Submission #671195

#	Time	Username	Problem	Language	Result	Execution time	Memory
671195		Forested	Rigged Roads (NOI19_riggedroads)	C++17	0 / 100	345 ms	44848 KiB

riggedroads

#ifndef LOCAL
#define FAST_IO
#endif

// ============
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i)
#define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)

using namespace std;

using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = __uint128_t;
using i32 = signed int;
using i64 = signed long long;
using i128 = __int128_t;
using f64 = double;
using f80 = long double;

template <typename T>
using Vec = vector<T>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64) x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64) x;
    return os;
}

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
// ============

#ifdef DEBUGF
#else
#define DBG(x) (void) 0
#endif

// ============

#include <algorithm>
#include <cassert>
#include <utility>
#include <vector>

class HeavyLightDecomposition {
    std::vector<int> siz;
    std::vector<int> par;
    std::vector<int> hea;
    std::vector<int> in;
    std::vector<int> out;
    std::vector<int> dep;
    std::vector<int> rev;

    template <typename G>
    void dfs1(G &g, int v) {
        if (!g[v].empty() && (int) g[v][0] == par[v]) {
            std::swap(g[v][0], g[v].back());
        }
        for (auto &e : g[v]) {
            int u = (int)e;
            if (u != par[v]) {
                par[u] = v;
                dfs1(g, u);
                siz[v] += siz[u];
                if (siz[u] > siz[(int) g[v][0]]) {
                    std::swap(g[v][0], e);
                }
            }
        }
    }

    template <typename G>
    void dfs2(const G &g, int v, int &time) {
        in[v] = time;
        rev[time++] = v;
        for (auto &e : g[v]) {
            int u = (int)e;
            if (u == par[v]) {
                continue;
            }
            if (u == (int) g[v][0]) {
                hea[u] = hea[v];
            } else {
                hea[u] = u;
            }
            dep[u] = dep[v] + 1;
            dfs2(g, u, time);
        }
        out[v] = time;
    }

public:
    template <typename G>
    HeavyLightDecomposition(G &g, int root = 0) :
        siz(g.size(), 1),
        par(g.size(), root),
        hea(g.size(), root),
        in(g.size(), 0),
        out(g.size(), 0),
        dep(g.size(), 0),
        rev(g.size(), 0) {
        assert(root >= 0 && root < (int) g.size());
        dfs1(g, root);
        int time = 0;
        dfs2(g, root, time);
    }

    int subtree_size(int v) const {
        assert(v >= 0 && v < (int) siz.size());
        return siz[v];
    }

    int parent(int v) const {
        assert(v >= 0 && v < (int) par.size());
        return par[v];
    }

    int in_time(int v) const {
        assert(v >= 0 && v < (int) in.size());
        return in[v];
    }

    int out_time(int v) const {
        assert(v >= 0 && v < (int) out.size());
        return out[v];
    }

    int depth(int v) const {
        assert(v >= 0 && v < (int) dep.size());
        return dep[v];
    }

    int time_to_vertex(int t) const {
        assert(t >= 0 && t < (int) rev.size());
        return rev[t];
    }
    
    int la(int v, int k) const {
        assert(v >= 0 && v < (int) dep.size());
        assert(k >= 0);
        if (k > dep[v]) {
            return -1;
        }
        while (true) {
            int u = hea[v];
            if (in[u] + k <= in[v]) {
                return rev[in[v] - k];
            }
            k -= in[v] - in[u] + 1;
            v = par[u];
        }
        return 0;
    }
    
    int forward(int v, int dst) const {
        assert(v >= 0 && v < (int) dep.size());
        assert(dst >= 0 && dst < (int) dep.size());
        assert(v != dst);
        int l = lca(v, dst);
        if (l == v) {
            return la(dst, dist(v, dst) - 1);
        } else {
            return par[v];
        }
    }

    int lca(int u, int v) const {
        assert(u >= 0 && u < (int) dep.size());
        assert(v >= 0 && v < (int) dep.size());
        while (u != v) {
            if (in[u] > in[v]) {
                std::swap(u, v);
            }
            if (hea[u] == hea[v]) {
                v = u;
            } else {
                v = par[hea[v]];
            }
        }
        return u;
    }

    int dist(int u, int v) const {
        assert(u >= 0 && u < (int) dep.size());
        assert(v >= 0 && v < (int) dep.size());
        return dep[u] + dep[v] - 2 * dep[lca(u, v)];
    }

