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Submission #1087874

# Submission time Handle Problem Language Result Execution time Memory
1087874 2024-09-13T10:42:48 Z alexander707070 Duathlon (APIO18_duathlon) C++14
71 / 100
 1000 ms 26868 KB 
#include<bits/stdc++.h>
#define MAXN 200007
using namespace std;

long long n,m,a[MAXN],b[MAXN],k;

vector< pair<int,int> > v[MAXN];
vector<int> tree[MAXN];

long long sz[MAXN],sum[MAXN],szcomp[MAXN],ans;

bool li[MAXN],bridge[MAXN];
int dp[MAXN],low[MAXN];

long long comp[MAXN],where[MAXN];

void bcc(int x,int p,int dep,int edge){
    li[x]=true; dp[x]=low[x]=dep;

    for(int i=0;i<v[x].size();i++){
        if(!li[v[x][i].first]){
            bcc(v[x][i].first,x,dep+1,v[x][i].second);
            low[x]=min(low[x],low[v[x][i].first]);
        }else if(v[x][i].first!=p){
            low[x]=min(low[x],dp[v[x][i].first]);
        }
    }

    if(p!=0 and low[x]==dp[x]){
        bridge[edge]=true;
    }
}

void mark(int x){
    comp[k]++;
    where[x]=k;
    li[x]=true;

    for(int i=0;i<v[x].size();i++){
        if(li[v[x][i].first] or bridge[v[x][i].second])continue;
        mark(v[x][i].first);
    }
}

void dfs(int x,int p){
    sz[x]=comp[x];

    for(int i=0;i<tree[x].size();i++){
        if(tree[x][i]==p or sz[tree[x][i]]!=0)continue;
        dfs(tree[x][i],x);

        sum[x]+=sz[tree[x][i]]*(sz[tree[x][i]]-1);
        sz[x]+=sz[tree[x][i]];
    }
}

void dfs2(int x,int p,int s){
    szcomp[x]=s;

    for(int i=0;i<tree[x].size();i++){
        if(tree[x][i]==p or szcomp[tree[x][i]]!=0)continue;
        dfs2(tree[x][i],x,s);
    }

    sum[x]+=(s-sz[x])*(s-sz[x]-1);
}

queue<int> q;
bool vis[MAXN];
int par[MAXN];

void dobfs(int x){
    for(int i=1;i<=n;i++)li[i]=false;

    for(int i=1;i<=n;i++){
        random_shuffle(v[i].begin(),v[i].end());
    }

    q.push(x); par[x]=0;
    li[x]=true;

    while(!q.empty()){
        int curr=q.front();
        q.pop();

        for(int i=0;i<v[curr].size();i++){
            if(li[v[curr][i].first] or vis[v[curr][i].first])continue;

            q.push(v[curr][i].first);
            li[v[curr][i].first]=true;
            par[v[curr][i].first]=curr;
        }
    }    
}

bool check(int x,int y,int z){
    for(int i=1;i<=n;i++)vis[i]=false;

    dobfs(x);

    if(!li[y])return false;

    int w=y;
    while(y!=x){
        y=par[y];
        vis[y]=true;
    }

    if(vis[z])return false;

    dobfs(z);

    return li[w];
}

void brute(){
    int res=0;

    for(int i=1;i<=n;i++){
        for(int f=1;f<=n;f++){
            for(int t=1;t<=n;t++){
                if(i==f or f==t or i==t or i>t)continue;

                for(int test=1;test<=10;test++){
                    if(check(i,f,t) or check(t,f,i)){
                        res+=2; break;
                    }
                }
            }
        }
    }

    cout<<res<<"\n";
}

int main(){

    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    cin>>n>>m;
    for(int i=1;i<=m;i++){
        cin>>a[i]>>b[i];
        v[a[i]].push_back({b[i],i});
        v[b[i]].push_back({a[i],i});
    }

    if(n<=50){
        brute();
        return 0;
    }

    for(int i=1;i<=n;i++){
        if(!li[i])bcc(i,0,0,0);
    }

    for(int i=1;i<=n;i++)li[i]=false;

    for(int i=1;i<=n;i++){
        if(!li[i]){
            k++; mark(i);
        }
    }

    for(int i=1;i<=m;i++){
        if(where[a[i]]==where[b[i]])continue;

        tree[where[a[i]]].push_back(where[b[i]]);
        tree[where[b[i]]].push_back(where[a[i]]);
    }

