parenthesis.cpp

// Parenthesis.cpp : calculate all expressions containing n pairs of matched parentheses ...
//

#include <string>
#include <iostream>

void brackets(int availableOpenBrackets, int availableCloseBrackets, std::string s, int& combinationCount);

int main()
{
	int combinations = 0; // Note: look-up "Catalan numbers" (1,1,2,5,14,42,132,429, ... )
	brackets(5, 0, " ",combinations);
	std::cout << "Combinations: " << combinations << std::endl;
    return 0;
}

void brackets(int availableOpenBrackets, int availableCloseBrackets, std::string s, int& combinationCount){
	if ((availableOpenBrackets == 0) && (availableCloseBrackets == 0)) {
		++combinationCount;
		std::cout << s << std::endl;
	}
	if (availableOpenBrackets > 0) {
		brackets(availableOpenBrackets - 1, availableCloseBrackets + 1, s + "<", combinationCount);
	}
	if (availableCloseBrackets > 0) {
		brackets(availableOpenBrackets, availableCloseBrackets - 1, s + ">", combinationCount);
	}
}