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feat: add well-formed parentheses generator
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/** | ||
* @file | ||
* @brief Generates all combinations of well-formed parentheses. | ||
* | ||
* @details a sequence of parentheses is well-formed if each opening parentheses | ||
has a corresponding closing parenthesis | ||
* and the closing parentheses are correctly ordered | ||
* | ||
* @author [Giuseppe Coco](https://github.com/WoWS17) | ||
*/ | ||
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#include <cassert> | ||
#include <iostream> | ||
#include <vector> | ||
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class generate_parentheses { | ||
private: | ||
std::vector<std::string> res; // Contains all possible valid patterns | ||
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/** | ||
* @brief function that implements backtracking | ||
* | ||
* @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 | ||
*/ | ||
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void makeStrings(std::string str, int n, int closed, int open) { | ||
if (closed > open) // We can never have more closed than open | ||
return; | ||
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if (str.length() == 2 * n and | ||
closed != open) // closed and open must be the same | ||
return; | ||
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if (str.length() == 2 * n) { | ||
res.push_back(str); | ||
return; | ||
} | ||
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makeStrings(str + ')', n, closed + 1, open); | ||
makeStrings(str + '(', n, closed, open + 1); | ||
} | ||
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public: | ||
/** | ||
* @brief wrapper interface | ||
* | ||
* @param n number of pairs of parentheses | ||
* @return all well-formed pattern of parentheses | ||
*/ | ||
std::vector<std::string> generate_parenthesis(int n) { | ||
res.clear(); | ||
std::string str = "("; | ||
makeStrings(str, n, 0, 1); | ||
return res; | ||
} | ||
}; | ||
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/** | ||
* @brief Self-test implementations | ||
* @returns void | ||
*/ | ||
static void test() { | ||
int n; | ||
std::vector<std::string> patterns; | ||
generate_parentheses p; | ||
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n = 1; | ||
patterns = {{"()"}}; | ||
assert(p.generate_parenthesis(n) == patterns); | ||
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n = 3; | ||
patterns = {{"()()()"}, {"()(())"}, {"(())()"}, {"(()())"}, {"((()))"}}; | ||
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assert(p.generate_parenthesis(n) == patterns); | ||
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n = 4; | ||
patterns = {{"()()()()"}, {"()()(())"}, {"()(())()"}, {"()(()())"}, | ||
{"()((()))"}, {"(())()()"}, {"(())(())"}, {"(()())()"}, | ||
{"(()()())"}, {"(()(()))"}, {"((()))()"}, {"((())())"}, | ||
{"((()()))"}, {"(((())))"}}; | ||
assert(p.generate_parenthesis(n) == patterns); | ||
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std::cout << "All tests passed\n"; | ||
} | ||
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/** | ||
* @brief Main function | ||
* @returns 0 on exit | ||
*/ | ||
int main() { | ||
test(); | ||
return 0; | ||
} |