oj.uz

Submission #161471

# Submission time Handle Problem Language Result Execution time Memory
161471 2019-11-02T16:33:58 Z rama_pang Fibonacci representations (CEOI18_fib) C++14
100 / 100
 516 ms 44332 KB 
#include <bits/stdc++.h>
using namespace std;
using lint = long long;

const lint MOD = 1e9 + 7;
const lint INF = 1e9 + 100000;

const int RIGHT_MUST = 0;   // Rightmost bit have to be pushed to the left
const int RIGHT_FREE = 1;   // Rightmost bit doesn't have to be pushed to the left
const int LEFT_MUST = 0;    // Leftmost bit have to be pushed to the left
const int LEFT_FREE = 1;    // Leftmost bit doesn't have to be pushed to the left


struct Matrix { // 2x2 Matrix

    array<array<lint, 2>, 2> mat;
    
    array<lint, 2> & operator [] (int i) { return mat[i]; }
    const array<lint, 2> & operator [] (int i) const { return mat[i]; }
    
    Matrix() {
        mat[0][0] = 0; mat[0][1] = 0;
        mat[1][0] = 0; mat[1][1] = 0;
    }

    Matrix operator * (const Matrix &m) const {
        Matrix res;
        for (int i = 0; i < 2; i++) 
            for (int j = 0; j < 2; j++) 
                for (int k = 0; k < 2; k++) 
                    res[i][j] += mat[i][k] * m[k][j], res[i][j] %= MOD;

        return res;        
    }

};


struct Segment {

    Matrix M; // 2 by 2 matrix, representing segment.

    int left, right; // left and right index of current segment

    bool exists = false;

    void init(pair<int, int> p) { // right and left position of segment
        right = p.second, left = p.first;
        int size = (right - left) / 2 + 1;

        M[RIGHT_MUST][LEFT_MUST] = 1;           M[RIGHT_MUST][LEFT_FREE] = 0;
        M[RIGHT_FREE][LEFT_MUST] = size - 1;    M[RIGHT_FREE][LEFT_FREE] = 1;

    }

    void merge(const Segment &L, const Segment &R) {
        exists = L.exists || R.exists;
        if (!L.exists) return void(*this = R);
        if (!R.exists) return void(*this = L);

        right = R.right, left = L.left;
        int dist = R.left - L.right;
        
        Matrix Mid;
        if (dist % 2 == 0) Mid[0][0] = Mid[1][0] = 1;
        Mid[0][1] = max(0, (dist - 1) / 2) % MOD;
        Mid[1][1] = (Mid[0][1] + 1) % MOD;

        M = R.M * Mid * L.M;
    }

};


struct SegmentTree {

    vector<Segment> Tree;
    vector<pair<int, int>> all;
    int sz;

    void init(vector<pair<int, int>> all) {
        this->all = all;
        sz = 1; 
        while (sz < all.size()) sz *= 2;
        Tree.resize(2 * sz);
        for (int i = 0; i < all.size(); i++) 
            Tree[i + sz].init(all[i]);

    }

    void update(vector<pair<int, int>> events) {
        for (auto p : events) {
            int id = lower_bound(all.begin(), all.end(), p) - all.begin();
            Tree[id + sz].exists = !Tree[id + sz].exists;
            for (int n = (id + sz) / 2; n >= 1; n /= 2)
                Tree[n].merge(Tree[n * 2], Tree[n * 2 + 1]);
        }
    } 

    lint query() {
        Segment BASE, QUERY;
        BASE.init({-1, -1}); BASE.exists = true;
        QUERY.merge(BASE, Tree[1]);
        return QUERY.M[RIGHT_FREE][LEFT_FREE];
    }

