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Submission #855968

# Submission time Handle Problem Language Result Execution time Memory
855968 2023-10-02T12:57:16 Z Cyanmond One-Way Streets (CEOI17_oneway) C++17
100 / 100
 129 ms 37120 KB 
#include <bits/stdc++.h>

using namespace std;

#define rep(i, l, r) for (int i = (l); i < (r); ++i)
#define per(i, l, r) for (int i = (r - 1); i >= l; --i)
#define ALL(x) (x).begin(), (x).end()

using i64 = long long;

vector<int> decomposite(const vector<vector<pair<int, int>>> &graph) {
    const int n = (int)graph.size();
    vector<bool> isUsed(n);
    vector<int> ord(n), low(n);

    auto dfs = [&](auto &&self, const int v, const int p, int &id) -> void {
        isUsed[v] = true;
        ord[v] = id++;
        low[v] = ord[v];
        for (const auto &[t, i] : graph[v]) {
            if (isUsed[t]) {
                if (i != p) low[v] = min(low[v], ord[t]);
                continue;
            }
            self(self, t, i, id);
            low[v] = min(low[v], low[t]);
        }
    };
    int id = 0;
    rep(i, 0, n) {
        if (not isUsed[i]) {
            dfs(dfs, i, -1, id);
        }
    }

    vector<int> group(n, -1);
    auto dfs2 = [&](auto &&self, const int v, const int p, int &id) -> void {
        assert(group[v] == -1);
        if (p != -1 and ord[p] >= low[v]) {
            group[v] = group[p];
        } else {
            group[v] = id++;
        }
        for (const auto &[t, i] : graph[v]) {
            if (group[t] != -1) continue;
            self(self, t, v, id);
        }
    };
    id = 0;
    rep(i, 0, n) {
        if (group[i] == -1) {
            dfs2(dfs2, i, -1, id);
        }
    }
    return group;
}

void main_() {
    int N, M;
    cin >> N >> M;
    vector<int> A(M), B(M);
    vector<vector<pair<int, int>>> graph(N);
    rep(i, 0, M) {
        cin >> A[i] >> B[i];
        graph[--A[i]].push_back({--B[i], i});
        graph[B[i]].push_back({A[i], i});
    }
    int P;
    cin >> P;
    vector<int> X(P), Y(P);
    rep(i, 0, P) {
        cin >> X[i] >> Y[i];
        --X[i], --Y[i];
    }

    const auto group = decomposite(graph);
    vector<char> ans(M, 'A');
    rep(i, 0, M) {
        if (group[A[i]] == group[B[i]]) {
            ans[i] = 'B';
        }
    }

    const int U = *max_element(ALL(group)) + 1;
    vector<vector<pair<int, int>>> tree(U);
    rep(i, 0, M) {
        if (group[A[i]] != group[B[i]]) {
            tree[group[A[i]]].push_back({group[B[i]], i});
            tree[group[B[i]]].push_back({group[A[i]], i});
        }
    }

    vector<vector<int>> F(N), T(N);
    rep(i, 0, P) {
        F[X[i]].push_back(i);
        T[Y[i]].push_back(i);
    }

    vector<int> par(U, -1), depth(U);
    constexpr int R = 20;
    vector<vector<int>> table(R);
    auto dfsC = [&](auto &&self, const int v, const int p, const int d) -> void {
        par[v] = p;
        depth[v] = d;
        for (const auto &[t, i] : tree[v]) {
            if (t == p) continue;
            self(self, t, v, d + 1);
        }
    };
    rep(i, 0, U) {
        if (par[i] != -1) continue;
        dfsC(dfsC, i, -1, 0);
    }

    table[0] = par;
    rep(rank, 1, R) {
        table[rank].assign(U, -1);
        rep(i, 0, U) {
            if (table[rank - 1][i] == -1) continue;
            else table[rank][i] = table[rank - 1][table[rank - 1][i]];
        }
    }

