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답안 #1102151

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
1102151 2024-10-17T14:47:54 Z Requiem 가로등 (APIO19_street_lamps) C++17
60 / 100
 797 ms 524288 KB 
#include<bits/stdc++.h>
#define int long long
#define pb push_back
#define fast ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
#define MOD 1000000007
#define inf 1e18
#define fi first
#define se second
#define FOR(i,a,b) for(int i=a;i<=b;i++)
#define FORD(i,a,b) for(int i=a;i>=b;i--)
#define sz(a) ((int)(a).size())
#define endl '\n'
#define pi 3.14159265359
#define TASKNAME "streetlamp"
using namespace std;
template<typename T> bool maximize(T &res, const T &val) { if (res < val){ res = val; return true; }; return false; }
template<typename T> bool minimize(T &res, const T &val) { if (res > val){ res = val; return true; }; return false; }
typedef pair<int,int> ii;
typedef pair<int,ii> iii;
typedef vector<int> vi;
/**
Street lamp:

Có n trạm dừng kết nối n + 1 cái stop.
ta biết trạng thái của cái stop

Ta có q truy vấn:
- query a b: Từ 1 đến i, ta, tổng các thời điểm mà ta có thể đi từ a b
- toggle i: lật ngược vị trí i

subtask 1: n <= 100, q <= 100. Chạy n * q^2.

subtask 2: b = a + 1.
Tức là ta chỉ quan tâm vị trí i được bật bao nhiêu lần.
cái này bỏ vào prefix sum.

subtask 3: Khi bật nút i, nó sẽ luôn bật.
Nó là bài toán dsu điển hình, tức là 2 đỉnh sẽ không bao giờ bị disconnect.

subtask 4:
Ta toggle trước xong mới đến các truy vấn.
Giả sử ta dsu rollback, khi ta thêm 1 cạnh vào, nó
sẽ liên kết các tplt bên trong đó.

Giả sử nó nối đoạn [1...3] với [4..5] thì ta thêm hình chữ nhật [1...3], [4...5]
với trọng số là thời gian t.

Khi này ta sẽ tính offline bằng sweepline. Giả sử ta cần truy vấn a, b: thì ta chỉ cần truy vấn đoạn [a, b].
Ta có n log n sự kiện thì có tối đa n log n hình chữ nhật,

subtask 5:
Bây giờ ta cần phải xử lý online. Làm thế nào cơ chứ.
Nếu ta cắm BIT2D vào thì nó cũng vẫn sẽ là N log ^ 3 N.
Ta chia các hcn thành 2 loại:
- Đã kết thúc
- Còn thời gian.
**/

const int MAXN = 3e5 + 9;
int n, q, u, v;
char lamp[MAXN];

struct query{
    string type;
    int l, r, u;
} Query[MAXN];

struct DSU{
    struct DSUnode{
        int par;
        int sz;
        int mn;
        int mx;
    };
    vector<DSUnode> D;
    vector<array<int, 6>> changes;
    int small_to_large, path_compression, roll_back;
    DSU(int sz = 0, int _small_to_large = 1, int _path_compression = 1, int _roll_back = 0){
        D.resize(sz + 9);
        small_to_large = _small_to_large;
        path_compression = _path_compression;
        roll_back = _roll_back;
        FOR(i, 0, D.size() - 1){
            D[i].par = i;
            D[i].sz = 1;
            D[i].mn = D[i].mx = i;
        }
    }

    void rollback(){
        if (changes.size() == 0) return;
        array<int, 6> tp = changes.back();
        int u = tp[0];
        int v = tp[1];
        D[u].sz -= D[v].sz;
        D[v].par = v;
        D[u].mn = tp[2], D[u].mx = tp[3];
        D[v].mn = tp[4], D[v].mx = tp[5];
        changes.pop_back();
    }
    int root(int u){
        if (D[u].par == u) return u;
        else {
            int p = root(D[u].par);
            if (path_compression) D[u].par = p;
            return p;
        }
    }

    bool unite(int u, int v){
        u = root(u);
        v = root(v);
        if (u != v){
            if (small_to_large and D[u].sz < D[v].sz) swap(u, v);
            D[u].sz += D[v].sz;
            D[v].par = u;
            if (roll_back) changes.pb({u, v, D[u].mn, D[u].mx, D[v].mn, D[v].mx});;