};


int current_time;
set<pair<int, int>> intervals; // pairs (A, B) such that A, A + 2, A + 4, ..., B is "1".
vector<vector<pair<int, int>>> events;

inline void add_interval(int l, int r) {
    if (l <= r && 0 <= l && r < INF) {
        events[current_time].push_back({l, r});
        intervals.insert({l, r});
    }
}

inline void erase(set<pair<int, int>>::iterator it) {
    events[current_time].push_back({it->first, it->second});
    intervals.erase(it);
}

void add_point(int x) { // x is not inside a segment
    auto R = intervals.upper_bound({x, INF});
    auto L = prev(R);
    if (x + 1 == R->first) {//  X1010101...1010 (before)
                            //  00000000...0001 (after)

        int new_x = R->second + 1;
        erase(R);
        add_point(new_x);
    } else if (L->second + 1 == x) { // ...10101X0 (before)
                                     // ...1010001 (after)

        add_interval(L->first, L->second - 2);
        erase(L);
        add_point(x + 1);
    } else {
        pair<int, int> new_interval = {x, x};
        if (L->second + 2 == x) new_interval.first = L->first, erase(L);
        if (x + 2 == R->first) new_interval.second = R->second, erase(R);
        add_interval(new_interval.first, new_interval.second);
    }
}

void add(int x) { // general case
    auto seg = prev(intervals.upper_bound({x, INF}));
    if (!(seg->first <= x && x <= seg->second)) return void(add_point(x));

    if (seg->first % 2 != x % 2) { // ...10101010...
                                   // ...00010000... +
                                   // ...10100001... =

        add_interval(seg->first, x - 1);
        int new_point = seg->second + 1;
        erase(seg);
        add_point(new_point);

    } else { // ...00101010100...
             // ...00000010000... +
             // ...10010101100... =

        vector<int> new_point{seg->first - 2, seg->second + 1};
        add_interval(seg->first + 1, x - 1);
        erase(seg);
        for (auto p : new_point) {
            if (p == -2) continue;  // F(-2) = 0
            if (p == -1) p = 0;     // F(-1) = F(0) = 1
            add_point(p);
        }  
    }
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);

    int N; cin >> N;
    events.resize(N);
    intervals.insert({-INF, -INF});
    intervals.insert({+INF, +INF});
    
    for (current_time = 0; current_time < N; current_time++) {
        int a; cin >> a; a--;
        add(a);
    }

    vector<pair<int, int>> all;
    for (auto e : events)
        for (auto p : e)
            all.push_back(p);

    sort(all.begin(), all.end());
    all.resize(unique(all.begin(), all.end()) - all.begin());

    SegmentTree segtree;
    segtree.init(all);

    for (current_time = 0; current_time < N; current_time++) {
        segtree.update(events[current_time]);
        cout << segtree.query() << "\n";
    }
}

Compilation message

fib.cpp: In member function 'void SegmentTree::init(std::vector<std::pair<int, int> >)':
fib.cpp:84:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         while (sz < all.size()) sz *= 2;
                ~~~^~~~~~~~~~~~
fib.cpp:86:27: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         for (int i = 0; i < all.size(); i++) 
                         ~~^~~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 2 ms 376 KB Output is correct
3 Correct 2 ms 376 KB Output is correct
4 Correct 2 ms 376 KB Output is correct
5 Correct 2 ms 376 KB Output is correct
6 Correct 2 ms 376 KB Output is correct

