test/aoj0439_virtual_tree_helper.test.cpp

• View this file on GitHub
• Last update: 2026-03-22 13:47:31+09:00
• Problem: https://onlinejudge.u-aizu.ac.jp/problems/0439

Depends on

• Sparse Table (datastructure/sparsetable.cpp)
• 補助木(Aux Tree) (tree/auxtree.cpp)
• Virtual Tree Helper (tree/virtual_tree_helper.cpp)
• 高速入出力(Fast IO) (util/fastio.cpp)

Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/0439"

#include <algorithm>
#include <functional>
#include <limits>
#include <queue>
#include <stack>
#include <vector>
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max() / 32 * 15 + 208;

#include <cstdio>
#include <cstring>
#include <string>
#include <type_traits>

#include "../util/fastio.cpp"
#include "../tree/virtual_tree_helper.cpp"

template <typename T>
using GPQ = priority_queue<T, vector<T>, greater<T>>;

int main() {
    Scanner sc;
    Printer pr;

    int n;
    sc.read(n);
    vector<vector<int>> color(n);
    VirtualTreeHelper vt(n);
    for (int i = 0; i < n; ++i) {
        int x;
        sc.read(x);
        color[x - 1].emplace_back(i);
    }
    for (int i = 0; i < n - 1; ++i) {
        int u, v;
        sc.read(u, v);
        --u;
        --v;
        vt.add_edge(u, v);
    }
    vt.build();

    vector<int> ans(n, INF<int>);
    vector<int> cmp(n), dist(n);
    vector<vector<int>> g(n);
    vector<int> is_target(n, 0);
    for (auto &&vs : color) {
        if (vs.empty()) continue;
        for (int v : vs) is_target[v] = 1;
        auto tree = vt.make(vs);
        for (int v : tree.vertices) g[v].clear();
        for (int i = 1; i < (int)tree.vertices.size(); ++i) {
            int v = tree.vertices[i];
            int p = tree.parent[i];
            g[v].emplace_back(p);
            g[p].emplace_back(v);
        }

        GPQ<pair<int, int>> q;
        for (int i = 0; i < (int)tree.vertices.size(); ++i) {
            int v = tree.vertices[i];
            if (is_target[v]) {
                dist[v] = 0;
                cmp[v] = v;
                q.emplace(0, v);
            } else {
                dist[v] = INF<int>;
            }
        }
        while (!q.empty()) {
            auto [d, v] = q.top();
            q.pop();
            if (d != dist[v]) continue;
            for (auto &&u : g[v]) {
                if (dist[u] > dist[v] + vt.distance(v, u)) {
                    dist[u] = dist[v] + vt.distance(v, u);
                    cmp[u] = cmp[v];
                    q.emplace(dist[u], u);
                }
            }
        }
        for (int v : tree.vertices) {
            for (auto &&u : g[v]) {
                int a = cmp[v], b = cmp[u];
                if (a != b) ans[a] = min(ans[a], vt.distance(a, b));
            }
        }
        for (int v : vs) is_target[v] = 0;
    }

    for (auto &&x : ans) pr.println(x);
    return 0;
}

#line 1 "test/aoj0439_virtual_tree_helper.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/0439"

#include <algorithm>
#include <functional>
#include <limits>
#include <queue>
#include <stack>
#include <vector>
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max() / 32 * 15 + 208;

#include <cstdio>
#include <cstring>
#include <string>
#include <type_traits>

#line 1 "util/fastio.cpp"
using namespace std;

extern "C" int fileno(FILE *);
extern "C" int isatty(int);

template<class T, class = void>
struct is_fastio_range : false_type {};

template<class T>
struct is_fastio_range<T, void_t<decltype(declval<T &>().begin()), decltype(declval<T &>().end())>> : true_type {};

template<class T, class = void>
struct has_fastio_value : false_type {};

template<class T>
struct has_fastio_value<T, void_t<decltype(declval<const T &>().value())>> : true_type {};

struct FastIoDigitTable {
    char num[40000];

    constexpr FastIoDigitTable() : num() {
        for (int i = 0; i < 10000; ++i) {
            int x = i;
            for (int j = 3; j >= 0; --j) {
                num[i * 4 + j] = char('0' + x % 10);
                x /= 10;
            }
        }
    }
};

struct Scanner {
    static constexpr int BUFSIZE = 1 << 17;
    static constexpr int OFFSET = 64;
    char buf[BUFSIZE + 1];
    int idx, size;
    bool interactive;

