icpc_library

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:heavy_check_mark: test/others/aoj_1300.test.cpp

Depends on

Code

#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1300"

#include "../../template/template.hpp"
#include "../../template/parsing_template.hpp"
#include "../../math/gauss_jordan.hpp"
#include "../../utility/rational.hpp"

using namespace lib;

std::vector<std::vector<rational>> chemical_equation(State &);
std::vector<std::map<std::string, ll>> molecule_sequence(State &);
std::map<std::string, ll> molecule(State &);
std::map<std::string, ll> group(State &);
std::map<std::string, ll> unit_group(State &);
std::pair<std::string, ll> chemical_element(State &);
ll number(State &);

std::vector<std::vector<rational>> chemical_equation(State &begin) {
    auto lhs = molecule_sequence(begin);
    consume(begin, '-');
    consume(begin, '>');
    auto rhs = molecule_sequence(begin);
    std::set<std::string> set;
    for (auto &map : lhs) {
        for (auto &p : map) set.insert(p.first);
    }
    int h = set.size();
    std::vector a(h, std::vector<rational>());
    rep(i, 0, lhs.size()) {
        int j = 0;
        for (auto &s : set) {
            a[j].emplace_back(lhs[i][s]);
            j++;
        }
    }
    rep(i, 0, rhs.size()) {
        int j = 0;
        for (auto &s : set) {
            a[j].emplace_back(-rhs[i][s]);
            j++;
        }
    }
    assert(a[0].size() == lhs.size() + rhs.size());
    return a;
}

std::vector<std::map<std::string, ll>> molecule_sequence(State &begin) {
    std::vector<std::map<std::string, ll>> mole;
    mole.emplace_back(molecule(begin));
    while (expect(begin, '+')) {
        consume(begin, '+');
        mole.emplace_back(molecule(begin));
    }
    return mole;
}

std::map<std::string, ll> molecule(State &begin) {
    auto ret = group(begin);
    while (isAlpha(*begin) || expect(begin, '(')) {
        for (auto [s, c] : group(begin)) {
            ret[s] += c;
        }
    }
    return ret;
}

std::map<std::string, ll> group(State &begin) {
    auto ret = unit_group(begin);
    if (isdigit(*begin)) {
        ll num = number(begin);
        for (auto &p : ret) {
            p.second *= num;
        }
    }
    return ret;
}

std::map<std::string, ll> unit_group(State &begin) {
    if (isAlpha(*begin)) {
        std::string ret = "";
        ret += *begin;
        consume(begin, *begin);
        if (isalpha(*begin)) {
            ret += *begin;
            consume(begin, *begin);
        }
        std::map<std::string, ll> map;
        map[ret] = 1;
        return map;
    } else {
        consume(begin, '(');
        auto ret = molecule(begin);
        consume(begin, ')');
        return ret;
    }
}

ll number(State &begin) {
    ll ret = 0;
    while (isdigit(*begin)) {
        ret *= 10;
        ret += *begin - '0';
        consume(begin, *begin);
    }
    return ret;
}

int main() {
    std::string s;
    while (std::cin >> s, !(s == ".")) {
        State begin = s.begin();
        auto a = chemical_equation(begin);
        consume(begin, '.');
        a = gauss_jordan<rational>(a);
        int n = a.size();
        int m = a[0].size();
        int x = -1;
        {
            bool is_break = false;
            rrep(i, 0, n) {
                if(is_break) break;
                rep(j, 0, m) {
                    if (a[i][j] != 0) {
                        x = j + 1;
                        is_break = true;
                        break;
                    }
                }
            }
        }
        std::vector<ll> ans(m, 1);
        rep(j,x,m) {
            rep(i,0,n) {
                if(a[i][j] != 0) {
                    ans[j] = std::lcm(ans[j], a[i][j].val().second);
                }
            }
        }
        rep(i,0,x) {
            ans[i] = 0;
            rep(j,x,m) {
                ans[i] -= (a[i][j] * ans[j]).val().first;
            }
        }
        rep(i,0,m) {
            std::cout << ans[i] << " \n"[i == m-1];
        }
    }
}
#line 1 "test/others/aoj_1300.test.cpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1300"

#line 2 "template/template.hpp"