            D[u].mx = max(D[u].mx, D[v].mx);
            D[u].mn = min(D[u].mn, D[v].mn);
            return true;
        }
        return false;
    }
};
namespace subtask1{
    bool check(){
        return n <= 100 and q <= 100;
    }


    DSU timelineDSU[103];
    void solve(){
        FOR(i, 1, q){
            timelineDSU[i] = DSU(n + 1);
            FOR(j, 1, n){
                if (lamp[j] == '1') {
                    timelineDSU[i].unite(j, j + 1);
                }
            }

            if (Query[i].type == "toggle"){
                int u = Query[i].u;
                lamp[u] = ((lamp[u] == '0') ? '1' : '0');
            }
            else{
                int ans = 0;
                FOR(j, 1, i){
                    if (timelineDSU[j].root(Query[i].l) == timelineDSU[j].root(Query[i].r)) {
                        ans++;
                    }
                }
                cout << ans << endl;
            }
        }
    }
}

namespace subtask2{
    bool check(){
        FOR(i, 1, q){
            if (Query[i].type == "query" and Query[i].l != Query[i].r - 1) return false;
        }
        return true;
    }

    int pre[300003], lastTime[MAXN];
    void solve(){
        FOR(i, 1, n){
            pre[i] = 0;
            if (lamp[i] == '1') lastTime[i] = 1;
        }
        FOR(i, 1, q){
            if (Query[i].type == "toggle"){
                int u = Query[i].u;
                if (lamp[u] == '1') {
                    pre[u] += i - lastTime[u] + 1;
                    lastTime[u] = 0;
                    lamp[u] = '0';
                }
                else{
                    lastTime[u] = i + 1;
                    lamp[u] = '1';
                }
            }
            if (Query[i].type == "query"){
                int ans = pre[Query[i].l];
                if (lamp[Query[i].l] == '1'){
                    ans += i - lastTime[Query[i].l] + 1;
                }
                cout << ans << endl;
            }
        }
    }
}

namespace subtask3{
    char tmp[300005];
    bool check(){
        FOR(i, 1, n){
            tmp[i] = lamp[i];
        }
        FOR(i, 1, q){
            if (Query[i].type == "toggle" and tmp[Query[i].u] == '1') return false;
            if (Query[i].type == "toggle") tmp[Query[i].u] = '1';
        }
        return true;
    }

    /**
    Voi 2 dinh a va b, ta can tim thoi gian dau tien ma hai thang do ket hop lam 1. Cái này có thể giải bằng
    chặt nhị phân song song.

    Dùng reachability Tree.
    **/

    vector<int> reachability[MAXN * 2];
    int edgeTime[MAXN * 2];

    int P[22][MAXN * 2], depth[MAXN * 2];

    void dfs(int u, int p){
        P[0][u] = p;
        for(auto v: reachability[u]){
            depth[v] = depth[u] + 1;
            dfs(v, u);
        }
    }

    int lca(int u, int v){
        if (depth[u] < depth[v]) swap(u, v);
        FORD(i, 20, 0){
            if (P[i][u] != -1 and depth[P[i][u]] >= depth[v]) u = P[i][u];
        }

        if (u == v) return u;