    Scanner() : idx(0), size(0), interactive(isatty(fileno(stdin))) {}

    inline void load() {
        int len = size - idx;
        memmove(buf, buf + idx, len);
        if (interactive) {
            if (fgets(buf + len, BUFSIZE + 1 - len, stdin)) size = len + (int)strlen(buf + len);
            else size = len;
        } else {
            size = len + (int)fread(buf + len, 1, BUFSIZE - len, stdin);
        }
        idx = 0;
        buf[size] = 0;
    }

    inline void ensure() {
        if (idx + OFFSET > size) load();
    }

    inline void ensure_interactive() {
        if (idx == size) load();
    }

    inline char skip() {
        if (interactive) {
            ensure_interactive();
            while (buf[idx] && buf[idx] <= ' ') {
                ++idx;
                ensure_interactive();
            }
            return buf[idx++];
        }
        ensure();
        while (buf[idx] && buf[idx] <= ' ') {
            ++idx;
            ensure();
        }
        return buf[idx++];
    }

    template<class T, typename enable_if<is_integral<T>::value, int>::type = 0>
    void read(T &x) {
        if (interactive) {
            char c = skip();
            bool neg = false;
            if constexpr (is_signed<T>::value) {
                if (c == '-') {
                    neg = true;
                    ensure_interactive();
                    c = buf[idx++];
                }
            }
            x = 0;
            while (c >= '0') {
                x = x * 10 + (c & 15);
                ensure_interactive();
                c = buf[idx++];
            }
            if constexpr (is_signed<T>::value) {
                if (neg) x = -x;
            }
            return;
        }
        char c = skip();
        bool neg = false;
        if constexpr (is_signed<T>::value) {
            if (c == '-') {
                neg = true;
                c = buf[idx++];
            }
        }
        x = 0;
        while (c >= '0') {
            x = x * 10 + (c & 15);
            c = buf[idx++];
        }
        if constexpr (is_signed<T>::value) {
            if (neg) x = -x;
        }
    }

    template<class T, typename enable_if<!is_integral<T>::value && !is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value && has_fastio_value<T>::value, int>::type = 0>
    void read(T &x) {
        long long v;
        read(v);
        x = T(v);
    }

    template<class Head, class Next, class... Tail>
    void read(Head &head, Next &next, Tail &...tail) {
        read(head);
        read(next, tail...);
    }

    template<class T, class U>
    void read(pair<T, U> &p) {
        read(p.first, p.second);
    }

    template<class T, typename enable_if<is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value, int>::type = 0>
    void read(T &a) {
        for (auto &x : a) read(x);
    }

    void read(char &c) {
        c = skip();
    }

    void read(string &s) {
        s.clear();
        if (interactive) {
            ensure_interactive();
            while (buf[idx] && buf[idx] <= ' ') {
                ++idx;
                ensure_interactive();
            }
            while (true) {
                int start = idx;
                while (idx < size && buf[idx] > ' ') ++idx;
                s.append(buf + start, idx - start);
                if (idx < size) break;
                load();
                if (size == 0) break;
            }
            if (idx < size) ++idx;
            return;
        }
        ensure();
        while (buf[idx] && buf[idx] <= ' ') {
            ++idx;
            ensure();
        }
        while (true) {
            int start = idx;
            while (idx < size && buf[idx] > ' ') ++idx;
            s.append(buf + start, idx - start);
            if (idx < size) break;
            load();
        }
        if (idx < size) ++idx;
    }
};

struct Printer {
    static constexpr int BUFSIZE = 1 << 17;
    static constexpr int OFFSET = 64;
    char buf[BUFSIZE];
    int idx;
    bool interactive;
    inline static constexpr FastIoDigitTable table{};