    for(int i=1;i<=k;i++){
        if(sz[i]==0){
            dfs(i,0);
            dfs2(i,0,sz[i]);
        }
    }

    for(int i=1;i<=k;i++){
        ans+=(long long) comp[i]*((szcomp[i]-1)*(szcomp[i]-2)-sum[i]);
        ans-=(long long) 2*(comp[i]-1)*(szcomp[i]-comp[i]);
    }

    for(int i=1;i<=n;i++){
        long long res=0,sq=0;

        for(int f=0;f<v[i].size();f++){
            if(where[i]==where[v[i][f].first])continue;
            
            if(sz[where[i]]>sz[where[v[i][f].first]]){
                res+=sz[where[v[i][f].first]];
                sq+=(sz[where[v[i][f].first]]-1)*sz[where[v[i][f].first]];
            }else{
                res+=(szcomp[where[i]]-sz[where[i]]);
                sq+=(szcomp[where[i]]-sz[where[i]])*(szcomp[where[i]]-sz[where[i]]-1);
            }
        }

        res=res*(res-1);
        res-=sq;

        ans-=(long long) (comp[where[i]]-1)*res;
    }

    cout<<ans<<"\n";

    return 0;
}

/**
 19 24
1 2
2 3
3 4
4 1
5 6
6 7
7 5
8 9
9 10
10 8
11 12
12 13
13 11
14 15
15 16
16 14
17 18
18 19
17 19
7 8
4 5
7 11
13 17
12 14
 */

Compilation message

count_triplets.cpp: In function 'void bcc(int, int, int, int)':
count_triplets.cpp:20:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   20 |     for(int i=0;i<v[x].size();i++){
      |                 ~^~~~~~~~~~~~
count_triplets.cpp: In function 'void mark(int)':
count_triplets.cpp:39:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   39 |     for(int i=0;i<v[x].size();i++){
      |                 ~^~~~~~~~~~~~
count_triplets.cpp: In function 'void dfs(int, int)':
count_triplets.cpp:48:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   48 |     for(int i=0;i<tree[x].size();i++){
      |                 ~^~~~~~~~~~~~~~~
count_triplets.cpp: In function 'void dfs2(int, int, int)':
count_triplets.cpp:60:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   60 |     for(int i=0;i<tree[x].size();i++){
      |                 ~^~~~~~~~~~~~~~~
count_triplets.cpp: In function 'void dobfs(int)':
count_triplets.cpp:86:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   86 |         for(int i=0;i<v[curr].size();i++){
      |                     ~^~~~~~~~~~~~~~~
count_triplets.cpp: In function 'int main()':
count_triplets.cpp:188:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  188 |         for(int f=0;f<v[i].size();f++){
      |                     ~^~~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 9816 KB Output is correct
2 Correct 4 ms 9820 KB Output is correct
3 Correct 4 ms 9820 KB Output is correct
4 Correct 4 ms 9820 KB Output is correct
5 Correct 4 ms 9876 KB Output is correct
6 Correct 4 ms 9820 KB Output is correct
7 Correct 7 ms 9820 KB Output is correct
8 Correct 7 ms 9828 KB Output is correct
9 Correct 5 ms 9820 KB Output is correct
10 Correct 5 ms 9820 KB Output is correct
11 Correct 7 ms 9820 KB Output is correct
12 Correct 7 ms 9816 KB Output is correct
13 Correct 6 ms 9820 KB Output is correct
14 Correct 8 ms 9884 KB Output is correct
15 Correct 6 ms 9820 KB Output is correct
16 Correct 5 ms 9820 KB Output is correct
17 Correct 5 ms 9820 KB Output is correct
18 Correct 5 ms 9892 KB Output is correct
19 Correct 4 ms 9820 KB Output is correct
20 Correct 4 ms 9820 KB Output is correct
21 Correct 6 ms 9888 KB Output is correct
22 Correct 7 ms 9820 KB Output is correct
23 Correct 5 ms 9820 KB Output is correct
24 Correct 5 ms 9820 KB Output is correct
25 Correct 5 ms 9884 KB Output is correct
26 Correct 7 ms 9816 KB Output is correct
27 Correct 4 ms 9820 KB Output is correct
28 Correct 5 ms 9820 KB Output is correct
29 Correct 7 ms 9820 KB Output is correct
30 Correct 5 ms 9888 KB Output is correct
31 Correct 5 ms 9820 KB Output is correct
32 Correct 6 ms 9820 KB Output is correct
33 Correct 5 ms 9820 KB Output is correct
34 Correct 5 ms 9820 KB Output is correct
35 Correct 5 ms 9816 KB Output is correct

