제출 #1190270

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1190270		omsincoconut	철인 이종 경기 (APIO18_duathlon)	C++17	31 / 100	139 ms	36948 KiB

count_triplets

/*
Do 2-edge connectivity => Get condensation tree

If s, c, f all in different components
Imagine the condensation tree having the vertices' weights = number of vertex in that component
Fix the position of c, it is easy to calculate the number of possible (s, f)

If s, c, f all in same components
For each component with n vertices, add n(n-1)(n-2)

If s, c in same component but f in different
We can have any (s, c, f) except if s is on the path fron c to f.
It is easier to subtract out that case.
*/

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

const int MAXN = 1e5+5;

ll n, m;
vector<int> edge[MAXN];
vector<pair<int, int>> edge_list;

int p[MAXN], tin[MAXN], low[MAXN];
void dfs(int u) {
    static int ct = 1;

    low[u] = tin[u] = ct++;
    for (int v : edge[u]) {
        if (tin[v] == -1) {
            p[v] = u;
            dfs(v);
        }

        if (p[u] != v || upper_bound(edge_list.begin(), edge_list.end(), make_pair(u, v))
        - lower_bound(edge_list.begin(), edge_list.end(), make_pair(u, v)) >= 2)
            low[u] = min(low[v], low[u]);
    }
}

vector<int> lowlist;
vector<int> comp[MAXN];
vector<int> treeedge[MAXN];

ll dp[MAXN];
vector<int> treechild[MAXN];
int treep[MAXN];
int cc = 1;
int treecomp[MAXN];
ll treecompsz[MAXN];

void treedfs(int u) {
    dp[u] = comp[u].size();
    treecomp[u] = cc;

    for (int v : treeedge[u]) {
        if (dp[v] != -1) continue;

        treechild[u].push_back(v);
        treep[v] = u;
        treedfs(v);
        dp[u] += dp[v];
    }
}

vector<pair<int, int>> temptemp;
vector<int> tempedge[MAXN];

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

    cin >> n >> m;
    for (int i = 1; i <= m; i++) {
        int u, v;
        cin >> u >> v;
        edge[u].push_back(v);
        edge[v].push_back(u);
        edge_list.emplace_back(u, v);
        edge_list.emplace_back(v, u);
    }

    sort(edge_list.begin(), edge_list.end());

    fill(tin, tin+n+1, -1);
    fill(p, p+n+1, -1);
    for (int i = 1; i <= n; i++) {
        if (p[i] == -1) {
            p[i] = i;
            dfs(i);
        }
    }

    for (int u = 1; u <= n; u++) {
        if (tin[u] > low[u]) continue;
        for (int v : edge[u]) {
            if (tin[v] < tin[u]) {
                temptemp.emplace_back(u, v);
                temptemp.emplace_back(v, u);
            }
        }
    }
    sort(temptemp.begin(), temptemp.end());

    for (int u = 1; u <= n; u++) {
        for (int v : edge[u]) {
            if (!binary_search(temptemp.begin(), temptemp.end(), make_pair(u, v))) {
                tempedge[u].push_back(v);
            }
        }
    }

    fill(low, low+n+1, -1);
    int llow = 1;
    for (int i = 1; i <= n; i++) {
        if (low[i] != -1) continue;

        queue<int> dt;
        dt.push(i);
        while (!dt.empty()) {
            int u = dt.front();
            dt.pop();
            if (low[u] != -1) continue;
            low[u] = llow;
            for (int v : tempedge[u]) dt.push(v);
        }

        llow++;
    }

    for (int i = 1; i <= n; i++) {
        lowlist.push_back(low[i]);
        comp[low[i]].push_back(i);
    }

    sort(lowlist.begin(), lowlist.end());
    lowlist.resize(unique(lowlist.begin(), lowlist.end()) - lowlist.begin());

    for (int u = 1; u <= n; u++) {
        for (int v : edge[u]) {
            if (low[u] != low[v]) {
                treeedge[low[u]].push_back(low[v]);
            }
        }
    }

    fill(dp, dp+n+1, -1);
    for (int i : lowlist) {
        if (dp[i] == -1) {
            treep[i] = i;
            treedfs(i);
            treecompsz[cc] = dp[i];
            cc++;
        }
    }

    // Case 1
    ll case1 = 0;
    for (int i : lowlist) {
        ll sm = 0, nans = 0;
        for (int j : treechild[i]) {
            nans += dp[j]*sm;
            sm += dp[j];
        }
        nans += (treecompsz[treecomp[i]]-dp[i])*sm;
        case1 += nans*(ll)(comp[i].size())*2;
    }

    // Case 2
    ll case2 = 0;
    for (int i : lowlist) {
        ll sz = comp[i].size();
        case2 += sz*(sz-1)*(sz-2);
    }

    // Case 3
    ll case3 = 0;
    for (int i : lowlist) {
        ll sz = comp[i].size();
        for (int j : treechild[i]) {
            case3 += (sz-1)*(sz-1)*dp[j];
        }
        case3 += (sz-1)*(sz-1)*(treecompsz[treecomp[i]]-dp[i]);
    }

    cout << case1 + case2 + 2*case3;

    return 0;
}

/*
4 4
1 2
2 3
3 4
4 2
*/

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• Subtask 2: 0 / 11
• Subtask 3: 8 / 8
• Subtask 4: 10 / 10
• Subtask 5: 13 / 13
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