#include <bits/stdc++.h>

#define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--)
#define all(v) v.begin(), v.end()

using ll = long long;
using ld = long double;
using ull = unsigned long long;

template <typename T> bool chmin(T &a, const T &b) {
    if (a <= b) return false;
    a = b;
    return true;
}
template <typename T> bool chmax(T &a, const T &b) {
    if (a >= b) return false;
    a = b;
    return true;
}

namespace lib {

using namespace std;

}  // namespace lib

// using namespace lib;
#line 2 "template/parsing_template.hpp"

#line 4 "template/parsing_template.hpp"

namespace lib {

typedef std::string::const_iterator State;

bool expect(State &begin, char expected) {
    return *begin == expected;
}

void consume(State &begin, char expected) {
    assert(*begin == expected);
    begin++;
}

bool isdigit(char c) {
    return '0' <= c && c <= '9';
}

bool isAlpha(char c) {
    return 'A' <= c && c <= 'Z';
}

bool isalpha(char c) {
    return 'a' <= c && c <= 'z';
}

}  // namespace lib
#line 3 "math/gauss_jordan.hpp"

namespace lib {
using namespace std;

template <typename T> vector<vector<T>> gauss_jordan(vector<vector<T>> &a) {
    int n = a.size();
    int m = a[0].size();
    vector<vector<T>> b = a;
    int piv = 0;
    rep(j, 0, m) rep(i, piv, n) {
        if (b[i][j] != T(0)) {
            swap(b[i], b[piv]);
            T ip = T(1) / b[piv][j];
            rep(l, 0, n) {
                if (l != piv) {
                    T tmp = ip * b[l][j];
                    rep(k, j, m) b[l][k] -= tmp * b[piv][k];
                }
            }
            rep(k, j, m) b[piv][k] *= ip;
            piv++;
            break;
        }
    }
    return b;
}

}  // namespace lib
#line 2 "utility/rational.hpp"

#line 4 "utility/rational.hpp"

namespace lib {

struct rational {
    rational() : p(0), q(1) {}
    rational(ll n) : p(n), q(1) {}
    rational(ll n, ll m) {
        assert(m != 0);
        if (m < 0) n = -n, m = -m;
        ll g = gcd(n, m);
        p = n / g;
        q = m / g;
    }
    explicit operator const ld () const { return ld(p) / ld(q); }
    rational& operator+=(const rational& rhs){
        ll g = gcd(q, rhs.q);
        ll np = rhs.q / g * p + q / g * rhs.p;
        ll nq = q / g * rhs.q;
        ll ng = gcd(np, nq);
        p = np / ng, q = nq / ng;
        return *this;
    }
    rational& operator-=(const rational& rhs) {
        (*this) += rational(-rhs.p, rhs.q);
        return *this;
    }
    rational& operator*=(const rational& rhs) {
        ll g1 = gcd(q, rhs.p), g2 = gcd(p, rhs.q);
        ll np = p / g2 * rhs.p / g1;
        ll nq = q / g1 * rhs.q / g2;
        p = np, q = nq;
        return *this;
    }
    rational& operator/=(const rational& rhs) {
        (*this) *= rational(rhs.q, rhs.p);
        return *this;
    }
    rational operator+() const {
        return *this;
    }
    rational operator-() const {
        return rational() - *this;
    }
    friend rational operator+(const rational& lhs, const rational& rhs) {
        return rational(lhs) += rhs;
    }
    friend rational operator-(const rational& lhs, const rational& rhs) {
        return rational(lhs) -= rhs;
    }
    friend rational operator*(const rational& lhs, const rational& rhs) {
        return rational(lhs) *= rhs;
    }
    friend rational operator/(const rational& lhs, const rational& rhs) {
        return rational(lhs) /= rhs;
    }
    friend bool operator==(const rational& lhs, const rational& rhs) {
        return lhs.p == rhs.p && lhs.q == rhs.q;
    }
    friend bool operator!=(const rational& lhs, const rational& rhs) {
        return lhs.p != rhs.p || lhs.q != rhs.q;
    }
    friend bool operator<(const rational lhs, const rational rhs) {
        return less_than(lhs, rhs);
    }
    friend bool operator>(const rational lhs, const rational rhs) {
        return less_than(rhs, lhs);
    }
    friend bool operator<=(const rational lhs, const rational rhs) {
        return lhs == rhs || lhs < rhs;
    }
    friend bool operator>=(const rational lhs, const rational rhs) {
        return lhs == rhs || lhs > rhs;
    }
    friend std::ostream& operator<<(std::ostream& os, const rational& r) {
        return os << r.p << " / " << r.q;
    }
    std::pair<ll,ll> val() const {
        return {p, q};
    }

  private:
    ll p, q;
    static bool less_than(rational lhs, rational rhs) {
        __int128_t lv = __int128_t(lhs.p) * __int128_t(rhs.q);
        __int128_t rv = __int128_t(lhs.q) * __int128_t(rhs.p);
        return lv < rv;
    }
};

