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답안 #955193

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
955193 2024-03-29T15:58:57 Z vjudge1 Min-max tree (BOI18_minmaxtree) C++17
100 / 100
 732 ms 113592 KB 
#include<bits/stdc++.h>
#define all(x) (x).begin(),(x).end()
#define int long long int
using namespace std;

const int64_t INF = 1e17;
const int mod = 1e9+7;

vector<int> tree[100001];

struct LCA {
    
    
    vector<int> height, euler, first, segtree;
    vector<bool> visited;
    int n;

    LCA(int n) : n(n) {
        height.resize(n + 1);
        first.resize(n + 1, -1);
        euler.reserve(n * 2);
        visited.assign(n + 1, false);
    }

    void dfs(int node, int h = 0) {
        visited[node] = true;
        height[node] = h;
        first[node] = euler.size();
        euler.push_back(node);
        for (auto to : tree[node]) {
            if (!visited[to]) {
                dfs(to, h + 1);
                euler.push_back(node);
            }
        }
    }

    int build(int node, int b, int e) {
        if (b == e) {
            return segtree[node] = euler[b];
        } else {
            int mid = (b + e) / 2;
            int left = build(node * 2, b, mid);
            int right = build(node * 2 + 1, mid + 1, e);
            return segtree[node] = (height[left] < height[right] ? left : right);
        }
    }

    void init() {
        dfs(1);
        int m = euler.size();
        segtree.assign(m * 4, -1);
        build(1, 0, m - 1);
    }

    int query(int node, int b, int e, int L, int R) {
        if (b > R || e < L)
            return -1;
        if (b >= L && e <= R)
            return segtree[node];
        int mid = (b + e) / 2;
        int left = query(node * 2, b, mid, L, R);
        int right = query(node * 2 + 1, mid + 1, e, L, R);
        if (left == -1) return right;
        if (right == -1) return left;
        return height[left] < height[right] ? left : right;
    }

    int lca(int u, int v) {
        int left = first[u], right = first[v];
        if (left > right)
            swap(left, right);
        return query(1, 0, euler.size() - 1, left, right);
    }

};

struct Dinic {

    struct Edge {
        int to, cap, rev;
    };
    vector<vector<Edge>> G;
    vector<int> level, iter;
    Dinic(int n) : G(n), level(n), iter(n) {}
    void add_edge(int from, int to, int cap) {
        G[from].push_back({to, cap, (int)G[to].size()});
        G[to].push_back({from, 0, (int)G[from].size() - 1});
    }
    void bfs(int s) {
        fill(level.begin(), level.end(), -1);
        queue<int> que;
        level[s] = 0;
        que.push(s);
        while (!que.empty()) {
            int v = que.front();
            que.pop();
            for (auto &e : G[v]) {
                if (e.cap > 0 && level[e.to] < 0) {
                    level[e.to] = level[v] + 1;
                    que.push(e.to);
                }
            }
        }
    }
    int dfs(int v, int t, int f) {
        if (v == t) return f;
        for (int &i = iter[v]; i < (int)G[v].size(); i++) {
            Edge &e = G[v][i];
            if (e.cap > 0 && level[v] < level[e.to]) {
                int d = dfs(e.to, t, min(f, e.cap));
                if (d > 0) {
                    e.cap -= d;
                    G[e.to][e.rev].cap += d;
                    return d;
                }
            }
        }
        return 0;
    }
    int max_flow(int s, int t) {
        int flow = 0;
        while (true) {
            bfs(s);
            if (level[t] < 0) return flow;
            fill(iter.begin(), iter.end(), 0);
            int f;
            while ((f = dfs(s, t, INT_MAX)) > 0) {
                flow += f;
            }
        }
    }

    set<pair<int, int>> get_full_edges() {
        set<pair<int, int>> full_edges;
        for (int i = 0; i < G.size(); i++) {
            for (auto &e : G[i]) {
                if (e.cap == 0) {
                    full_edges.insert({i, e.to});
                }
            }
        }
        return full_edges;
    }