Subtask #2
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 2 ms 376 KB Output is correct
3 Correct 2 ms 376 KB Output is correct
4 Correct 2 ms 376 KB Output is correct
5 Correct 2 ms 376 KB Output is correct
6 Correct 2 ms 376 KB Output is correct
7 Correct 2 ms 376 KB Output is correct
8 Correct 2 ms 376 KB Output is correct
9 Correct 2 ms 376 KB Output is correct
10 Correct 3 ms 376 KB Output is correct
11 Correct 2 ms 376 KB Output is correct
12 Correct 2 ms 380 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 380 KB Output is correct
2 Correct 2 ms 376 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 2 ms 376 KB Output is correct
3 Correct 2 ms 376 KB Output is correct
4 Correct 2 ms 376 KB Output is correct
5 Correct 2 ms 376 KB Output is correct
6 Correct 2 ms 376 KB Output is correct
7 Correct 2 ms 376 KB Output is correct
8 Correct 2 ms 376 KB Output is correct
9 Correct 2 ms 376 KB Output is correct
10 Correct 3 ms 376 KB Output is correct
11 Correct 2 ms 376 KB Output is correct
12 Correct 2 ms 380 KB Output is correct
13 Correct 2 ms 380 KB Output is correct
14 Correct 2 ms 376 KB Output is correct
15 Correct 2 ms 376 KB Output is correct
16 Correct 2 ms 376 KB Output is correct
17 Correct 2 ms 376 KB Output is correct
18 Correct 2 ms 376 KB Output is correct
19 Correct 2 ms 380 KB Output is correct
20 Correct 2 ms 376 KB Output is correct
21 Correct 2 ms 376 KB Output is correct
22 Correct 2 ms 376 KB Output is correct
23 Correct 2 ms 376 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 355 ms 25568 KB Output is correct
3 Correct 368 ms 24796 KB Output is correct

Subtask #6
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 2 ms 376 KB Output is correct
3 Correct 2 ms 376 KB Output is correct
4 Correct 2 ms 376 KB Output is correct
5 Correct 2 ms 376 KB Output is correct
6 Correct 2 ms 376 KB Output is correct
7 Correct 2 ms 376 KB Output is correct
8 Correct 2 ms 376 KB Output is correct
9 Correct 2 ms 376 KB Output is correct
10 Correct 3 ms 376 KB Output is correct
11 Correct 2 ms 376 KB Output is correct
12 Correct 2 ms 380 KB Output is correct
13 Correct 2 ms 380 KB Output is correct
14 Correct 2 ms 376 KB Output is correct
15 Correct 2 ms 376 KB Output is correct
16 Correct 2 ms 376 KB Output is correct
17 Correct 2 ms 376 KB Output is correct
18 Correct 2 ms 376 KB Output is correct
19 Correct 2 ms 380 KB Output is correct
20 Correct 2 ms 376 KB Output is correct
21 Correct 2 ms 376 KB Output is correct
22 Correct 2 ms 376 KB Output is correct
23 Correct 2 ms 376 KB Output is correct
24 Correct 2 ms 376 KB Output is correct
25 Correct 355 ms 25568 KB Output is correct
26 Correct 368 ms 24796 KB Output is correct
27 Correct 84 ms 7692 KB Output is correct
28 Correct 146 ms 13668 KB Output is correct
29 Correct 75 ms 5872 KB Output is correct
30 Correct 158 ms 13284 KB Output is correct
31 Correct 172 ms 22408 KB Output is correct
32 Correct 160 ms 14824 KB Output is correct
33 Correct 214 ms 22108 KB Output is correct
34 Correct 214 ms 22260 KB Output is correct
35 Correct 283 ms 21864 KB Output is correct
36 Correct 370 ms 22052 KB Output is correct
37 Correct 265 ms 10188 KB Output is correct
38 Correct 345 ms 26592 KB Output is correct
39 Correct 111 ms 8556 KB Output is correct
40 Correct 169 ms 11496 KB Output is correct
41 Correct 395 ms 15044 KB Output is correct
42 Correct 341 ms 26432 KB Output is correct
43 Correct 187 ms 12780 KB Output is correct
44 Correct 327 ms 44332 KB Output is correct
45 Correct 398 ms 43564 KB Output is correct
46 Correct 388 ms 44044 KB Output is correct
47 Correct 394 ms 29076 KB Output is correct
48 Correct 444 ms 44184 KB Output is correct
49 Correct 516 ms 43748 KB Output is correct
50 Correct 395 ms 27628 KB Output is correct