        FORD(i, 20, 0){
            if (P[i][u] != -1 and P[i][v] != -1 and P[i][u] != P[i][v]) {
                u = P[i][u];
                v = P[i][v];
            }
        }

        return P[0][u];
    }

    void solve(){
        int small_to_large = 0;
        int path_compression = 1;
        int roll_back = 0;
        DSU D(2 * n + 9, small_to_large, path_compression, roll_back);
        int cntEdge = n + 1;
        FOR(i, 1, n){
            if (lamp[i] == '1') {
                ++cntEdge;
                edgeTime[cntEdge] = 1;

                int r1 = D.root(i);
                int r2 = D.root(i + 1);

                if (D.unite(cntEdge, r1)){
//                    cerr << cntEdge << ' ' << r1 << endl;
                    reachability[cntEdge].pb(r1);
                }

                if (D.unite(cntEdge, r2)){
//                    cerr << cntEdge << ' ' << r2 << endl;
                    reachability[cntEdge].pb(r2);
                }

            }

        }


        FOR(i, 1, q){
            if (Query[i].type == "toggle"){
                int u = Query[i].u;
                ++cntEdge;
                edgeTime[cntEdge] = i + 1;
                int r1 = D.root(u);
                int r2 = D.root(u + 1);
                if (D.unite(cntEdge, r1)){
//                    cerr << cntEdge << ' ' << r1 << endl;
                    reachability[cntEdge].pb(r1);
                }

                if (D.unite(cntEdge, r2)){
//                    cerr << cntEdge << ' ' << r2 << endl;

                    reachability[cntEdge].pb(r2);
                }
            }
        }

        FORD(i, 2 * n + 3, 1){
            if (P[0][i] == 0) dfs(i, -1);
        }

        FOR(i, 1, 20){
            FOR(j, 1, 2 * n + 3){
                if (P[i - 1][j] == -1) P[i][j] = -1;
                P[i][j] = P[i - 1][P[i - 1][j]];
            }
        }

        FOR(i, 1, q){
            int ans = 0;
            if (Query[i].type == "query"){
                int l = Query[i].l;
                int r = Query[i].r;
                if (D.root(l) == D.root(r)){
                    int acs = lca(l, r);
                    if (i >= edgeTime[acs]) ans += i - edgeTime[acs] + 1;
                }
                cout << ans << endl;
            }
        }
    }
}

struct BinaryIndexedTree{
    vector<int> BIT;
    BinaryIndexedTree(int sz = 0){
        BIT.resize(sz + 9);
    }

    void update(int id, int val){
        for(int i = id; i < BIT.size(); i += i & (-i)){
            BIT[i] += val;
        }
    }

    int get(int id){
        int res = 0;
        for(int i = id; i > 0; i -= i & (-i)){
            res += BIT[i];
        }
        return res;
    }

    void updateRange(int l, int r, int val){
        update(l, val);
        update(r + 1, -val);
    }
};
namespace subtask4{
    bool check(){
        bool alreadyQuery = 0;
        FOR(i, 1, q){
            if (Query[i].type == "toggle" and alreadyQuery) return false;
            if (Query[i].type == "query") alreadyQuery = true;
        }
        return true;
    }

    struct rectangle{
        int L, R, B, T, val;
        rectangle(int _L = 0, int _R = 0, int _B = 0, int _T = 0, int _v = 0){
            L = _L;
            R = _R;
            B = _B;
            T = _T;
            val = _v;
        }

    };

    vector<rectangle> rect;
    vector<iii> points;

    struct event{
        int x, type, l, r;
        event(int _x = 0, int _type = 0, int _l = 0, int _r = 0): x(_x), type(_type), l(_l), r(_r) {}
    };
    vector<int> valRectangleInclude(vector<rectangle> rect, vector<iii> points){
        vector<int> result(points.size());
        vector<event> events;
        BinaryIndexedTree BIT(300005);

        FOR(i, 0, (int) rect.size() - 1){
            events.pb(event(rect[i].L, rect[i].val, rect[i].B, rect[i].T));
            events.pb(event(rect[i].R + 1,-rect[i].val, rect[i].B, rect[i].T));
//            cerr << rect[i].L << ' ' << rect[i].R << ' ' << rect[i].B << ' ' << rect[i].T << ' ' << rect[i].val << endl;
        }