}; 

const int MAXN = 1e5 + 5;

vector<pair<int, int>> edges;

map<int, int> enumerate_assignments;
map<pair<int, int>, int> enumerate_edges;

map<pair<int, int>, int> max_assignments;
map<pair<int, int>, int> min_assignments;

vector<int> max_path_removal[MAXN];
vector<int> min_path_removal[MAXN];
set<int> path_max[MAXN];
set<int> path_min[MAXN];

struct Query {
    char type;
    int u, v, z;
};
vector<Query> queries;




void assign_max(int u, int p) {
    
    for (int v : tree[u]) {
        if (v == p) continue;
        assign_max(v, u);

        if (path_max[v].size() > path_max[u].size()) {
            swap(path_max[u], path_max[v]);
        }

        for (auto z : path_max[v]) {
            path_max[u].insert(z);
        }
    }

    for (int z : max_path_removal[u]) {
        path_max[u].erase(z);
    }

    if (p != 0 && !path_max[u].empty()) {
        max_assignments[{min(u, p), max(u, p)}] = *path_max[u].begin();
    }

}

void assign_min(int u, int p) {
        
    for (int v : tree[u]) {
        if (v == p) continue;
        assign_min(v, u);

        if (path_min[v].size() > path_min[u].size()) {
            swap(path_min[u], path_min[v]);
        }

        for (auto z : path_min[v]) {
            path_min[u].insert(z);
        }
    }

    for (int z : min_path_removal[u]) {
        path_min[u].erase(z);
    }

    if (p != 0 && !path_min[u].empty()) {
        min_assignments[{min(u, p), max(u, p)}] = *path_min[u].rbegin();
    }
}

Dinic run_flow() {

    int source = 1, sink = 2;
    int last = 3;

    for (auto query : queries) {
        enumerate_assignments[query.z] = last++;
    }

    for (auto& itr : edges) {
        enumerate_edges[itr] = last++;
    }

    Dinic dinic(last + 1);

    for (auto& itr : enumerate_assignments) {
        dinic.add_edge(source, itr.second, 1);
    }

    for (auto& itr : max_assignments) {
        dinic.add_edge(enumerate_assignments[itr.second], enumerate_edges[itr.first], 1);
    }

    for (auto& itr : min_assignments) {
        dinic.add_edge(enumerate_assignments[itr.second], enumerate_edges[itr.first], 1);
    }

    for (auto& itr : edges) {
        dinic.add_edge(enumerate_edges[itr], sink, 1);
    }
    
    int flow = dinic.max_flow(source, sink);

    // cerr << flow << '\n';

    return dinic;

}


int32_t main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int n;
    cin >> n;

    for(int i = 0; i < n - 1; i++){
        int u, v;
        cin >> u >> v;
        tree[u].push_back(v);
        tree[v].push_back(u);

        if (u > v) swap(u, v);
        edges.push_back({u, v});
    }

    LCA lca(n + 1);

    lca.init();

    int q;
    cin >> q;

    while (q--) {
        char type;
        int u, v, z;
        cin >> type >> u >> v >> z;

        queries.push_back({type, u, v, z});

        if (type == 'M') {
            max_path_removal[lca.lca(u, v)].push_back(z);
            path_max[u].insert(z);
            path_max[v].insert(z);
        }
        else {
            min_path_removal[lca.lca(u, v)].push_back(z);
            path_min[u].insert(z);
            path_min[v].insert(z);
        }

    }

    assign_max(1, 0);
    assign_min(1, 0);
    
    Dinic dinic = run_flow();

    set<pair<int, int>> full_edges = dinic.get_full_edges();
    map<pair<int, int>, int> answer;

     for (auto& itr : max_assignments) {
        if (full_edges.count({enumerate_assignments[itr.second], enumerate_edges[itr.first]})) {
            answer[itr.first] = itr.second;
        }
    }

    for (auto& itr : min_assignments) {
        if (full_edges.count({enumerate_assignments[itr.second], enumerate_edges[itr.first]})) {
            answer[itr.first] = itr.second;
        }
    }

    for (auto itr : edges) {
        cout << itr.first << ' ' << itr.second << ' ';
        if (answer.count(itr)) {
            cout << answer[itr] << '\n';
        }
        else if (max_assignments.count(itr)) {
            cout << max_assignments[itr] << '\n';
        }
        else if (min_assignments.count(itr)) {
            cout << min_assignments[itr] << '\n';
        }
        else {
            cout << 0 << '\n';
        }
    }

