#include <cassert> /// for assert
#include <iostream> /// for I/O operation
#include <vector> /// for vector container
/**
* @brief Backtracking algorithms
* @namespace backtracking
*/
namespace backtracking {
/**
* @brief generate_parentheses class
*/
class generate_parentheses {
private:
std::vector<std::string> res; ///< Contains all possible valid patterns
void makeStrings(std::string str, int n, int closed, int open);
public:
std::vector<std::string> generate(int n);
};
/**
* @brief function that adds parenthesis to the string.
*
* @param str string build during backtracking
* @param n number of pairs of parentheses
* @param closed number of closed parentheses
* @param open number of open parentheses
*/
void generate_parentheses::makeStrings(std::string str, int n,
int closed, int open) {
if (closed > open) // We can never have more closed than open
return;
if ((str.length() == 2 * n) &&
(closed != open)) { // closed and open must be the same
return;
}
if (str.length() == 2 * n) {
res.push_back(str);
return;
}
makeStrings(str + ')', n, closed + 1, open);
makeStrings(str + '(', n, closed, open + 1);
}
/**
* @brief wrapper interface
*
* @param n number of pairs of parentheses
* @return all well-formed pattern of parentheses
*/
std::vector<std::string> generate_parentheses::generate(int n) {
backtracking::generate_parentheses::res.clear();
std::string str = "(";
generate_parentheses::makeStrings(str, n, 0, 1);
return res;
}
} // namespace backtracking
/**
* @brief Self-test implementations
* @returns void
*/
static void test() {
int n = 0;
std::vector<std::string> patterns;
backtracking::generate_parentheses p;
n = 1;
patterns = {{"()"}};
assert(p.generate(n) == patterns);
n = 3;
patterns = {{"()()()"}, {"()(())"}, {"(())()"}, {"(()())"}, {"((()))"}};
assert(p.generate(n) == patterns);
n = 4;
patterns = {{"()()()()"}, {"()()(())"}, {"()(())()"}, {"()(()())"},
{"()((()))"}, {"(())()()"}, {"(())(())"}, {"(()())()"},
{"(()()())"}, {"(()(()))"}, {"((()))()"}, {"((())())"},
{"((()()))"}, {"(((())))"}};
assert(p.generate(n) == patterns);
std::cout << "All tests passed\n";
}
/**
* @brief Main function
* @returns 0 on exit
*/
int main() {
test(); // run self-test implementations
return 0;
}
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