        FOR(i, 0, (int) points.size() - 1){
//            cerr << points[i].fi << ' ' << points[i].se.fi << ' ' << points[i].se.se << endl;
            events.pb(event(points[i].se.fi, 0, points[i].fi, points[i].se.se));
        }

        sort(events.begin(), events.end(), [&](const event &a, const event &b){
             return a.x < b.x;
        });

        for(int i = 0, j = 0; i < events.size(); i = j){
            j = i;
//            cerr << "X: " << events[i].x << endl;
            while(j < events.size() and events[j].x == events[i].x){
                if (events[j].type != 0) {
                    BIT.updateRange(events[j].l, events[j].r, events[j].type);
//                    cerr << "UPDATE: " << events[j].l << ' ' << events[j].r << ' ' << events[j].type << endl;
                }
                j++;
            }

            j = i;
            while(j < events.size() and events[j].x == events[i].x){
                 if (events[j].type == 0) {
//                    cerr << "GET: " << events[j].x << ' ' << events[j].r << endl;
                    result[events[j].l] = BIT.get(events[j].r);
                 }
                 j++;
            }
        }
        return result;
    }


    /**
    Moi lan ta them canh vao, ta chac no se tao 1 thanh phan lien thong moi, ta chi quan tam rang la
    2 doan ma no dang o thoi.
    Khi ta add 2 thang vao thi chac chan no se la hai thang tien de tao thanh 2 thang lon hon.
    **/

    vector<int> dsuRollback[MAXN << 2];
    DSU D;

    void addEvent(int nn, int l, int r, int u, int v, int e){
        if (l >= u and r <= v){
            dsuRollback[nn].pb(e);
            return;
        }
        if (l > v or r < u) return;
        int mid = (l + r) >> 1;
        addEvent(nn << 1, l, mid, u, v, e);
        addEvent(nn << 1 | 1, mid + 1, r, u, v, e);
    }

    void go(int nn, int l, int r){
        int sz = D.changes.size();
        for(auto p: dsuRollback[nn]){
            D.unite(p, p + 1);
            int rt = D.root(p);
            rect.pb(rectangle(D.D[rt].mn, p, p + 1, D.D[rt].mx, r - l + 1));
        }

        if (l != r){
            int mid = (l + r) >> 1;
            go(nn << 1, l, mid);
            go(nn << 1 | 1, mid + 1, r);
        }

        while(D.changes.size() > sz) D.rollback();


    }

    int lastTime[MAXN];
    void solve(){
        int startAsking = q + 1;
        FOR(i, 1, q){
            if (Query[i].type == "query") {
                startAsking = i;
                break;
            }
        }

        D = DSU(n + 1, 1, 0, 1);
        DSU current = DSU(n + 1, 1, 1, 0);

        FOR(i, 1, n){
            if (lamp[i] == '1') lastTime[i] = 1;
        }

        FOR(i, 1, startAsking - 1){
            int u = Query[i].u;
            if (lamp[u] == '1'){
                addEvent(1, 1, startAsking, lastTime[u], i, u);
                lastTime[u] = 0;
                lamp[u] = '0';
            }
            else{
                lamp[u] = '1';
                lastTime[u] = i + 1;
            }
        }

        FOR(i, 1, n){
            if (lastTime[i] > 0) addEvent(1, 1, startAsking, lastTime[i], startAsking, i);
        }

        go(1, 1, startAsking);

        FOR(i, 1, n){
            if (lamp[i] == '1') current.unite(i, i + 1);
        }


        FOR(i, startAsking, q){
            points.pb({i - startAsking, ii(Query[i].l, Query[i].r)});
        }

