oj.uz

Submission #899404

# Submission time Handle Problem Language Result Execution time Memory
899404 2024-01-06T03:43:11 Z math_rabbit_1028 Fibonacci representations (CEOI18_fib) C++14
100 / 100
 1350 ms 20964 KB 
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
ll MOD = 1e9 + 7;

int n, arr[101010];
struct Matrixseg{
    struct Matrix {
        ll a, b, c, d;
    } tree[404040];
    Matrix E;

    Matrix get_mat(int d) {
        assert(d >= 0);
        if (d == 0) return E;
        if (d % 2 == 0) return {d/2 + 1, MOD-1, 1, 0};
        else return {d/2 + 1, 0, 1, 0};
    }

    Matrix mat_pow(Matrix A, int p) {
        if (p == 0) return E;
        Matrix ret = mat_pow(A, p/2);
        ret = prod(ret, ret);
        if (p%2 == 0) return ret;
        else return prod(ret, A);
    }

    Matrix prod(Matrix A, Matrix B) {
        Matrix ret;
        ret.a = (A.a * B.a + A.b * B.c) % MOD;
        ret.b = (A.a * B.b + A.b * B.d) % MOD;
        ret.c = (A.c * B.a + A.d * B.c) % MOD;
        ret.d = (A.c * B.b + A.d * B.d) % MOD;
        return ret;
    }

    void init(int v, int st, int ed) {
        if (st == ed) {
            tree[v] = E;
            return;
        }
        int mid = (st + ed) / 2;
        init(2 * v, st, mid);
        init(2 * v + 1, mid + 1, ed);
        tree[v] = prod(tree[2 * v + 1], tree[2 * v]);
    }

    void upd(int v, int st, int ed, int idx, Matrix mat) {
        if (st == idx && ed == idx) {
            tree[v] = mat;
            return;
        }
        if (st > idx || ed < idx) return;
        int mid = (st + ed) / 2;
        upd(2 * v, st, mid, idx, mat);
        upd(2 * v + 1, mid + 1, ed, idx, mat);
        tree[v] = prod(tree[2 * v + 1], tree[2 * v]);
    }

    Matrix get(int v, int st, int ed, int lt, int rt) {
        if (lt <= st && ed <= rt) return tree[v];
        if (st > rt || lt > ed) return E;
        int mid = (st + ed) / 2;
        return prod(get(2 * v + 1, mid + 1, ed, lt, rt), get(2 * v, st, mid, lt, rt));
    }
} seg;

set<pii> s;
set<int> nums;
vector<int> vec;
int m;

int get_idx(int val) {
    return lower_bound(vec.begin(), vec.end(), val) - vec.begin() + 1;
}

void _modify(set<pii>::iterator it, pii temp) {
    auto up = it, dn = it; up++;
    seg.upd(1, 1, m, get_idx(it->first), seg.E);
    seg.upd(1, 1, m, get_idx(it->second), seg.E);
    int bot = 0;
    if (it != s.begin()) { dn--; bot = dn->second; }
    seg.upd(1, 1, m, get_idx(temp.first), seg.get_mat(temp.first - bot));
    if (temp.first != temp.second)
        seg.upd(1, 1, m, get_idx(temp.second), seg.mat_pow(seg.get_mat(2), (temp.second - temp.first) / 2));
    if (up != s.end()) {
        seg.upd(1, 1, m, get_idx(up->first), seg.get_mat(up->first - temp.second));
    }
}

void modify(set<pii>::iterator *it, pii temp) {
    if (vec.size() > 0) _modify(*it, temp);
    s.erase(*it);
    *it = s.insert(temp).first;
    nums.insert(temp.first);
    nums.insert(temp.second);
}

void _add(pii temp) {
    auto up = s.lower_bound(temp), dn = up;
    int bot = 0;
    if (up != s.begin()) { dn--; bot = dn->second; }
    seg.upd(1, 1, m, get_idx(temp.first), seg.get_mat(temp.first - bot));
    if (temp.first != temp.second)
        seg.upd(1, 1, m, get_idx(temp.second), seg.mat_pow(seg.get_mat(2), (temp.second - temp.first) / 2));
    if (up != s.end()) {
        seg.upd(1, 1, m, get_idx(up->first), seg.get_mat(up->first - temp.second));
    }
}

set<pii>::iterator add(pii temp) {
    if (vec.size() > 0) _add(temp);
    nums.insert(temp.first);
    nums.insert(temp.second);
    return s.insert(temp).first;
}

void _rem(set<pii>::iterator it) {
    auto up = it, dn = it; up++;
    seg.upd(1, 1, m, get_idx(it->first), seg.E);
    seg.upd(1, 1, m, get_idx(it->second), seg.E);
    int bot = 0;
    if (it != s.begin()) { dn--; bot = dn->second; }
    if (up != s.end()) {
        seg.upd(1, 1, m, get_idx(up->first), seg.get_mat(up->first - bot));
    }
}

set<pii>::iterator rem(set<pii>::iterator it) {
    if (vec.size() > 0) _rem(it);
    return s.erase(it);
}