    std::vector<std::pair<int, int>> path(int u, int v, bool edge) const {
        assert(u >= 0 && u < (int) dep.size());
        assert(v >= 0 && v < (int) dep.size());
        std::vector<std::pair<int, int>> fromu, fromv;
        bool rev = false;
        while (true) {
            if (u == v && edge) {
                break;
            }
            if (in[u] > in[v]) {
                std::swap(u, v);
                std::swap(fromu, fromv);
                rev ^= true;
            }
            if (hea[u] == hea[v]) {
                fromv.emplace_back(in[v], in[u] + (int)edge);
                v = u;
                break;
            } else {
                fromv.emplace_back(in[v], in[hea[v]]);
                v = par[hea[v]];
            }
        }
        if (rev) {
            std::swap(fromu, fromv);
        }
        std::reverse(fromv.begin(), fromv.end());
        fromu.reserve(fromv.size());
        for (auto [x, y] : fromv) {
            fromu.emplace_back(y, x);
        }
        return fromu;
    }
    
    int jump(int u, int v, int k) const {
        assert(u >= 0 && u < (int) dep.size());
        assert(v >= 0 && v < (int) dep.size());
        assert(k >= 0);
        int l = lca(u, v);
        int dis = dep[u] + dep[v] - 2 * dep[l];
        if (k > dis) {
            return -1;
        }
        if (k <= dep[u] - dep[l]) {
            return la(u, k);
        } else {
            return la(v, dis - k);
        }
    }
    
    int meet(int u, int v, int w) const {
        return lca(u, v) ^ lca(v, w) ^ lca(w, u);
    }
};

// ============
// ============

#include <cassert>
#include <utility>
#include <vector>

template <typename MonoidFunc>
class LazySegmentTree {
public:
    using Value = typename MonoidFunc::Value;
    using Func = typename MonoidFunc::Func;

private:
    int old_length;
    int lg;
    int length;
    std::vector<Value> values;
    std::vector<Func> funcs;

    static int lg2(int n) {
        int x = 1;
        int l = 0;
        while (x < n) {
            x <<= 1;
            ++l;
        }
        return l;
    }

    void _apply(int idx, const Func &func) {
        values[idx] = MonoidFunc::apply(func, values[idx]);
        funcs[idx] = MonoidFunc::composite(func, funcs[idx]);
    }

    void push(int idx) {
        _apply(idx << 1, funcs[idx]);
        _apply(idx << 1 | 1, funcs[idx]);
        funcs[idx] = MonoidFunc::func_id();
    }

    void recalc_values(int idx) {
        values[idx] = MonoidFunc::op(values[idx << 1], values[idx << 1 | 1]);
    }

public:
    LazySegmentTree(int n) :
        old_length(n),
        lg(lg2(n)),
        length(1 << lg),
        values(length << 1, MonoidFunc::id()),
        funcs(length << 1, MonoidFunc::func_id()) {
        assert(n >= 0);    
    }

    LazySegmentTree(const std::vector<Value> &v) :
        old_length((int) v.size()),
        lg(lg2(old_length)),
        length(1 << lg),
        values(length << 1, MonoidFunc::id()),
        funcs(length << 1, MonoidFunc::func_id()) {
        for (int i = 0; i < old_length; ++i) {
            values[i + length] = v[i];
        }
        for (int i = length - 1; i > 0; --i) {
            recalc_values(i);
        }
    }

    template <typename F>
    LazySegmentTree(int n, const F &f) :
        old_length(n),
        lg(lg2(n)),
        length(1 << lg),
        values(length << 1, MonoidFunc::id()),
        funcs(length << 1, MonoidFunc::func_id()) {
        for (int i = 0; i < old_length; ++i) {
            values[i + length] = f(i);
        }
        for (int i = length - 1; i > 0; --i) {
            recalc_values(i);
        }
    }

    void update(int idx, Value val) {
        assert(idx >= 0 && idx < old_length);
        idx += length;
        for (int i = lg; i > 0; --i) {
            push(idx >> i);
        }
        values[idx] = std::move(val);
        while (idx >>= 1) {
            recalc_values(idx);
        }
    }

    void apply(int l, int r, const Func &func) {
        assert(l >= 0 && l <= r && r <= old_length);
        if (l == r) {
            return;
        }
        l += length;
        r += length;
        int _l = l;
        int _r = r;
        for (int i = lg; i > 0; --i) {
            push(_l >> i);
            push((_r - 1) >> i);
        }
        while (l < r) {
            if (l & 1) {
                _apply(l++, func);
            }
            if (r & 1) {
                _apply(--r, func);
            }
            l >>= 1;
            r >>= 1;
        }
        for (int i = 1; i <= lg; ++i) {
            if ((_l >> i << i) != _l) {
                recalc_values(_l >> i);
            }
            if ((_r >> i << i) != _r) {
                recalc_values((_r - 1) >> i);
            }
        }
    }

