oj.uz

Submission #581204

# Submission time Handle Problem Language Result Execution time Memory
581204 2022-06-22T11:24:25 Z qwerasdfzxcl Toll (APIO13_toll) C++14
100 / 100
 2288 ms 19640 KB 
#include <bits/stdc++.h>
#define int long long
#pragma GCC optimize("O3")
#pragma GCC target("avx2")

typedef long long ll;
using namespace std;
struct Edge{
    int s, e, x;
    Edge(){}
    Edge(int _s, int _e, int _x): s(_s), e(_e), x(_x) {}
    bool operator<(const Edge &E) const{
        return x < E.x;
    }
}a[500500], b[44], aa[44][44];

struct DSU{
    int path[500500];
    vector<int> st;

    void init(int n){for (int i=1;i<=n;i++) path[i] = i;}
    void clear(){for (auto &x:st) path[x] = x; st.clear();}

    int find(int s){
        if (s==path[s]) return s;
        return path[s] = find(path[s]);
    }
    bool merge(int s, int v){
        s = find(s), v = find(v);
        if (s==v) return 0;
        path[s] = v;
        st.push_back(s);
        return 1;
    }
}dsu1, dsu2;

int n, m, k, w[500500];

bool valid_bit(int z){
    dsu1.clear();
    for (int i=0;i<k;i++) if (z&(1<<i)){
        if (!dsu1.merge(b[i].s, b[i].e)) return 0;
    }
    return 1;
}

ll sw[44], P[44];
int idx[500500], mn[44], ns, aaa[500500];
vector<pair<int, int>> adj[44];

ll dfs0(int s, int pa = -1){
    ll ret = sw[s];
    for (auto &[v, i]:adj[s]) if (v!=pa){
        ll tmp = dfs0(v, s);
        ret += tmp;
        P[i] = tmp;
    }
    return ret;
}

int ST[44], stc;
bool dfs(int s, int e, int pa = -1){
    if (s==e) return 1;
    for (auto &[v, i]:adj[s]) if (v!=pa){
        ST[stc++] = i;
        if (dfs(v, e, s)) return 1;
        stc--;
    }
    return 0;
}

ll solve(int z, bool flag = 0){
    if (!z) return 0;
    if (!valid_bit(z)){
        if (!flag) return 0;
    }

    ///init
    dsu2.clear();
    for (int i=0;i<=k+10;i++){
        adj[i].clear();
        sw[i] = 0;
        P[i] = 0;
        mn[i] = 1e9;
    }

    for (int i=0;i<=n;i++) aaa[i] = -1;
    ///

    for (int i=1;i<=m;i++) if (dsu1.merge(a[i].s, a[i].e)){
        dsu2.merge(a[i].s, a[i].e);
    }

    int aac = 1;
    for (int i=1;i<=n;i++) if (aaa[dsu2.find(i)]==-1) aaa[dsu2.find(i)] = aac++;



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

        idx[i] = aaa[dsu2.find(i)];
        sw[idx[i]] += w[i];
        //printf(" YES %d %d\n", i, w[i]);
    }

    for (int i=0;i<k;i++) if (z&(1<<i)){
        adj[idx[b[i].s]].emplace_back(idx[b[i].e], i);
        adj[idx[b[i].e]].emplace_back(idx[b[i].s], i);
    }


    ///new graph

    if (flag){
        int nc = aac-1;
        ns = idx[1];

        for (int i=1;i<=m;i++) if (idx[a[i].s]!=idx[a[i].e]){
            int x = idx[a[i].s], y = idx[a[i].e];
            if (x>y){
                swap(a[i].s, a[i].e);
                swap(x, y);
            }
            if (aa[x][y].x) aa[x][y] = min(aa[x][y], Edge(idx[a[i].s], idx[a[i].e], a[i].x));
            else aa[x][y] = Edge(idx[a[i].s], idx[a[i].e], a[i].x);
        }