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

    seg.E = {1, 0, 0, 1};

    cin >> n;
    for (int i = 1; i <= n; i++) cin >> arr[i];

    for (int i = 1; i <= n; i++) {

        do {
            auto up = s.lower_bound({arr[i]+1, 0}), dn = up;
            if (up != s.begin()) dn--;

            if (up != s.begin() && dn->first <= arr[i] && arr[i] <= dn->second) {
                if (dn->first%2 == arr[i]%2) {
                    int val = dn->second + 1;
                    if (up != s.end() && val+2 == up->first) modify(&up, {val, up->second});
                    else up = add({val, val});

                    val = dn->first-2;
                    modify(&dn, {dn->first+1, arr[i]-1});
                    if (dn->first > dn->second) dn = rem(dn);
                    if (up->first == dn->second+2) {
                        pii val = {dn->first, up->second};
                        rem(up);
                        rem(dn);
                        dn = add(val);
                    }
                    if (dn == s.begin()) {
                        if (val != -1) {
                            up = add({max(val, 1), max(val, 1)});
                            up++;
                            if (up->first == max(val, 1)+2) {
                                modify(&up, {max(val, 1), up->second});
                                up = rem(--up);
                            }
                        }
                    }
                    else {
                        dn--;
                        if (dn->second == val-2) {
                            modify(&dn, {dn->first, val});
                        }
                        else if (dn->second == val-1) {
                            if (dn->first == dn->second) dn = --rem(dn);
                            else modify(&dn, {dn->first, dn->second-2});
                            up = add({val+1, val+1});
                            up++;
                            if (up->first == val+3) {
                                modify(&up, {val+1, up->second});
                                up = rem(--up);
                            }
                        }
                        else {
                            add({val, val});
                        }
                    }
                }
                else {
                    int val = dn->second + 1;
                    if (up != s.end() && val+2 == up->first) modify(&up, {val, up->second});
                    else add({val, val});
                    modify(&dn, {dn->first, arr[i]-1});
                }
                continue;
            }

            if (up != s.end() && up->first == arr[i]+1) {
                int val = up->second + 1;
                up = rem(up);
                if (up != s.end() && up->first == val+2) modify(&up, {val, up->second});
                else add({val, val});
                continue;
            }

            if (up != s.begin() && dn->second == arr[i]-1) {
                if (dn->second-2 < dn->first) dn = --rem(dn);
                else modify(&dn, {dn->first, dn->second-2});
                if (up != s.end() && up->first == arr[i]+2) {
                    int val = up->second + 1;
                    up = rem(up);
                    if (up != s.end() && up->first == val+2) modify(&up, {val, up->second});
                    else add({val, val});
                }
                else if (up != s.end() && up->first == arr[i]+3) modify(&up, {arr[i]+1, up->second});
                else add({arr[i]+1, arr[i]+1});
                continue;
            }

            if (up != s.begin() && dn->second == arr[i]-2) {
                if (up != s.end() && up->first == arr[i]+2) {
                    pii val = {dn->first, up->second};
                    rem(up);
                    rem(dn);
                    add(val);
                }
                else modify(&dn, {dn->first, arr[i]});
                continue;
            }

            if (up != s.end() && up->first == arr[i]+2) {
                modify(&up, {arr[i], up->second});
                continue;
            }

            add({arr[i], arr[i]});

        } while(0);

    }

    for (auto iter = nums.begin(); iter != nums.end(); iter++) {
        vec.push_back(*iter);
    }

    m = vec.size();
    seg.init(1, 1, m);
    s.clear();

    for (int i = 1; i <= n; i++) {

        do {
            auto up = s.lower_bound({arr[i]+1, 0}), dn = up;
            if (up != s.begin()) dn--;

            if (up != s.begin() && dn->first <= arr[i] && arr[i] <= dn->second) {
                if (dn->first%2 == arr[i]%2) {
                    int val = dn->second + 1;
                    if (up != s.end() && val+2 == up->first) modify(&up, {val, up->second});
                    else up = add({val, val});