Subtask #2
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 9816 KB Output is correct
2 Correct 4 ms 9820 KB Output is correct
3 Correct 4 ms 9820 KB Output is correct
4 Correct 4 ms 9820 KB Output is correct
5 Correct 4 ms 9876 KB Output is correct
6 Correct 4 ms 9820 KB Output is correct
7 Correct 7 ms 9820 KB Output is correct
8 Correct 7 ms 9828 KB Output is correct
9 Correct 5 ms 9820 KB Output is correct
10 Correct 5 ms 9820 KB Output is correct
11 Correct 7 ms 9820 KB Output is correct
12 Correct 7 ms 9816 KB Output is correct
13 Correct 6 ms 9820 KB Output is correct
14 Correct 8 ms 9884 KB Output is correct
15 Correct 6 ms 9820 KB Output is correct
16 Correct 5 ms 9820 KB Output is correct
17 Correct 5 ms 9820 KB Output is correct
18 Correct 5 ms 9892 KB Output is correct
19 Correct 4 ms 9820 KB Output is correct
20 Correct 4 ms 9820 KB Output is correct
21 Correct 6 ms 9888 KB Output is correct
22 Correct 7 ms 9820 KB Output is correct
23 Correct 5 ms 9820 KB Output is correct
24 Correct 5 ms 9820 KB Output is correct
25 Correct 5 ms 9884 KB Output is correct
26 Correct 7 ms 9816 KB Output is correct
27 Correct 4 ms 9820 KB Output is correct
28 Correct 5 ms 9820 KB Output is correct
29 Correct 7 ms 9820 KB Output is correct
30 Correct 5 ms 9888 KB Output is correct
31 Correct 5 ms 9820 KB Output is correct
32 Correct 6 ms 9820 KB Output is correct
33 Correct 5 ms 9820 KB Output is correct
34 Correct 5 ms 9820 KB Output is correct
35 Correct 5 ms 9816 KB Output is correct
36 Correct 80 ms 9820 KB Output is correct
37 Correct 365 ms 9860 KB Output is correct
38 Execution timed out 1036 ms 9816 KB Time limit exceeded
39 Halted 0 ms 0 KB -

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 41 ms 23888 KB Output is correct
2 Correct 43 ms 24048 KB Output is correct
3 Correct 52 ms 23380 KB Output is correct
4 Correct 54 ms 23632 KB Output is correct
5 Correct 47 ms 20820 KB Output is correct
6 Correct 52 ms 22264 KB Output is correct
7 Correct 51 ms 21420 KB Output is correct
8 Correct 55 ms 22100 KB Output is correct
9 Correct 54 ms 20896 KB Output is correct
10 Correct 49 ms 20796 KB Output is correct
11 Correct 44 ms 19480 KB Output is correct
12 Correct 41 ms 19536 KB Output is correct
13 Correct 47 ms 19792 KB Output is correct
14 Correct 40 ms 19436 KB Output is correct
15 Correct 31 ms 19548 KB Output is correct
16 Correct 32 ms 19112 KB Output is correct
17 Correct 8 ms 14680 KB Output is correct
18 Correct 9 ms 14940 KB Output is correct
19 Correct 8 ms 14684 KB Output is correct
20 Correct 8 ms 14684 KB Output is correct
21 Correct 8 ms 14684 KB Output is correct
22 Correct 7 ms 14684 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 9816 KB Output is correct
2 Correct 5 ms 9820 KB Output is correct
3 Correct 4 ms 9820 KB Output is correct
4 Correct 5 ms 10076 KB Output is correct
5 Correct 4 ms 9892 KB Output is correct
6 Correct 5 ms 9864 KB Output is correct
7 Correct 5 ms 10076 KB Output is correct
8 Correct 4 ms 10020 KB Output is correct
9 Correct 5 ms 9816 KB Output is correct
10 Correct 4 ms 10028 KB Output is correct
11 Correct 4 ms 9816 KB Output is correct
12 Correct 7 ms 9820 KB Output is correct
13 Correct 4 ms 9820 KB Output is correct
14 Correct 7 ms 10000 KB Output is correct
15 Correct 7 ms 9820 KB Output is correct
16 Correct 8 ms 9904 KB Output is correct
17 Correct 4 ms 9820 KB Output is correct
18 Correct 5 ms 9848 KB Output is correct
19 Correct 4 ms 10076 KB Output is correct
20 Correct 4 ms 9820 KB Output is correct