    Printer() : idx(0), interactive(isatty(fileno(stdout))) {}
    ~Printer() { flush(); }

    inline void flush() {
        if (idx) {
            fwrite(buf, 1, idx, stdout);
            idx = 0;
        }
    }

    inline void pc(char c) {
        if (idx > BUFSIZE - OFFSET) flush();
        buf[idx++] = c;
        if (interactive && c == '\n') flush();
    }

    inline void print_range(const char *s, size_t n) {
        size_t pos = 0;
        while (pos < n) {
            if (idx == BUFSIZE) flush();
            size_t chunk = min(n - pos, (size_t)(BUFSIZE - idx));
            memcpy(buf + idx, s + pos, chunk);
            idx += (int)chunk;
            pos += chunk;
        }
    }

    void print(const char *s) {
        print_range(s, strlen(s));
    }

    void print(const string &s) {
        print_range(s.data(), s.size());
    }

    void print(char c) {
        pc(c);
    }

    void print(bool b) {
        pc(char('0' + (b ? 1 : 0)));
    }

    template<class T, typename enable_if<is_integral<T>::value && !is_same<T, bool>::value, int>::type = 0>
    void print(T x) {
        if (idx > BUFSIZE - 100) flush();
        using U = typename make_unsigned<T>::type;
        U y;
        if constexpr (is_signed<T>::value) {
            if (x < 0) {
                buf[idx++] = '-';
                y = U(0) - static_cast<U>(x);
            } else {
                y = static_cast<U>(x);
            }
        } else {
            y = x;
        }
        if (y == 0) {
            buf[idx++] = '0';
            return;
        }
        static constexpr int TMP_SIZE = sizeof(U) * 10 / 4;
        char tmp[TMP_SIZE];
        int pos = TMP_SIZE;
        while (y >= 10000) {
            pos -= 4;
            memcpy(tmp + pos, table.num + (y % 10000) * 4, 4);
            y /= 10000;
        }
        if (y >= 1000) {
            memcpy(buf + idx, table.num + (y << 2), 4);
            idx += 4;
        } else if (y >= 100) {
            memcpy(buf + idx, table.num + (y << 2) + 1, 3);
            idx += 3;
        } else if (y >= 10) {
            unsigned q = (unsigned(y) * 205) >> 11;
            buf[idx] = char('0' + q);
            buf[idx + 1] = char('0' + (unsigned(y) - q * 10));
            idx += 2;
        } else {
            buf[idx++] = char('0' + y);
        }
        memcpy(buf + idx, tmp + pos, TMP_SIZE - pos);
        idx += TMP_SIZE - pos;
    }

    template<class T, typename enable_if<!is_integral<T>::value && !is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value && has_fastio_value<T>::value, int>::type = 0>
    void print(const T &x) {
        print(x.value());
    }

    template<class T, typename enable_if<is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value, int>::type = 0>
    void print(const T &a) {
        bool first = true;
        for (auto &&x : a) {
            if (!first) pc(' ');
            first = false;
            print(x);
        }
    }

    template<class T>
    void println(const T &x) {
        print(x);
        pc('\n');
    }

    template<class Head, class... Tail>
    void println(const Head &head, const Tail &...tail) {
        print(head);
        ((pc(' '), print(tail)), ...);
        pc('\n');
    }

    void println() {
        pc('\n');
    }
};

template<class T>
Scanner &operator>>(Scanner &in, T &x) {
    in.read(x);
    return in;
}

template<class T>
Printer &operator<<(Printer &out, const T &x) {
    out.print(x);
    return out;
}