}  // namespace lib
#line 7 "test/others/aoj_1300.test.cpp"

using namespace lib;

std::vector<std::vector<rational>> chemical_equation(State &);
std::vector<std::map<std::string, ll>> molecule_sequence(State &);
std::map<std::string, ll> molecule(State &);
std::map<std::string, ll> group(State &);
std::map<std::string, ll> unit_group(State &);
std::pair<std::string, ll> chemical_element(State &);
ll number(State &);

std::vector<std::vector<rational>> chemical_equation(State &begin) {
    auto lhs = molecule_sequence(begin);
    consume(begin, '-');
    consume(begin, '>');
    auto rhs = molecule_sequence(begin);
    std::set<std::string> set;
    for (auto &map : lhs) {
        for (auto &p : map) set.insert(p.first);
    }
    int h = set.size();
    std::vector a(h, std::vector<rational>());
    rep(i, 0, lhs.size()) {
        int j = 0;
        for (auto &s : set) {
            a[j].emplace_back(lhs[i][s]);
            j++;
        }
    }
    rep(i, 0, rhs.size()) {
        int j = 0;
        for (auto &s : set) {
            a[j].emplace_back(-rhs[i][s]);
            j++;
        }
    }
    assert(a[0].size() == lhs.size() + rhs.size());
    return a;
}

std::vector<std::map<std::string, ll>> molecule_sequence(State &begin) {
    std::vector<std::map<std::string, ll>> mole;
    mole.emplace_back(molecule(begin));
    while (expect(begin, '+')) {
        consume(begin, '+');
        mole.emplace_back(molecule(begin));
    }
    return mole;
}

std::map<std::string, ll> molecule(State &begin) {
    auto ret = group(begin);
    while (isAlpha(*begin) || expect(begin, '(')) {
        for (auto [s, c] : group(begin)) {
            ret[s] += c;
        }
    }
    return ret;
}

std::map<std::string, ll> group(State &begin) {
    auto ret = unit_group(begin);
    if (isdigit(*begin)) {
        ll num = number(begin);
        for (auto &p : ret) {
            p.second *= num;
        }
    }
    return ret;
}

std::map<std::string, ll> unit_group(State &begin) {
    if (isAlpha(*begin)) {
        std::string ret = "";
        ret += *begin;
        consume(begin, *begin);
        if (isalpha(*begin)) {
            ret += *begin;
            consume(begin, *begin);
        }
        std::map<std::string, ll> map;
        map[ret] = 1;
        return map;
    } else {
        consume(begin, '(');
        auto ret = molecule(begin);
        consume(begin, ')');
        return ret;
    }
}

ll number(State &begin) {
    ll ret = 0;
    while (isdigit(*begin)) {
        ret *= 10;
        ret += *begin - '0';
        consume(begin, *begin);
    }
    return ret;
}

int main() {
    std::string s;
    while (std::cin >> s, !(s == ".")) {
        State begin = s.begin();
        auto a = chemical_equation(begin);
        consume(begin, '.');
        a = gauss_jordan<rational>(a);
        int n = a.size();
        int m = a[0].size();
        int x = -1;
        {
            bool is_break = false;
            rrep(i, 0, n) {
                if(is_break) break;
                rep(j, 0, m) {
                    if (a[i][j] != 0) {
                        x = j + 1;
                        is_break = true;
                        break;
                    }
                }
            }
        }
        std::vector<ll> ans(m, 1);
        rep(j,x,m) {
            rep(i,0,n) {
                if(a[i][j] != 0) {
                    ans[j] = std::lcm(ans[j], a[i][j].val().second);
                }
            }
        }
        rep(i,0,x) {
            ans[i] = 0;
            rep(j,x,m) {
                ans[i] -= (a[i][j] * ans[j]).val().first;
            }
        }
        rep(i,0,m) {
            std::cout << ans[i] << " \n"[i == m-1];
        }
    }
}
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