Print the balanced bracket expression using given brackets in C Program

Given four variables a, b, c, d with predefined values that represent different types of bracket pairs. The task is to use all the given brackets and print a balanced bracket expression using these bracket types.

Where variables represent −

a for ((
b for ()
c for )(
d for ))

If we cannot form a balanced bracket expression then print "can't be formed". In case of multiple valid answers, we can print any of them.

Syntax

void print(int a, int b, int c, int d);

Algorithm

To form a balanced expression, we need to ensure that the number of opening brackets equals the number of closing brackets. The condition for a valid balanced expression is −

• Either a equals d and both are non-zero (equal opening and closing double brackets)
• Or a, c, and d are all zero (only complete bracket pairs)

The printing order is: (( brackets first, then )( brackets, then )) brackets, and finally () brackets.

Example

#include <stdio.h>

void print(int a, int b, int c, int d) {
    int i;
    /* Check if balanced expression can be formed */
    if ((a == d && a) || (a == 0 && c == 0 && d == 0)) {
        /* Print (( brackets */
        for (i = 1; i <= a; i++)
            printf("((");
        
        /* Print )( brackets */
        for (i = 1; i <= c; i++)
            printf(")(");
        
        /* Print )) brackets */
        for (i = 1; i <= d; i++)
            printf("))");
        
        /* Print () brackets */
        for (i = 1; i <= b; i++)
            printf("()");
        
        printf("<br>");
    }
    else {
        printf("can't be formed<br>");
    }
}

int main() {
    int a = 3, b = 2, c = 4, d = 3;
    printf("Input: a = %d, b = %d, c = %d, d = %d<br>", a, b, c, d);
    printf("Output: ");
    print(a, b, c, d);
    return 0;
}

Input: a = 3, b = 2, c = 4, d = 3
Output: (((((()()()()())))))()()

How It Works

The algorithm works by −

1. Validation: Check if a balanced expression is possible using the condition (a == d && a) || (a == 0 && c == 0 && d == 0)
2. Pattern Formation: Print brackets in the sequence that ensures balance: opening doubles, middle pairs, closing doubles, complete pairs
3. Balance Maintenance: The )( brackets maintain internal balance while (( and )) provide outer structure

Conclusion

This solution efficiently generates balanced bracket expressions by validating input constraints and following a specific printing order. The key insight is that balanced expressions require equal opening and closing brackets with proper nesting structure.