}

Compilation message

minmaxtree.cpp: In member function 'std::set<std::pair<long long int, long long int> > Dinic::get_full_edges()':
minmaxtree.cpp:136:27: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<std::vector<Dinic::Edge> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  136 |         for (int i = 0; i < G.size(); i++) {
      |                         ~~^~~~~~~~~~
minmaxtree.cpp: In function 'Dinic run_flow()':
minmaxtree.cpp:252:9: warning: unused variable 'flow' [-Wunused-variable]
  252 |     int flow = dinic.max_flow(source, sink);
      |         ^~~~

Subtask #1
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 6 ms 16732 KB Output is correct
2 Correct 4 ms 16728 KB Output is correct
3 Correct 5 ms 16708 KB Output is correct
4 Correct 4 ms 16728 KB Output is correct

Subtask #2
22.0 / 22.0

# 결과 실행 시간 메모리 Grader output
1 Correct 486 ms 94400 KB Output is correct
2 Correct 517 ms 93692 KB Output is correct
3 Correct 474 ms 88756 KB Output is correct
4 Correct 526 ms 100196 KB Output is correct
5 Correct 484 ms 90700 KB Output is correct
6 Correct 505 ms 93096 KB Output is correct
7 Correct 479 ms 89836 KB Output is correct

Subtask #3
29.0 / 29.0

# 결과 실행 시간 메모리 Grader output
1 Correct 301 ms 63500 KB Output is correct
2 Correct 299 ms 66500 KB Output is correct
3 Correct 264 ms 66236 KB Output is correct
4 Correct 269 ms 70076 KB Output is correct
5 Correct 314 ms 69168 KB Output is correct
6 Correct 340 ms 71720 KB Output is correct
7 Correct 325 ms 69176 KB Output is correct
8 Correct 327 ms 68316 KB Output is correct

Subtask #4
42.0 / 42.0

# 결과 실행 시간 메모리 Grader output
1 Correct 6 ms 16732 KB Output is correct
2 Correct 4 ms 16728 KB Output is correct
3 Correct 5 ms 16708 KB Output is correct
4 Correct 4 ms 16728 KB Output is correct
5 Correct 486 ms 94400 KB Output is correct
6 Correct 517 ms 93692 KB Output is correct
7 Correct 474 ms 88756 KB Output is correct
8 Correct 526 ms 100196 KB Output is correct
9 Correct 484 ms 90700 KB Output is correct
10 Correct 505 ms 93096 KB Output is correct
11 Correct 479 ms 89836 KB Output is correct
12 Correct 301 ms 63500 KB Output is correct
13 Correct 299 ms 66500 KB Output is correct
14 Correct 264 ms 66236 KB Output is correct
15 Correct 269 ms 70076 KB Output is correct
16 Correct 314 ms 69168 KB Output is correct
17 Correct 340 ms 71720 KB Output is correct
18 Correct 325 ms 69176 KB Output is correct
19 Correct 327 ms 68316 KB Output is correct
20 Correct 635 ms 101640 KB Output is correct
21 Correct 555 ms 91228 KB Output is correct
22 Correct 536 ms 92040 KB Output is correct
23 Correct 547 ms 91064 KB Output is correct
24 Correct 710 ms 111780 KB Output is correct
25 Correct 667 ms 113592 KB Output is correct
26 Correct 630 ms 108992 KB Output is correct
27 Correct 732 ms 113120 KB Output is correct
28 Correct 671 ms 102632 KB Output is correct
29 Correct 673 ms 102852 KB Output is correct
30 Correct 603 ms 94260 KB Output is correct
31 Correct 714 ms 96640 KB Output is correct
32 Correct 715 ms 101208 KB Output is correct
33 Correct 651 ms 97492 KB Output is correct
34 Correct 648 ms 97668 KB Output is correct
35 Correct 628 ms 93760 KB Output is correct