `len = str.Length; ` `    ``int``[] open = ``new` `int``[len + 1]; ` `    ``int``[] close = ``new` `int``[len + 1]; ` `    ``int` `index = -1; ` ` `  `    ``open = 0; ` `    ``close[len] = 0; ` `    ``if` `(str == ``'('``) ` `        ``open = 1; ` `    ``if` `(str[len - 1] == ``')'``) ` `        ``close[len - 1] = 1; ` ` `  `    ``// Store the number of  ` `    ``// opening brackets ` `    ``// at each index ` `    ``for` `(``int` `i = 1; i < len; i++) ` `    ``{ ` `        ``if` `(str[i] == ``'('``) ` `            ``open[i + 1] = open[i] + 1; ` `        ``else` `            ``open[i + 1] = open[i]; ` `    ``} ` ` `  `    ``// Store the number  ` `    ``// of closing brackets ` `    ``// at each index ` `    ``for` `(``int` `i = len - 2; i >= 0; i--) ` `    ``{ ` `        ``if` `(str[i] == ``')'``) ` `            ``close[i] = close[i + 1] + 1; ` `        ``else` `            ``close[i] = close[i + 1]; ` `    ``} ` ` `  `    ``// check if there is no ` `    ``// opening or closing ` `    ``// brackets ` `    ``if` `(open[len] == 0) ` `        ``return` `len; ` `    ``if` `(close == 0) ` `        ``return` `0; ` ` `  `    ``// check if there is any ` `    ``// index at which both  ` `    ``// brackets are equal ` `    ``for` `(``int` `i = 0; i <= len; i++) ` `        ``if` `(open[i] == close[i]) ` `            ``index = i; ` ` `  `    ``return` `index; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main() ` `{ ` `    ``string` `str = ``"(()))(()()())))"``; ` `    ``Console.Write(findIndex(str)); ` `} ` `} ` ` `  `// This code is contributed  ` `// by ChitraNayal `

## PHP

 `= 0; ``\$i``--) ` `    ``{ ` `        ``if` `(``\$str``[``\$i``] == ``')'``) ` `        ``\$close``[``\$i``] = ``\$close``[``\$i` `+ 1] + 1; ` `        ``else` `        ``\$close``[``\$i``] = ``\$close``[``\$i` `+ 1]; ` `    ``} ` `     `  `    ``// check if there is no  ` `    ``// opening or closing ` `    ``// brackets ` `    ``if` `(``\$open``[``\$len``] == 0) ` `        ``return` `\$len``; ` `    ``if` `(``\$close`` == 0) ` `        ``return` `0; ` `     `  `    ``// check if there is any  ` `    ``// index at which both ` `    ``// brackets are equal ` `    ``for` `(``\$i` `= 0; ``\$i` `<= ``\$len``; ``\$i``++) ` `        ``if` `(``\$open``[``\$i``] == ``\$close``[``\$i``]) ` `            ``\$index` `= ``\$i``; ` `     `  `    ``return` `\$index``; ` `} ` `     `  `// Driver Code ` `\$str` `= ``"(()))(()()())))"``; ` `echo` `(findIndex(``\$str``)); ` ` `  `// This code is contributed ` `// by ChitraNayal ` `?> `

Output:

```9
```

Time Complexity : O(n)

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