結果

問題 No.529 帰省ラッシュ
ユーザー PachicobuePachicobue
提出日時 2017-12-31 03:28:04
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 719 ms / 4,500 ms
コード長 10,916 bytes
コンパイル時間 2,945 ms
コンパイル使用メモリ 236,076 KB
実行使用メモリ 54,448 KB
最終ジャッジ日時 2023-08-23 11:22:51
合計ジャッジ時間 10,482 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge15
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
4,380 KB
testcase_01 AC 1 ms
4,376 KB
testcase_02 AC 2 ms
4,376 KB
testcase_03 AC 2 ms
4,380 KB
testcase_04 AC 6 ms
4,380 KB
testcase_05 AC 7 ms
4,376 KB
testcase_06 AC 7 ms
4,380 KB
testcase_07 AC 6 ms
4,376 KB
testcase_08 AC 370 ms
28,484 KB
testcase_09 AC 356 ms
30,092 KB
testcase_10 AC 413 ms
40,092 KB
testcase_11 AC 453 ms
40,152 KB
testcase_12 AC 339 ms
28,752 KB
testcase_13 AC 248 ms
54,448 KB
testcase_14 AC 362 ms
31,528 KB
testcase_15 AC 700 ms
43,100 KB
testcase_16 AC 719 ms
43,856 KB
testcase_17 AC 560 ms
51,640 KB
testcase_18 AC 499 ms
51,576 KB
testcase_19 AC 501 ms
47,848 KB
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ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<int, int>;
template <typename T>
constexpr T INF = numeric_limits<T>::max() / 10;

struct Graph {
    Graph(const int v) : V{v}
    {
        edge.resize(v);
        rev_edge.resize(v);
    }
    void addEdge(const int from, const int to)
    {
        edge[from].push_back(to);
        rev_edge[to].push_back(from);
    }
    vector<vector<int>> edge;
    vector<vector<int>> rev_edge;
    const int V;
};

class BiconnectedComponent
{
public:
    BiconnectedComponent(const Graph& g_) : num{0}, comp_num{0}, size{g_.V}, bridge(0), ord(size, -1), low(size, 0), comp(size, -1)
    {
        for (int i = 0; i < size; i++) {
            if (ord[i] == -1) {
                bridge_dfs(g_, i);
            }
        }
        for (int i = 0; i < size; i++) {
            if (comp[i] >= 0) {
                continue;
            }
            comp_dfs(g_, i, comp_num);
            comp_num++;
        }
    }

    Graph toTree() const
    {
        Graph tree(comp_num);
        for (const auto& p : bridge) {
            tree.addEdge(comp[p.first], comp[p.second]);
            tree.addEdge(comp[p.second], comp[p.first]);
        }
        return tree;
    }
    const vector<pair<int, int>>& getEdge() const
    {
        return bridge;
    }
    bool isBridge(const int i, const int j) const
    {
        return (ord[i] < ord[j]) ? ord[i] < low[j] : ord[j] < low[i];
    }
    const vector<int>& getComp() const
    {
        return comp;
    }
    const vector<pair<int, int>>& getBridge() const
    {
        return bridge;
    }

private:
    void bridge_dfs(const Graph& g_, const int s, const int par = -1)
    {
        ord[s] = num;
        low[s] = num;
        num++;
        for (const int to : g_.edge[s]) {
            if (to == par) {
                continue;
            }
            if (ord[to] >= 0) {
                low[s] = min(low[s], ord[to]);
            } else {
                bridge_dfs(g_, to, s);
                low[s] = min(low[s], low[to]);
                if (isBridge(s, to)) {
                    bridge.push_back(make_pair(s, to));
                }
            }
        }
    }

    void comp_dfs(const Graph& g_, const int s, const int c)
    {
        comp[s] = c;
        for (const int to : g_.edge[s]) {
            if ((comp[to] == -1) and (not isBridge(s, to))) {
                comp_dfs(g_, to, c);
            }
        }
    }

    int num;
    int comp_num;
    const int size;
    vector<pair<int, int>> bridge;
    vector<int> ord;
    vector<int> low;
    vector<int> comp;
};