                    val = dn->first-2;
                    modify(&dn, {dn->first+1, arr[i]-1});
                    if (dn->first > dn->second) dn = rem(dn);
                    if (up->first == dn->second+2) {
                        pii val = {dn->first, up->second};
                        rem(up);
                        rem(dn);
                        dn = add(val);
                    }
                    if (dn == s.begin()) {
                        if (val != -1) {
                            up = add({max(val, 1), max(val, 1)});
                            up++;
                            if (up->first == max(val, 1)+2) {
                                modify(&up, {max(val, 1), up->second});
                                up = rem(--up);
                            }
                        }
                    }
                    else {
                        dn--;
                        if (dn->second == val-2) {
                            modify(&dn, {dn->first, val});
                        }
                        else if (dn->second == val-1) {
                            if (dn->first == dn->second) dn = --rem(dn);
                            else modify(&dn, {dn->first, dn->second-2});
                            up = add({val+1, val+1});
                            up++;
                            if (up->first == val+3) {
                                modify(&up, {val+1, up->second});
                                up = rem(--up);
                            }
                        }
                        else {
                            add({val, val});
                        }
                    }
                }
                else {
                    int val = dn->second + 1;
                    if (up != s.end() && val+2 == up->first) modify(&up, {val, up->second});
                    else add({val, val});
                    modify(&dn, {dn->first, arr[i]-1});
                }
                continue;
            }

            if (up != s.end() && up->first == arr[i]+1) {
                int val = up->second + 1;
                up = rem(up);
                if (up != s.end() && up->first == val+2) modify(&up, {val, up->second});
                else add({val, val});
                continue;
            }

            if (up != s.begin() && dn->second == arr[i]-1) {
                if (dn->second-2 < dn->first) dn = --rem(dn);
                else modify(&dn, {dn->first, dn->second-2});
                if (up != s.end() && up->first == arr[i]+2) {
                    int val = up->second + 1;
                    up = rem(up);
                    if (up != s.end() && up->first == val+2) modify(&up, {val, up->second});
                    else add({val, val});
                }
                else if (up != s.end() && up->first == arr[i]+3) modify(&up, {arr[i]+1, up->second});
                else add({arr[i]+1, arr[i]+1});
                continue;
            }

            if (up != s.begin() && dn->second == arr[i]-2) {
                if (up != s.end() && up->first == arr[i]+2) {
                    pii val = {dn->first, up->second};
                    rem(up);
                    rem(dn);
                    add(val);
                }
                else modify(&dn, {dn->first, arr[i]});
                continue;
            }

            if (up != s.end() && up->first == arr[i]+2) {
                modify(&up, {arr[i], up->second});
                continue;
            }

            add({arr[i], arr[i]});

        } while(0);

        Matrixseg::Matrix ans = seg.get(1, 1, m, 1, m);
        cout << (ans.a + ans.b) % MOD << "\n";
    }

    return 0;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct

Subtask #2
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 344 KB Output is correct
12 Correct 1 ms 348 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 1 ms 344 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 344 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 344 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 468 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 348 ms 20208 KB Output is correct
3 Correct 398 ms 18956 KB Output is correct

Subtask #6
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 344 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 344 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 468 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 348 ms 20208 KB Output is correct
26 Correct 398 ms 18956 KB Output is correct
27 Correct 72 ms 6236 KB Output is correct
28 Correct 146 ms 10856 KB Output is correct
29 Correct 69 ms 876 KB Output is correct
30 Correct 145 ms 10444 KB Output is correct
31 Correct 587 ms 8664 KB Output is correct
32 Correct 331 ms 9932 KB Output is correct
33 Correct 578 ms 8728 KB Output is correct
34 Correct 626 ms 8432 KB Output is correct
35 Correct 652 ms 9304 KB Output is correct
36 Correct 716 ms 8952 KB Output is correct
37 Correct 319 ms 2008 KB Output is correct
38 Correct 338 ms 20964 KB Output is correct
39 Correct 109 ms 1320 KB Output is correct
40 Correct 160 ms 1668 KB Output is correct
41 Correct 502 ms 4656 KB Output is correct
42 Correct 409 ms 20928 KB Output is correct
43 Correct 187 ms 2900 KB Output is correct
44 Correct 1225 ms 16324 KB Output is correct
45 Correct 1193 ms 16404 KB Output is correct
46 Correct 1249 ms 16092 KB Output is correct
47 Correct 736 ms 18884 KB Output is correct
48 Correct 1316 ms 16400 KB Output is correct
49 Correct 1350 ms 16676 KB Output is correct
50 Correct 479 ms 20516 KB Output is correct