    auto calcLCA = [&](int u, int v) {
        if (depth[u] > depth[v]) swap(u, v);
        per(rank, 0, 20) {
            const int a = table[rank][v];
            if (a != -1 and depth[a] >= depth[u]) v = a;
        }
        assert(depth[u] == depth[v]);
        if (u == v) return u;
        per(rank, 0, 20) {
            const int a = table[rank][u], b = table[rank][v];
            if (a != b) {
                u = a;
                v = b;
            }
        }
        assert(par[u] == par[v]);
        return par[u];
    };

    vector<int> e1(U), e2(U);
    rep(i, 0, P) {
        const int lca = calcLCA(group[X[i]], group[Y[i]]);
        ++e1[group[X[i]]];
        ++e2[group[Y[i]]];
        --e1[lca];
        --e2[lca];
    }

    auto setVal = [&](int a, int b, int i, int v) {
        if (group[A[i]] != a) {
            // rev
            if (v != 3) v ^= 3;
        }
        ans[i] = v == 1 ? 'R' : (v == 2 ? 'L' : 'B');
    };

    vector<bool> isUsed(U);
    auto dfs = [&](auto &&self, const int v, const int p) -> pair<int, int> {
        isUsed[v] = true;
        pair<int, int> val = {e1[v], e2[v]};
        for (const auto &[t, i] : tree[v]) {
            if (t == p) continue;
            const auto res = self(self, t, v);
            {
                if (res.first != 0) setVal(t, v, i, 1);
                else if (res.second != 0) setVal(v, t, i, 1);
                else setVal(v, t, i, 3);
            }
            val.first += res.first;
            val.second += res.second;
        }
        return val;
    };
    rep(i, 0, U) {
        if (not isUsed[i]) {
            dfs(dfs, i, -1);
        }
    }

    for (const auto e : ans) cout << e;
    cout << endl;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    main_();
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 604 KB Output is correct
5 Correct 1 ms 856 KB Output is correct
6 Correct 1 ms 464 KB Output is correct
7 Correct 1 ms 604 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 552 KB Output is correct
10 Correct 1 ms 348 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 604 KB Output is correct
5 Correct 1 ms 856 KB Output is correct
6 Correct 1 ms 464 KB Output is correct
7 Correct 1 ms 604 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 552 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 26 ms 6740 KB Output is correct
12 Correct 30 ms 8272 KB Output is correct
13 Correct 33 ms 10696 KB Output is correct
14 Correct 41 ms 16360 KB Output is correct
15 Correct 45 ms 18832 KB Output is correct
16 Correct 58 ms 28792 KB Output is correct
17 Correct 56 ms 30100 KB Output is correct
18 Correct 57 ms 28676 KB Output is correct
19 Correct 53 ms 31312 KB Output is correct
20 Correct 30 ms 9172 KB Output is correct
21 Correct 29 ms 9248 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 604 KB Output is correct
5 Correct 1 ms 856 KB Output is correct
6 Correct 1 ms 464 KB Output is correct
7 Correct 1 ms 604 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 552 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 26 ms 6740 KB Output is correct
12 Correct 30 ms 8272 KB Output is correct
13 Correct 33 ms 10696 KB Output is correct
14 Correct 41 ms 16360 KB Output is correct
15 Correct 45 ms 18832 KB Output is correct
16 Correct 58 ms 28792 KB Output is correct
17 Correct 56 ms 30100 KB Output is correct
18 Correct 57 ms 28676 KB Output is correct
19 Correct 53 ms 31312 KB Output is correct
20 Correct 30 ms 9172 KB Output is correct
21 Correct 29 ms 9248 KB Output is correct
22 Correct 129 ms 34120 KB Output is correct
23 Correct 126 ms 32648 KB Output is correct
24 Correct 107 ms 32836 KB Output is correct
25 Correct 115 ms 37120 KB Output is correct
26 Correct 117 ms 33896 KB Output is correct
27 Correct 108 ms 32692 KB Output is correct
28 Correct 26 ms 5968 KB Output is correct
29 Correct 56 ms 12744 KB Output is correct
30 Correct 58 ms 12860 KB Output is correct
31 Correct 55 ms 13036 KB Output is correct
32 Correct 93 ms 20464 KB Output is correct