//        for(int i = 0; i < rect.size(); i++){
//            cerr << rect[i].val << endl;
//        }

        vector<int> result = valRectangleInclude(rect, points);

        FOR(i, startAsking, q){
            int l = Query[i].l;
            int r = Query[i].r;
            if (current.root(l) == current.root(r)){
                result[i - startAsking] += i - startAsking;
            }
            cout << result[i - startAsking] << endl;
        }


    }
}
main()
{
    fast;
    if (fopen(TASKNAME".inp","r")){
        freopen(TASKNAME".inp","r",stdin);
        freopen(TASKNAME".out","w",stdout);
    }
    cin >> n >> q;
    FOR(i, 1, n){
        cin >> lamp[i];
    }
    FOR(i, 1, q){
        cin >> Query[i].type;
        if (Query[i].type == "toggle"){
            cin >> Query[i].u;

        }
        else if (Query[i].type == "query"){
            cin >> Query[i].l >> Query[i].r;
        }
    }

    if (subtask1::check()) return subtask1::solve(), 0;
    if (subtask2::check()) return subtask2::solve(), 0;
    if (subtask3::check()) return subtask3::solve(), 0;
    if (subtask4::check()) return subtask4::solve(), 0;
}
/**
Warning:
Cận lmao
Code imple thiếu case nào không.
Limit.
**/

Compilation message

street_lamps.cpp: In constructor 'DSU::DSU(long long int, long long int, long long int, long long int)':
street_lamps.cpp:9:33: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<DSU::DSUnode>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
    9 | #define FOR(i,a,b) for(int i=a;i<=b;i++)
......
   83 |         FOR(i, 0, D.size() - 1){
      |             ~~~~~~~~~~~~~~~~~~   
street_lamps.cpp:83:9: note: in expansion of macro 'FOR'
   83 |         FOR(i, 0, D.size() - 1){
      |         ^~~
street_lamps.cpp: In member function 'void BinaryIndexedTree::update(long long int, long long int)':
street_lamps.cpp:330:27: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  330 |         for(int i = id; i < BIT.size(); i += i & (-i)){
      |                         ~~^~~~~~~~~~~~
street_lamps.cpp: In function 'std::vector<long long int> subtask4::valRectangleInclude(std::vector<subtask4::rectangle>, std::vector<std::pair<long long int, std::pair<long long int, long long int> > >)':
street_lamps.cpp:397:33: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<subtask4::event>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  397 |         for(int i = 0, j = 0; i < events.size(); i = j){
      |                               ~~^~~~~~~~~~~~~~~
street_lamps.cpp:400:21: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<subtask4::event>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  400 |             while(j < events.size() and events[j].x == events[i].x){
      |                   ~~^~~~~~~~~~~~~~~
street_lamps.cpp:409:21: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<subtask4::event>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  409 |             while(j < events.size() and events[j].x == events[i].x){
      |                   ~~^~~~~~~~~~~~~~~
street_lamps.cpp: In function 'void subtask4::go(long long int, long long int, long long int)':
street_lamps.cpp:455:32: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<long long int, 6> >::size_type' {aka 'long unsigned int'} and 'long long int' [-Wsign-compare]
  455 |         while(D.changes.size() > sz) D.rollback();
      |               ~~~~~~~~~~~~~~~~~^~~~
street_lamps.cpp: At global scope:
street_lamps.cpp:523:1: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
  523 | main()
      | ^~~~
street_lamps.cpp: In function 'int main()':
street_lamps.cpp:527:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  527 |         freopen(TASKNAME".inp","r",stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~
street_lamps.cpp:528:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  528 |         freopen(TASKNAME".out","w",stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 10 ms 62032 KB Output is correct
2 Correct 11 ms 62032 KB Output is correct
3 Correct 12 ms 62032 KB Output is correct
4 Correct 11 ms 62476 KB Output is correct
5 Correct 11 ms 62288 KB Output is correct
6 Correct 12 ms 62544 KB Output is correct
7 Correct 11 ms 62300 KB Output is correct

