Submission #880888

#	Time	Username	Problem	Language	Result	Execution time	Memory
880888		marvinthang	Fibonacci representations (CEOI18_fib)	C++17	65 / 100	603 ms	32384 KiB

fib

/*************************************
*    author: marvinthang             *
*    created: 29.11.2023 20:32:14    *
*************************************/

#include <bits/stdc++.h>

using namespace std;

#define                  fi  first
#define                  se  second
#define                left  ___left
#define               right  ___right
#define                TIME  (1.0 * clock() / CLOCKS_PER_SEC)
#define             MASK(i)  (1LL << (i))
#define           BIT(x, i)  ((x) >> (i) & 1)
#define  __builtin_popcount  __builtin_popcountll
#define              ALL(v)  (v).begin(), (v).end()
#define           REP(i, n)  for (int i = 0, _n = (n); i < _n; ++i)
#define          REPD(i, n)  for (int i = (n); i-- > 0; )
#define        FOR(i, a, b)  for (int i = (a), _b = (b); i < _b; ++i) 
#define       FORD(i, b, a)  for (int i = (b), _a = (a); --i >= _a; ) 
#define       FORE(i, a, b)  for (int i = (a), _b = (b); i <= _b; ++i) 
#define      FORDE(i, b, a)  for (int i = (b), _a = (a); i >= _a; --i) 
#define        scan_op(...)  istream & operator >> (istream &in, __VA_ARGS__ &u)
#define       print_op(...)  ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
    #include "debug.h"
#else
    #define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
    #define DB(...) 23
    #define db(...) 23
    #define debug(...) 23
#endif

template <class U, class V> scan_op(pair <U, V>)  { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>)  { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>)  { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")";  else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }

const int MOD = 1e9 + 7;
namespace MODULAR {
    inline void fasterLLDivMod(unsigned long long x, unsigned y, unsigned &out_d, unsigned &out_m) {
        unsigned xh = (unsigned)(x >> 32), xl = (unsigned)x, d, m;
    #ifdef __GNUC__
        asm(
            "divl %4 \n\t"
            : "=a" (d), "=d" (m)
            : "d" (xh), "a" (xl), "r" (y)
        );
    #else
        __asm {
            mov edx, dword ptr[xh];
            mov eax, dword ptr[xl];
            div dword ptr[y];
            mov dword ptr[d], eax;
            mov dword ptr[m], edx;
        };
    #endif
        out_d = d; out_m = m;
    }
    template <class T> T invGeneral(T a, T b) {
        a %= b;
        if (!a) return b == 1 ? 0 : -1;
        T x = invGeneral(b, a);
        return x == -1 ? -1 : ((1 - 1LL * b * x) / a + b) % b;
    }
    template <int MOD> struct ModInt {
        unsigned int val;
        ModInt(void): val(0) {}
        ModInt(const long long &x) { *this = x; }
        ModInt & normalize(const unsigned int &v) {
            val = v >= MOD ? v - MOD : v;
            return *this;
        }
        bool operator ! (void) { return !val; }
        ModInt & operator = (const ModInt &x) { val = x.val; return *this; }
        ModInt & operator = (const long long &x) { return normalize(x % MOD + MOD); }
        ModInt operator - (void) { return ModInt(MOD - val); }
        ModInt & operator += (const ModInt &other) { return normalize(val + other.val); }
        ModInt & operator -= (const ModInt &other) { return normalize(val + MOD - other.val); }
        ModInt & operator /= (const ModInt &other) { return *this *= other.inv(); }
        ModInt & operator *= (const ModInt &other) {
            unsigned dummy;
            fasterLLDivMod((unsigned long long) val * other.val, MOD, dummy, val);
            return *this;
        }
        ModInt operator + (const ModInt &other) const { return ModInt(*this) += other; }
        ModInt operator - (const ModInt &other) const { return ModInt(*this) -= other; }
        ModInt operator * (const ModInt &other) const { return ModInt(*this) *= other; }
        ModInt operator / (const ModInt &other) const { return ModInt(*this) /= other; }
        ModInt pow(long long n) const {
            assert(n >= 0);
            ModInt res = 1, a = *this;
            for (; n; n >>= 1, a *= a) if (n & 1) res *= a;
            return res;
        }
        ModInt inv(void) const {
            int i = invGeneral((int) val, MOD);
            assert(~i);
            return i;
        }
        ModInt & operator ++ (void) { return *this += 1; }
        ModInt & operator -- (void) { return *this -= 1; }
        ModInt operator ++ (int) { ModInt old = *this; operator ++(); return old; }
        ModInt operator -- (int) { ModInt old = *this; operator --(); return old; }
        friend ModInt operator + (const long long &x, const ModInt &y) { return ModInt(x) + y; }
        friend ModInt operator - (const long long &x, const ModInt &y) { return ModInt(x) - y; }
        friend ModInt operator * (const long long &x, const ModInt &y) { return ModInt(x) * y; }
        friend ModInt operator / (const long long &x, const ModInt &y) { return ModInt(x) / y; }
        friend ostream & operator << (ostream &out, const ModInt &x) { return out << x.val; }
        friend istream & operator >> (istream &in, ModInt &x) { long long a; in >> a; x = a; return in; }
        explicit operator bool(void) const { return val; }
        explicit operator int(void) const { return val; }
    };  
    using Modular = ModInt <MOD>;
}
using namespace MODULAR;