Subtask #5
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 64 ms 23304 KB Output is correct
2 Correct 97 ms 23124 KB Output is correct
3 Correct 59 ms 23116 KB Output is correct
4 Correct 60 ms 23124 KB Output is correct
5 Correct 62 ms 23216 KB Output is correct
6 Correct 68 ms 26868 KB Output is correct
7 Correct 65 ms 25740 KB Output is correct
8 Correct 70 ms 24940 KB Output is correct
9 Correct 66 ms 24352 KB Output is correct
10 Correct 59 ms 23124 KB Output is correct
11 Correct 57 ms 23328 KB Output is correct
12 Correct 58 ms 23084 KB Output is correct
13 Correct 83 ms 23216 KB Output is correct
14 Correct 50 ms 22608 KB Output is correct
15 Correct 83 ms 22116 KB Output is correct
16 Correct 31 ms 20060 KB Output is correct
17 Correct 37 ms 23752 KB Output is correct
18 Correct 37 ms 23628 KB Output is correct
19 Correct 41 ms 24128 KB Output is correct
20 Correct 45 ms 23676 KB Output is correct

Subtask #6
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 9820 KB Output is correct
2 Correct 6 ms 9820 KB Output is correct
3 Correct 4 ms 9820 KB Output is correct
4 Correct 4 ms 9820 KB Output is correct
5 Correct 4 ms 9824 KB Output is correct
6 Correct 4 ms 9820 KB Output is correct
7 Correct 4 ms 9820 KB Output is correct
8 Correct 4 ms 9820 KB Output is correct
9 Correct 4 ms 9824 KB Output is correct
10 Correct 6 ms 9820 KB Output is correct
11 Correct 5 ms 9828 KB Output is correct
12 Correct 5 ms 10072 KB Output is correct
13 Correct 5 ms 9820 KB Output is correct
14 Correct 7 ms 9816 KB Output is correct
15 Correct 8 ms 10012 KB Output is correct
16 Correct 5 ms 9820 KB Output is correct
17 Correct 5 ms 9816 KB Output is correct
18 Correct 4 ms 10020 KB Output is correct
19 Correct 5 ms 9820 KB Output is correct
20 Correct 5 ms 9820 KB Output is correct
21 Correct 4 ms 9820 KB Output is correct
22 Correct 5 ms 9820 KB Output is correct
23 Correct 4 ms 9820 KB Output is correct
24 Correct 5 ms 9820 KB Output is correct
25 Correct 5 ms 9944 KB Output is correct
26 Correct 4 ms 9820 KB Output is correct
27 Correct 5 ms 9820 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 57 ms 23152 KB Output is correct
2 Correct 66 ms 23128 KB Output is correct
3 Correct 63 ms 21532 KB Output is correct
4 Correct 55 ms 19640 KB Output is correct
5 Correct 56 ms 18256 KB Output is correct
6 Correct 47 ms 17488 KB Output is correct
7 Correct 45 ms 17396 KB Output is correct
8 Correct 45 ms 16904 KB Output is correct
9 Correct 40 ms 16732 KB Output is correct
10 Correct 62 ms 16724 KB Output is correct
11 Correct 40 ms 16512 KB Output is correct
12 Correct 45 ms 16424 KB Output is correct
13 Correct 61 ms 16464 KB Output is correct
14 Correct 39 ms 18260 KB Output is correct
15 Correct 68 ms 24404 KB Output is correct
16 Correct 75 ms 23372 KB Output is correct
17 Correct 61 ms 23380 KB Output is correct
18 Correct 62 ms 22404 KB Output is correct
19 Correct 57 ms 19792 KB Output is correct
20 Correct 54 ms 19792 KB Output is correct
21 Correct 54 ms 19796 KB Output is correct
22 Correct 46 ms 19280 KB Output is correct
23 Correct 42 ms 18596 KB Output is correct
24 Correct 50 ms 21556 KB Output is correct
25 Correct 56 ms 21716 KB Output is correct
26 Correct 50 ms 20424 KB Output is correct
27 Correct 50 ms 20820 KB Output is correct