/**
 * @brief 高速入出力(Fast IO)
 */
#line 1 "datastructure/sparsetable.cpp"
template <class F>
struct SparseTable {
    using T = typename F::T;
    vector<vector<T>> table;
    vector<int> u;
    SparseTable() = default;
    explicit SparseTable(const vector<T> &v){ build(v); }
 
    void build(const vector<T> &v){
        int n = v.size(), m = 1;
        while((1<<m) <= n) m++;
        table.assign(m, vector<T>(n));
        u.assign(n+1, 0);
        for (int i = 2; i <= n; ++i) {
            u[i] = u[i>>1] + 1;
        }
        for (int i = 0; i < n; ++i) {
            table[0][i] = v[i];
        }
        for (int i = 1; i < m; ++i) {
            int x = (1<<(i-1));
            for (int j = 0; j < n; ++j) {
                table[i][j] = F::f(table[i-1][j], table[i-1][min(j+x, n-1)]);
            }
        }
    }
 
    T query(int a, int b){
        int l = b-a;
        return F::f(table[u[l]][a], table[u[l]][b-(1<<u[l])]);
    }
};

/**
 * @brief Sparse Table
 */
#line 2 "tree/auxtree.cpp"

struct F {
    using T = pair<int, int>;
    static T f(T a, T b) { return min(a, b); }
    static T e() { return T{INF<int>, -1}; }
};

class AuxTree {
    SparseTable<F> table;
    void dfs_euler(int v, int p, int d, int &k, int &l){
        id[v] = k;
        vs[k] = v;
        depth[k++] = d;
        dep[v] = d;
        fi[v] = l++;
        for (auto &&u : G[v]) {
            if(u != p){
                dfs_euler(u, v, d+1, k, l);
                vs[k] = v;
                depth[k++] = d;
            }
        }
    }
public:
    int n;
    vector<vector<int>> G, out;
    vector<int> vs, depth, dep, id, fi;
    explicit AuxTree(int n) : table(), n(n), G(n), out(n), vs(2*n-1), depth(2*n-1), dep(n), id(n), fi(n) {};
    void add_edge(int a, int b){
        G[a].emplace_back(b);
        G[b].emplace_back(a);
    }

    void eulertour(int root) {
        int k = 0, l = 0;
        dfs_euler(root, -1, 0, k, l);
    }

    void buildLCA(int root = 0){
        eulertour(root);
        vector<pair<int, int>> v(2*n-1);
        for (int i = 0; i < 2*n-1; ++i) {
            v[i] = make_pair(depth[i], vs[i]);
        }
        table.build(v);
    }

    void make(vector<int> &v){
        sort(v.begin(),v.end(), [&](int a, int b){ return fi[a] < fi[b]; });
        v.erase(unique(v.begin(), v.end()), v.end());
        int k = v.size();
        stack<int> s;
        s.emplace(v.front());
        for (int i = 0; i+1 < k; ++i) {
            int w = LCA(v[i], v[i+1]);
            if(w != v[i]){
                int u = s.top(); s.pop();
                while(!s.empty() && dep[w] < dep[s.top()]){
                    out[s.top()].emplace_back(u);
                    out[u].emplace_back(s.top());
                    u = s.top(); s.pop();
                }
                if(s.empty() || s.top() != w){
                    s.emplace(w);
                    v.emplace_back(w);
                }
                out[w].emplace_back(u);
                out[u].emplace_back(w);
            }
            s.emplace(v[i+1]);
        }
        while(s.size() > 1){
            int u = s.top(); s.pop();
            out[s.top()].emplace_back(u);
            out[u].emplace_back(s.top());
        }
    }

    void clear(vector<int> &v){
        for (auto &&i : v) {
            out[i].clear();
            out[i].shrink_to_fit();
        }
    }

    int LCA(int u, int v){
        if(id[u] > id[v]) swap(u, v);
        return table.query(id[u], id[v]+1).second;
    }

    int distance(int u, int v){
        return dep[u]+dep[v]-2*dep[LCA(u, v)];
    }
};