template <class T> struct Matrix {
    int numRow, numCol; vector <T> val;
    // accessors
    typename vector<T>::iterator operator [] (int r) { return val.begin() + r * numCol; }
    inline T & at(int r, int c) { return val[r * numCol + c]; }
    inline T get(int r, int c) const { return val[r * numCol + c]; }
    // constructors
    Matrix() {}
    Matrix(int r, int c): numRow(r), numCol(c), val(r * c) {}
    Matrix(const vector <vector <T>> &d) {
        numRow = d.size();
        numCol = numRow ? d[0].size() : 0;
        for (int i = 0; i < numRow; ++i) {
            assert((int) d[i].size() == numCol);
            copy(d[i].begin(), d[i].end(), back_inserter(val));
        }
    }
    Matrix & set_value(T v) {
        for (int i = 0; i < numRow * numCol; ++i) val[i] = v;
        return *this;
    }
    // convert to 2D vector
    vector <vector <T>> vecvec(void) const {
        vector <vector <T>> res(numRow);
        for (int i = 0; i < numRow; ++i)
            copy(val.begin() + i * numCol, val.begin() + (i + 1) * numCol, back_inserter(res[i]));
        return res;
    }
    operator vector <vector <T>> () const { return vecvec(); }
    static Matrix identity(int n) {
        Matrix res(n, n);
        for (int i = 0; i < n; ++i) res.at(i, i) = T(1);
        return res;
    }
    friend istream & operator >> (istream &in, Matrix &res) {
        for (T &x: res.val) in >> x;
        return in;
    }
    friend ostream & operator << (ostream &out, const Matrix &res) {
        for (int i = 0; i < res.numRow * res.numCol; ++i)
            cout << res.val[i] << " \n"[i % res.numCol == res.numCol - 1];
        return out;
    }
    Matrix operator - (void) {
        Matrix res(numRow, numCol);
        for (int i = 0; i < numRow * numCol; ++i) res.val[i] = -val[i];
        return res;
    }
    Matrix operator * (const T &v) {
        Matrix res = *this;
        for (T &x: res.val) x *= v;
        return res;
    } 
    Matrix operator / (const T &v) {
        Matrix res = *this;
        const T inv = T(1) / v;
        for (T &x: res.val) x *= inv;
        return res;
    }
    Matrix operator + (const Matrix &other) const {
        int M = numRow, N = numCol;
        assert(M == other.numRow); assert(N == other.numCol);
        Matrix res = *this;
        for (int i = 0; i < numRow * numCol; ++i) res.val[i] += other.val[i];
        return res;
    }
    Matrix operator - (const Matrix &other) const {
        int M = numRow, N = numCol;
        assert(M == other.numRow); assert(N == other.numCol);
        Matrix res = *this;
        for (int i = 0; i < numRow * numCol; ++i) res.val[i] -= other.val[i];
        return res;
    }
    Matrix operator * (const Matrix &other) const {
        int M = numRow, N = numCol, P = other.numCol;
        assert(N == other.numRow);
        Matrix t_other = other.transpose();
        Matrix res(M, P);
        for (int i = 0; i < M; ++i)
            for (int j = 0; j < P; ++j)
                res.at(i, j) = inner_product(this->val.begin() + N * i, this->val.begin() + N * (i + 1), t_other.val.begin() + t_other.numCol * j, T(0));
        return res;
    }
    Matrix & operator *= (const T &v) { return *this = *this * v; }
    Matrix & operator /= (const T &v) { return *this = *this / v; }
    Matrix & operator += (const Matrix &other) { return *this = *this + other; }
    Matrix & operator -= (const Matrix &other) { return *this = *this - other; }
    Matrix & operator *= (const Matrix &other) { return *this = *this * other; }
    Matrix pow(long long Exp) const {
        int M = numRow;
        assert(M == numCol); assert(Exp >= 0);
        Matrix res = identity(M);
        if (!Exp) return res;
        bool is_id = true;
        for (int i = 63 - __builtin_clzll(Exp); i >= 0; --i) {
            if (!is_id) res *= res;
            if (Exp >> i & 1) res *= *this, is_id = false;
        }
        return res;
    }
    Matrix transpose(void) const {
        Matrix res(numCol, numRow);
        for (int i = 0; i < numRow; ++i)
            for (int j = 0; j < numCol; ++j)
                res.at(j, i) = this->get(i, j);
        return res;
    }
};