Subtask #8
0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 9816 KB Output is correct
2 Correct 4 ms 9820 KB Output is correct
3 Correct 4 ms 9820 KB Output is correct
4 Correct 4 ms 9820 KB Output is correct
5 Correct 4 ms 9876 KB Output is correct
6 Correct 4 ms 9820 KB Output is correct
7 Correct 7 ms 9820 KB Output is correct
8 Correct 7 ms 9828 KB Output is correct
9 Correct 5 ms 9820 KB Output is correct
10 Correct 5 ms 9820 KB Output is correct
11 Correct 7 ms 9820 KB Output is correct
12 Correct 7 ms 9816 KB Output is correct
13 Correct 6 ms 9820 KB Output is correct
14 Correct 8 ms 9884 KB Output is correct
15 Correct 6 ms 9820 KB Output is correct
16 Correct 5 ms 9820 KB Output is correct
17 Correct 5 ms 9820 KB Output is correct
18 Correct 5 ms 9892 KB Output is correct
19 Correct 4 ms 9820 KB Output is correct
20 Correct 4 ms 9820 KB Output is correct
21 Correct 6 ms 9888 KB Output is correct
22 Correct 7 ms 9820 KB Output is correct
23 Correct 5 ms 9820 KB Output is correct
24 Correct 5 ms 9820 KB Output is correct
25 Correct 5 ms 9884 KB Output is correct
26 Correct 7 ms 9816 KB Output is correct
27 Correct 4 ms 9820 KB Output is correct
28 Correct 5 ms 9820 KB Output is correct
29 Correct 7 ms 9820 KB Output is correct
30 Correct 5 ms 9888 KB Output is correct
31 Correct 5 ms 9820 KB Output is correct
32 Correct 6 ms 9820 KB Output is correct
33 Correct 5 ms 9820 KB Output is correct
34 Correct 5 ms 9820 KB Output is correct
35 Correct 5 ms 9816 KB Output is correct
36 Correct 80 ms 9820 KB Output is correct
37 Correct 365 ms 9860 KB Output is correct
38 Execution timed out 1036 ms 9816 KB Time limit exceeded
39 Halted 0 ms 0 KB -

Subtask #9
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 9816 KB Output is correct
2 Correct 4 ms 9820 KB Output is correct
3 Correct 4 ms 9820 KB Output is correct
4 Correct 4 ms 9820 KB Output is correct
5 Correct 4 ms 9876 KB Output is correct
6 Correct 4 ms 9820 KB Output is correct
7 Correct 7 ms 9820 KB Output is correct
8 Correct 7 ms 9828 KB Output is correct
9 Correct 5 ms 9820 KB Output is correct
10 Correct 5 ms 9820 KB Output is correct
11 Correct 7 ms 9820 KB Output is correct
12 Correct 7 ms 9816 KB Output is correct
13 Correct 6 ms 9820 KB Output is correct
14 Correct 8 ms 9884 KB Output is correct
15 Correct 6 ms 9820 KB Output is correct
16 Correct 5 ms 9820 KB Output is correct
17 Correct 5 ms 9820 KB Output is correct
18 Correct 5 ms 9892 KB Output is correct
19 Correct 4 ms 9820 KB Output is correct
20 Correct 4 ms 9820 KB Output is correct
21 Correct 6 ms 9888 KB Output is correct
22 Correct 7 ms 9820 KB Output is correct
23 Correct 5 ms 9820 KB Output is correct
24 Correct 5 ms 9820 KB Output is correct
25 Correct 5 ms 9884 KB Output is correct
26 Correct 7 ms 9816 KB Output is correct
27 Correct 4 ms 9820 KB Output is correct
28 Correct 5 ms 9820 KB Output is correct
29 Correct 7 ms 9820 KB Output is correct
30 Correct 5 ms 9888 KB Output is correct
31 Correct 5 ms 9820 KB Output is correct
32 Correct 6 ms 9820 KB Output is correct
33 Correct 5 ms 9820 KB Output is correct
34 Correct 5 ms 9820 KB Output is correct
35 Correct 5 ms 9816 KB Output is correct
36 Correct 80 ms 9820 KB Output is correct
37 Correct 365 ms 9860 KB Output is correct
38 Execution timed out 1036 ms 9816 KB Time limit exceeded
39 Halted 0 ms 0 KB -