    Value prod(int l, int r) {
        assert(l >= 0 && l <= r && r <= old_length);
        if (l == r) {
            return MonoidFunc::id();
        }
        l += length;
        r += length;
        for (int i = lg; i > 0; --i) {
            push(l >> i);
            push((r - 1) >> i);
        }
        Value lp = MonoidFunc::id();
        Value rp = MonoidFunc::id();
        while (l < r) {
            if (l & 1) {
                lp = MonoidFunc::op(lp, values[l++]);
            }
            if (r & 1) {
                rp = MonoidFunc::op(values[--r], rp);
            }
            l >>= 1;
            r >>= 1;
        }
        return MonoidFunc::op(lp, rp);
    }
    
    Value all_prod() const {
        return values[1];
    }
};

// ============

struct Upd1 {
    using Value = pair<i32, i32>;
    using Func = bool;
    static Value id() {
        return Value(0, 0);
    }
    static Value op(const Value &x, const Value &y) {
        return Value(x.first + y.first, x.second + y.second);
    }
    static Func func_id() {
        return false;
    }
    static Func composite(Func f, Func g) {
        return f || g;
    }
    static Value apply(Func f, const Value &x) {
        if (f) {
            return Value(x.second, x.second);
        } else {
            return x;
        }
    }
};

class RangeChmin {
    i32 n;
    Vec<i32> data;
    
public:
    RangeChmin(i32 n) : n(n), data(2 * n, INF) {}
    
    void range_chmin(i32 l, i32 r, i32 v) {
        l += n;
        r += n;
        while (l < r) {
            if (l % 2 == 1) {
                chmin(data[l++], v);
            }
            if (r % 2 == 1) {
                chmin(data[--r], v);
            }
            l /= 2;
            r /= 2;
        }
    }
    
    i32 at(i32 idx) const {
        i32 ret = INF;
        idx += n;
        while (idx > 0) {
            chmin(ret, data[idx]);
            idx /= 2;
        }
        return ret;
    } 
};

int main() {
    i32 n, m;
    cin >> n >> m;
    Vec<pair<i32, i32>> edges(m);
    for (auto &[u, v] : edges) {
        cin >> u >> v;
        --u;
        --v;
    }
    Vec<i32> r(n - 1);
    REP(i, n - 1) {
        cin >> r[i];
        --r[i];
    }
    
    Vec<i32> is_in(m, 0);
    for (i32 ei : r) {
        is_in[ei] = 1;
    }
    
    Vec<Vec<i32>> tree(n);
    for (i32 ei : r) {
        auto [u, v] = edges[ei];
        tree[u].emplace_back(v);
        tree[v].emplace_back(u);
    }
    HeavyLightDecomposition hld(tree);
    
    LazySegmentTree<Upd1> seg(n, [&](i32) -> Upd1::Value {
        return Upd1::Value(0, 1);
    });
    RangeChmin rc(n);
    
    i32 nxt = 0;
    Vec<i32> ans(m, -1);
    Vec<i32> used(m, 0);
    REP(i, m) {
        if (is_in[i]) {
            auto &[u, v] = edges[i];
            if (hld.depth(u) > hld.depth(v)) {
                swap(u, v);
            }
            if (rc.at(hld.in_time(v)) != INF) {
                continue;
            }
            seg.apply(hld.in_time(v), hld.in_time(v) + 1, true);
            ans[i] = nxt;
            used[nxt++] = 1;
        } else {
            auto [u, v] = edges[i];
            Upd1::Value path = Upd1::id();
            for (auto [l, r] : hld.path(u, v, true)) {
                if (l > r) {
                    swap(l, r);
                }
                path = Upd1::op(path, seg.prod(l, r + 1));
            }
            nxt += path.second - path.first;
            for (auto [l, r] : hld.path(u, v, true)) {
                if (l > r) {
                    swap(l, r);
                }
                rc.range_chmin(l, r + 1, nxt);
                seg.apply(l, r + 1, true);
            }
            ans[i] = nxt;
            used[nxt++] = 1;
        }
    }
    
    Vec<i32> pct;
    for (i32 ei : r) {
        if (ans[ei] == -1) {
            pct.push_back(ei);
        }
    }
    stable_sort(ALL(pct), [&](i32 i, i32 j) -> bool {
        return rc.at(hld.in_time(edges[i].second)) < rc.at(hld.in_time(edges[j].second));
    });
    nxt = 0;
    for (i32 i : pct) {
        while (used[nxt]) {
            ++nxt;
        }
        ans[i] = nxt++;
    }
    
    REP(i, m) {
        cout << ans[i] + 1 << " \n"[i + 1 == m];
    }
}

• Subtask 1: 0 / 8
• Subtask 2: 0 / 19
• Subtask 3: 0 / 9
• Subtask 4: 0 / 10
• Subtask 5: 0 / 10
• Subtask 6: 0 / 12
• Subtask 7: 0 / 32