// end of template

void process(void) {
	int n; cin >> n;
    vector <int> a(n); cin >> a;
    if (n <= 100) {
        map <int, int> cnt;
        function<void(int)> fix = [&] (int u) {
            if (!cnt.count(u) || !cnt[u]) return;
            if (cnt[u] == 1) {
                if (u && cnt[u - 1]) {
                    --cnt[u - 1]; --cnt[u]; ++cnt[u + 1];
                    fix(u + 1);
                }
                if (cnt[u] && cnt.count(u + 1) && cnt[u + 1]) {
                    --cnt[u]; --cnt[u + 1]; ++cnt[u + 2];
                    fix(u + 2);
                }
            } else {
                cnt[u] = 0;
                ++cnt[u + 1];
                if (u > 1) {
                    ++cnt[u - 2];
                    fix(u - 2);
                } else if (u == 1) {
                    ++cnt[0];
                    fix(0);
                }
                fix(u + 1);
     
            }
        };
        REP(i, n) {
            ++cnt[--a[i]];
            fix(a[i]);
            vector <int> pos;
            for (auto [x, y]: cnt) if (y) pos.push_back(x);
            vector <Modular> dp(pos.size());
            Modular sum = 1;
            dp[0] = pos[0] / 2;
            FOR(i, 1, pos.size()) {
                dp[i] = (pos[i] - pos[i - 1]) / 2 * dp[i - 1] + (pos[i] - pos[i - 1] - 1) / 2 * sum;
                sum += dp[i - 1];
            }
            cout << dp[(int) pos.size() - 1] + sum << '\n';
        }
        return;
    }
    vector <int> order(n);
    iota(ALL(order), 0);
    sort(ALL(order), [&] (int x, int y) { return a[x] < a[y]; });
    vector <int> pos(n);
    REP(i, n) pos[order[i]] = i;
    vector <Matrix <Modular>> st(n * 4 + 23, Matrix<Modular>::identity(2));
    function<void(int, int, int, int, int)> update = [&] (int i, int l, int r, int u, int val) {
        if (r - l == 1) {
            st[i] = Matrix<Modular>({
                {val / 2, 1},
                {(val - 1) / 2, 1}
            });
            return;
        }
        int m = l + r >> 1;
        if (u < m) update(i << 1, l, m, u, val);
        else update(i << 1 | 1, m, r, u, val);
        st[i] = st[i << 1] * st[i << 1 | 1];
    };
    set <int> s;
    REP(i, n) {
        auto it = s.insert(pos[i]).fi;
        int prv = it == s.begin() ? -1 : *prev(it);
        int nxt = next(it) == s.end() ? -1 : *next(it);
        if (prv != -1) {
            update(1, 0, n, pos[i], a[i] - a[order[prv]]);
        }
        if (nxt != -1) {
            update(1, 0, n, nxt, a[order[nxt]] - a[i]);
        }
        Matrix <Modular> base({
            {(a[order[*s.begin()]] - 1) / 2, 1}
        });
        base *= st[1];
        cout << base[0][0] + base[0][1] << '\n';
    }
}

int main(void) {
	ios_base::sync_with_stdio(false); cin.tie(nullptr); // cout.tie(nullptr);
	file("fib");
	// int t; cin >> t; while (t--)
	process();
	// cerr << "Time elapsed: " << TIME << " s.\n";
	return (0^0);
}

Compilation message (stderr)

fib.cpp: In lambda function:
fib.cpp:293:19: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  293 |         int m = l + r >> 1;
      |                 ~~^~~
fib.cpp: In function 'int main()':
fib.cpp:30:61: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   30 |     #define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
      |                                                      ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
fib.cpp:319:2: note: in expansion of macro 'file'
  319 |  file("fib");
      |  ^~~~
fib.cpp:30:94: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   30 |     #define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
      |                                                                                       ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
fib.cpp:319:2: note: in expansion of macro 'file'
  319 |  file("fib");
      |  ^~~~

• Subtask 1: 5 / 5
• Subtask 2: 20 / 20
• Subtask 3: 15 / 15
• Subtask 4: 10 / 10
• Subtask 5: 15 / 15
• Subtask 6: 0 / 35