Subtask #2
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 62 ms 64968 KB Output is correct
2 Correct 63 ms 65096 KB Output is correct
3 Correct 64 ms 65104 KB Output is correct
4 Correct 73 ms 67052 KB Output is correct
5 Correct 73 ms 67400 KB Output is correct
6 Correct 63 ms 67144 KB Output is correct
7 Correct 91 ms 67144 KB Output is correct
8 Correct 79 ms 68424 KB Output is correct

Subtask #3
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 14 ms 105464 KB Output is correct
2 Correct 14 ms 105296 KB Output is correct
3 Correct 15 ms 105296 KB Output is correct
4 Correct 16 ms 105296 KB Output is correct
5 Correct 149 ms 197192 KB Output is correct
6 Correct 238 ms 197464 KB Output is correct
7 Correct 327 ms 197608 KB Output is correct
8 Correct 797 ms 206920 KB Output is correct
9 Correct 102 ms 105928 KB Output is correct
10 Correct 103 ms 106056 KB Output is correct
11 Correct 105 ms 106056 KB Output is correct
12 Correct 120 ms 182088 KB Output is correct
13 Correct 728 ms 207176 KB Output is correct

Subtask #4
0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 11 ms 64848 KB Output is correct
2 Correct 14 ms 65016 KB Output is correct
3 Correct 14 ms 65240 KB Output is correct
4 Correct 16 ms 65580 KB Output is correct
5 Correct 217 ms 171476 KB Output is correct
6 Correct 453 ms 285732 KB Output is correct
7 Correct 703 ms 413044 KB Output is correct
8 Runtime error 496 ms 524288 KB Execution killed with signal 9
9 Halted 0 ms 0 KB -

Subtask #5
0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 10 ms 62032 KB Output is correct
2 Correct 11 ms 62032 KB Output is correct
3 Correct 12 ms 62032 KB Output is correct
4 Correct 11 ms 62476 KB Output is correct
5 Correct 11 ms 62288 KB Output is correct
6 Correct 12 ms 62544 KB Output is correct
7 Correct 11 ms 62300 KB Output is correct
8 Correct 62 ms 64968 KB Output is correct
9 Correct 63 ms 65096 KB Output is correct
10 Correct 64 ms 65104 KB Output is correct
11 Correct 73 ms 67052 KB Output is correct
12 Correct 73 ms 67400 KB Output is correct
13 Correct 63 ms 67144 KB Output is correct
14 Correct 91 ms 67144 KB Output is correct
15 Correct 79 ms 68424 KB Output is correct
16 Correct 14 ms 105464 KB Output is correct
17 Correct 14 ms 105296 KB Output is correct
18 Correct 15 ms 105296 KB Output is correct
19 Correct 16 ms 105296 KB Output is correct
20 Correct 149 ms 197192 KB Output is correct
21 Correct 238 ms 197464 KB Output is correct
22 Correct 327 ms 197608 KB Output is correct
23 Correct 797 ms 206920 KB Output is correct
24 Correct 102 ms 105928 KB Output is correct
25 Correct 103 ms 106056 KB Output is correct
26 Correct 105 ms 106056 KB Output is correct
27 Correct 120 ms 182088 KB Output is correct
28 Correct 728 ms 207176 KB Output is correct
29 Correct 11 ms 64848 KB Output is correct
30 Correct 14 ms 65016 KB Output is correct
31 Correct 14 ms 65240 KB Output is correct
32 Correct 16 ms 65580 KB Output is correct
33 Correct 217 ms 171476 KB Output is correct
34 Correct 453 ms 285732 KB Output is correct
35 Correct 703 ms 413044 KB Output is correct
36 Runtime error 496 ms 524288 KB Execution killed with signal 9
37 Halted 0 ms 0 KB -