        int ncnt = 1;
        for (int i=1;i<=nc;i++){
            for (int j=1;j<=nc;j++) if (aa[i][j].x) a[ncnt++] = aa[i][j];
        }
        for (int i=0;i<k;i++){
            b[i].s = idx[b[i].s];
            b[i].e = idx[b[i].e];
        }

        m = ncnt-1;
        n = nc;
        for (int i=1;i<=n;i++) w[i] = sw[i];

        sort(a+1, a+m+1);
        vector<Edge> tmptmp;
        dsu1.clear();
        for (int i=1;i<=m;i++) if (dsu1.merge(a[i].s, a[i].e)) tmptmp.push_back(a[i]);
        for (int i=0;i<(int)tmptmp.size();i++) a[i+1] = tmptmp[i];

        m = tmptmp.size();

        return 0;

    }


    ///subtask 3
    dfs0(idx[ns]);
    for (int i=1;i<=m;i++) if (idx[a[i].s]!=idx[a[i].e]){
        stc = 0;
        assert(dfs(idx[a[i].s], idx[a[i].e]));

        for (int j=0;j<stc;j++) mn[ST[j]] = min(mn[ST[j]], a[i].x);
    }

    ll ret = 0;
    for (int i=0;i<k;i++) if (z&(1<<i)){
        ret += P[i] * mn[i];
        //printf("%lld %d\n", P[i], mn[i]);
    }

    return ret;
}

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

    cin >> n >> m >> k;
    for (int i=1;i<=m;i++) cin >> a[i].s >> a[i].e >> a[i].x;
    for (int i=0;i<k;i++) cin >> b[i].s >> b[i].e;
    sort(a+1, a+m+1);
    for (int i=1;i<=n;i++) cin >> w[i];

    dsu1.init(n); dsu2.init(n);

    solve((1<<k)-1, 1);

    assert(m<=30);

    //printf(" %d %d %d %d\n", n, m, k, ns);
    //for (int i=1;i<=m;i++) printf(" %d %d %d\n", a[i].s, a[i].e, a[i].x);
    //for (int i=1;i<=n;i++) printf(" %d ", w[i]);
    //printf("\n");

    ll ans = 0;
    for (int z=1;z<(1<<k);z++) ans = max(ans, solve(z));
    printf("%lld\n", ans);
    return 0;
}

Compilation message

toll.cpp: In function 'll dfs0(long long int, long long int)':
toll.cpp:53:16: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
   53 |     for (auto &[v, i]:adj[s]) if (v!=pa){
      |                ^
toll.cpp: In function 'bool dfs(long long int, long long int, long long int)':
toll.cpp:64:16: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
   64 |     for (auto &[v, i]:adj[s]) if (v!=pa){
      |                ^

Subtask #1
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct

Subtask #2
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 2 ms 340 KB Output is correct
4 Correct 2 ms 340 KB Output is correct

Subtask #3
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 2 ms 340 KB Output is correct
4 Correct 2 ms 340 KB Output is correct
5 Correct 3 ms 468 KB Output is correct
6 Correct 3 ms 468 KB Output is correct

Subtask #4
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 2 ms 340 KB Output is correct
4 Correct 2 ms 340 KB Output is correct
5 Correct 3 ms 468 KB Output is correct
6 Correct 3 ms 468 KB Output is correct
7 Correct 194 ms 13012 KB Output is correct
8 Correct 197 ms 13116 KB Output is correct
9 Correct 192 ms 13128 KB Output is correct

Subtask #5
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 2 ms 340 KB Output is correct
4 Correct 2 ms 340 KB Output is correct
5 Correct 3 ms 468 KB Output is correct
6 Correct 3 ms 468 KB Output is correct
7 Correct 194 ms 13012 KB Output is correct
8 Correct 197 ms 13116 KB Output is correct
9 Correct 192 ms 13128 KB Output is correct
10 Correct 1825 ms 13116 KB Output is correct
11 Correct 2214 ms 13084 KB Output is correct
12 Correct 2288 ms 19640 KB Output is correct