Print the balanced bracket expression using given brackets

Given four integers a, b, c and d which signifies the number of four types of brackets.

1. “((“
2. “()”
3. “)(“
4. “))”

The task is to print any balanced bracket expression using all the given brackets. If we cannot form a balanced bracket expression then print -1. In case of multiple answers, print any one.
Examples:

Input: a = 3, b = 1, c = 4, d = 3
Output: (((((()()()()())))))()
Input: a = 3, b = 1, c = 4, d = 8
Output: -1
No balanced bracket expression is possible with the given brackets.

Approach: First check if the balanced bracket expression can be formed with the given number of brackets. We can form the expression if the number of type1 brackets is equal to the number of type4 brackets with any number of type3 brackets or if there are only type 2 brackets. Hence the combining condition will be:

(a == d && a) || (a == 0 && c == 0 && d == 0)

The following steps can be followed to print the balanced bracket expression if the above condition is satisfied:

• Print number of type1 brackets.
• Print number of type3 brackets.
• Print number of type4 brackets.
• Print number of type2 brackets.

Below is the implementation of the above approach:

C++

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;`   `// Function to print balanced bracket` `// expression if it is possible` `void` `printBalancedExpression(``int` `a, ``int` `b, ``int` `c, ``int` `d)` `{`   `    ``// If the condition is met` `    ``if` `((a == d && a) || (a == 0 && c == 0 && d == 0)) {`   `        ``// Print brackets of type-1` `        ``for` `(``int` `i = 1; i <= a; i++)` `            ``cout << ``"(("``;`   `        ``// Print brackets of type-3` `        ``for` `(``int` `i = 1; i <= c; i++)` `            ``cout << ``")("``;`   `        ``// Print brackets of type-4` `        ``for` `(``int` `i = 1; i <= d; i++)` `            ``cout << ``"))"``;`   `        ``// Print brackets of type-2` `        ``for` `(``int` `i = 1; i <= b; i++)` `            ``cout << ``"()"``;` `    ``}`   `    ``// If the condition is not met` `    ``else` `        ``cout << -1;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `a = 3, b = 1, c = 4, d = 3;` `    ``printBalancedExpression(a, b, c, d);`   `    ``return` `0;` `}`

Java

 `// Java implementation of the above approach ` `class` `GFG ` `{ ` `    `  `    ``// Function to print balanced bracket ` `    ``// expression if it is possible ` `    ``static` `void` `printBalancedExpression(``int` `a, ` `                            ``int` `b, ``int` `c, ``int` `d) ` `    ``{ ` `    `  `        ``// If the condition is met ` `        ``if` `(((a == d) && (a != ``0``)) || ` `        ``((a == ``0``) && (c == ``0``) && (d == ``0``))) ` `        ``{ ` `    `  `            ``// Print brackets of type-1 ` `            ``for` `(``int` `i = ``1``; i <= a; i++) ` `                ``System.out.print(``"(("``); ` `    `  `            ``// Print brackets of type-3 ` `            ``for` `(``int` `i = ``1``; i <= c; i++) ` `                ``System.out.print(``")("``); ` `    `  `            ``// Print brackets of type-4 ` `            ``for` `(``int` `i = ``1``; i <= d; i++) ` `                ``System.out.print(``"))"``); ` `    `  `            ``// Print brackets of type-2 ` `            ``for` `(``int` `i = ``1``; i <= b; i++) ` `                ``System.out.print(``"()"``); ` `        ``} ` `    `  `        ``// If the condition is not met ` `        ``else` `            ``System.out.print(-``1``); ` `    ``} ` `    `  `    ``// Driver code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `a = ``3``, b = ``1``, c = ``4``, d = ``3``; ` `        ``printBalancedExpression(a, b, c, d); ` `    ``} ` `} `   `// This code is contributed by Ryuga `

Python3

 `# Python3 implementation of the approach`   `# Function to print balanced bracket` `# expression if it is possible` `def` `printBalancedExpression(a, b, c, d):`   `    ``# If the condition is met` `    ``if` `((a ``=``=` `d ``and` `a) ``or` `        ``(a ``=``=` `0` `and` `c ``=``=` `0` `and` `d ``=``=` `0``)): `   `        ``# Print brackets of type-1` `        ``for` `i ``in` `range``(``1``, a ``+` `1``):` `            ``print``(``"(("``, end ``=` `"")`   `        ``# Print brackets of type-3` `        ``for` `i ``in` `range``(``1``, c ``+` `1``):` `            ``print``(``")("``, end ``=` `"")`   `        ``# Print brackets of type-4` `        ``for` `i ``in` `range``(``1``, d ``+` `1``):` `            ``print``(``"))"``, end ``=` `"")`   `        ``# Print brackets of type-2` `        ``for` `i ``in` `range``(``1``, b ``+` `1``):` `            ``print``(``"()"``, end ``=` `"")` `    `  `    ``# If the condition is not met` `    ``else``:` `        ``print``(``"-1"``)`   `# Driver code` `if` `__name__ ``=``=` `"__main__"``:`   `    ``a, b, c, d ``=` `3``, ``1``, ``4``, ``3` `    ``printBalancedExpression(a, b, c, d)`   `# This code is contributed by Rituraj Jain`

C#

 `// C# implementation of the approach` `using` `System;`   `class` `GFG` `{` `    `  `// Function to print balanced bracket` `// expression if it is possible` `static` `void` `printBalancedExpression(``int` `a, ` `                        ``int` `b, ``int` `c, ``int` `d)` `{`   `    ``// If the condition is met` `    ``if` `(((a == d) && (a != 0)) || ` `       ``((a == 0) && (c == 0) && (d == 0))) ` `    ``{`   `        ``// Print brackets of type-1` `        ``for` `(``int` `i = 1; i <= a; i++)` `            ``Console.Write(``"(("``);`   `        ``// Print brackets of type-3` `        ``for` `(``int` `i = 1; i <= c; i++)` `            ``Console.Write(``")("``);`   `        ``// Print brackets of type-4` `        ``for` `(``int` `i = 1; i <= d; i++)` `            ``Console.Write(``"))"``);`   `        ``// Print brackets of type-2` `        ``for` `(``int` `i = 1; i <= b; i++)` `            ``Console.Write(``"()"``);` `    ``}`   `    ``// If the condition is not met` `    ``else` `        ``Console.Write(-1);` `}`   `// Driver code` `public` `static` `void` `Main()` `{` `    ``int` `a = 3, b = 1, c = 4, d = 3;` `    ``printBalancedExpression(a, b, c, d);` `}` `}`   `// This code is contributed by Akanksha Rai`

PHP

 ``

Javascript

 ``

Output:

`(((((()()()()())))))()`

Time Complexity: O(max(a,b,c,d)), as we are using loop to traverse a, b, c, and d times.

Auxiliary Space: O(1), as we are not using any extra space.

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