class HeavyLightDecomposition
{
private:
    using P = pair<int, int>;

public:
    HeavyLightDecomposition(const Graph& g, const int root = 0) : N(g.V), sub(N, 0), prev(N, -1), next(N, -1), depth(N, 0), head{root}, index(N, {-1, 0}), chains(0)
    {
        dfs(g, root, 0);
        chains.resize(head.size());
        for (int i = 0; i < head.size(); i++) {
            int pos = head[i];
            int v = -1;
            for (int ind = 0; pos != -1; ind++) {
                v = pos;
                chains[i].push_back(pos);
                index[pos] = {i, ind};
                pos = next[pos];
            }
            tail.push_back(v);
        }
    }
    P getIndex(const int v) const
    {
        return index[v];
    }
    int getChainIndex(const int v) const
    {
        return index[v].first;
    }
    int getPosition(const int v) const
    {
        return index[v].second;
    }
    int getHead(const int v) const
    {
        return head[index[v].first];
    }
    int getTail(const int v) const
    {
        return tail[index[v].first];
    }
    const vector<int>& getDepth() const
    {
        return depth;
    }
    int prevChainNode(const int v) const
    {
        return prev[getHead(v)];
    }
    P prevChainIndex(const int v) const
    {
        return getIndex(prevChainNode(v));
    }
    int getLCA(int u, int v) const
    {
        while (getChainIndex(u) != getChainIndex(v)) {
            if (depth[getHead(u)] > depth[getHead(v)]) {
                u = prevChainNode(u);
            } else {
                v = prevChainNode(v);
            }
        }
        return depth[u] < depth[v] ? u : v;
    }

    const vector<vector<int>>& getChains() const
    {
        return chains;
    }

    int prevChain(const int v) const
    {
        return prev[head[index[v].first]];
    }

    const int N;

private:
    int dfs(const Graph& g, const int s, const int d)
    {
        sub[s] = 1;
        depth[s] = d;
        vector<P> child;
        for (const int to : g.edge[s]) {
            if (sub[to] == 0) {
                prev[to] = s;
                const int size = dfs(g, to, d + 1);
                sub[s] += size;
                child.push_back({s, to});
            }
        }
        sort(child.begin(), child.end(), greater<P>{});
        if (child.size()) {
            next[s] = child[0].second;
            for (int i = 1; i < child.size(); i++) {
                head.push_back(child[i].second);
            }
        }
        return sub[s];
    }

    vector<int> sub;
    vector<int> prev;
    vector<int> next;
    vector<int> tail;
    vector<int> depth;
    vector<int> head;
    vector<P> index;
    vector<vector<int>> chains;
};

template <typename Monoid>
class FenwickTree
{
public:
    using BaseMonoid = Monoid;
    using T = typename Monoid::T;

    FenwickTree(const int n) : data_num(n), size(1 << (1 + __lg(2 * data_num - 1))), half(size >> 1), value(size, Monoid::identity()) { assert(n > 0); }
    FenwickTree(const std::vector<T>& val) : data_num(val.size()), size(1 << (1 + __lg(2 * data_num - 1))), half(size >> 1), value(size)
    {
        for (int data = 0; data < half; data++) {
            if (data < data_num) {
                value[data + half] = val[data];
            } else {
                value[data + half] = Monoid::identity();
            }
        }
        for (int node = half - 1; node >= 1; node--) {
            value[node] = acc(value[2 * node], value[2 * node + 1]);
        }
    }

    T get(const int a) const
    {
        assert(0 <= a and a < data_num);
        return accumulate(a, a + 1);
    }

    void set(const int a, const T& val)
    {
        assert(0 <= a and a < data_num);
        const int node = a + half;
        value[node] = val;
        for (int i = node / 2; i > 0; i /= 2) {
            value[i] = acc(value[2 * i], value[2 * i + 1]);
        }
    }

    T accumulate(const int a, const int b) const  // Accumulate (a,b]
    {
        assert(0 <= a and a < b and b <= data_num);
        return accumulateRec(1, 0, half, a, b);
    }

    int query(const int a, const int b) const  // query (a,b]
    {
        assert(0 <= a and a < b and b <= data_num);
        return queryRec(1, 0, half, a, b);
    }

private:
    T accumulateRec(const int range_index, const int range_left, const int range_right, const int op_left, const int op_right) const
    {
        if (op_left <= range_left and range_right <= op_right) {
            return value[range_index];
        } else if (range_right <= op_left or op_right <= range_left) {
            return Monoid::identity();
        } else {
            return acc(accumulateRec(2 * range_index, range_left, (range_left + range_right) / 2, op_left, op_right),
                accumulateRec(2 * range_index + 1, (range_left + range_right) / 2, range_right, op_left, op_right));
        }
    }

    int queryRec(const int range_index, const int range_left, const int range_right, const int op_left, const int op_right) const
    {
        if (op_left <= range_left and range_right <= op_right) {
            return value[range_index];
        } else if (range_right <= op_left or op_right <= range_left) {
            return Monoid::identity();
        } else {
            return queryRec(2 * range_index, range_left, (range_left + range_right) / 2, op_left, op_right) + queryRec(2 * range_index + 1, (range_left + range_right) / 2, range_right, op_left, op_right);
        }
    }

    const int data_num;  // Num of valid data on leaves.
    const int size;
    const int half;
    vector<T> value;  // Tree for value(length: size)
    const Monoid acc{};
};

struct Max {
    using T = pair<ll, int>;
    T operator()(const T& a, const T& b) const { return max(a, b); }
    static constexpr T identity() { return make_pair(-INF<ll>, -1); }
};

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N, M, Q;
    cin >> N >> M >> Q;
    Graph g_(N);
    for (int i = 0; i < M; i++) {
        int a, b;
        cin >> a >> b;
        a--, b--;
        g_.addEdge(a, b);
        g_.addEdge(b, a);
    }

    BiconnectedComponent bic(g_);
    const int comp = bic.getComp().size();
    auto g = bic.toTree();

    vector<priority_queue<ll>> value(comp);
    HeavyLightDecomposition hld(g);
    vector<FenwickTree<Max>> segs;
    for (const auto& chain : hld.getChains()) {
        vector<pair<ll, int>> v(chain.size());
        for (int i = 0; i < chain.size(); i++) {
            v[i] = {-1, i};
        }
        segs.push_back(FenwickTree<Max>{v});
    }


    for (int q = 0; q < Q; q++) {
        int t;
        cin >> t;
        if (t == 1) {
            int u;
            ll v;
            cin >> u >> v;
            u--;
            u = bic.getComp()[u];
            value[u].push(v);
            const P chind = hld.getIndex(u);
            segs[chind.first].set(chind.second, {value[u].top(), chind.second});
        } else {
            int s, t;
            cin >> s >> t;
            s--, t--;
            s = bic.getComp()[s];
            t = bic.getComp()[t];
            const int lca = hld.getLCA(s, t);
            const P lca_ch = hld.getIndex(lca);
            int pos[2] = {s, t};
            pair<ll, int> ans{-1, -1};
            int maxchain = -1;
            for (int i = 0; i < 2; i++) {
                while (true) {
                    const P index = hld.getIndex(pos[i]);
                    const int head = (lca_ch.first == index.first ? lca_ch.second : 0);
                    const auto val = segs[index.first].accumulate(head, index.second + 1);
                    if (ans < val) {
                        ans = val;
                        maxchain = index.first;
                    }
                    if (lca_ch.first == index.first) {
                        break;
                    }

                    pos[i] = hld.prevChainNode(pos[i]);
                }
            }
            if (ans.first > 0) {
                const int node = hld.getChains()[maxchain][ans.second];
                value[node].pop();
                const ll val = (value[node].empty() ? -1 : value[node].top());
                segs[maxchain].set(ans.second, make_pair(val, ans.second));
            }
            cout << ans.first << endl;
        }
    }

    return 0;
}
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