/**
 * @brief 補助木(Aux Tree)
 */
#line 2 "tree/virtual_tree_helper.cpp"

struct VirtualTree {
    int root;
    vector<int> vertices;
    vector<int> parent;
};

class VirtualTreeHelper {
    AuxTree aux;
    vector<int> mark, parent_buf;
    int stamp = 0;

public:
    explicit VirtualTreeHelper(int n) : aux(n), mark(n, 0), parent_buf(n, -1) {}

    void add_edge(int u, int v) {
        aux.add_edge(u, v);
    }

    void build(int root = 0) {
        aux.buildLCA(root);
    }

    int lca(int u, int v) {
        return aux.LCA(u, v);
    }

    int distance(int u, int v) {
        return aux.distance(u, v);
    }

    VirtualTree make(vector<int> vertices) {
        aux.make(vertices);
        sort(vertices.begin(), vertices.end(), [&](int a, int b) { return aux.fi[a] < aux.fi[b]; });
        vertices.erase(unique(vertices.begin(), vertices.end()), vertices.end());

        VirtualTree res;
        res.root = vertices.front();
        ++stamp;
        vector<int> st = {res.root};
        mark[res.root] = stamp;
        parent_buf[res.root] = -1;

        while (!st.empty()) {
            int v = st.back();
            st.pop_back();
            res.vertices.emplace_back(v);
            res.parent.emplace_back(parent_buf[v]);
            for (auto &&u : aux.out[v]) {
                if (mark[u] == stamp) continue;
                mark[u] = stamp;
                parent_buf[u] = v;
                st.emplace_back(u);
            }
        }

        aux.clear(vertices);
        return res;
    }
};

/**
 * @brief Virtual Tree Helper
 */
#line 20 "test/aoj0439_virtual_tree_helper.test.cpp"

template <typename T>
using GPQ = priority_queue<T, vector<T>, greater<T>>;

int main() {
    Scanner sc;
    Printer pr;

    int n;
    sc.read(n);
    vector<vector<int>> color(n);
    VirtualTreeHelper vt(n);
    for (int i = 0; i < n; ++i) {
        int x;
        sc.read(x);
        color[x - 1].emplace_back(i);
    }
    for (int i = 0; i < n - 1; ++i) {
        int u, v;
        sc.read(u, v);
        --u;
        --v;
        vt.add_edge(u, v);
    }
    vt.build();

    vector<int> ans(n, INF<int>);
    vector<int> cmp(n), dist(n);
    vector<vector<int>> g(n);
    vector<int> is_target(n, 0);
    for (auto &&vs : color) {
        if (vs.empty()) continue;
        for (int v : vs) is_target[v] = 1;
        auto tree = vt.make(vs);
        for (int v : tree.vertices) g[v].clear();
        for (int i = 1; i < (int)tree.vertices.size(); ++i) {
            int v = tree.vertices[i];
            int p = tree.parent[i];
            g[v].emplace_back(p);
            g[p].emplace_back(v);
        }

        GPQ<pair<int, int>> q;
        for (int i = 0; i < (int)tree.vertices.size(); ++i) {
            int v = tree.vertices[i];
            if (is_target[v]) {
                dist[v] = 0;
                cmp[v] = v;
                q.emplace(0, v);
            } else {
                dist[v] = INF<int>;
            }
        }
        while (!q.empty()) {
            auto [d, v] = q.top();
            q.pop();
            if (d != dist[v]) continue;
            for (auto &&u : g[v]) {
                if (dist[u] > dist[v] + vt.distance(v, u)) {
                    dist[u] = dist[v] + vt.distance(v, u);
                    cmp[u] = cmp[v];
                    q.emplace(dist[u], u);
                }
            }
        }
        for (int v : tree.vertices) {
            for (auto &&u : g[v]) {
                int a = cmp[v], b = cmp[u];
                if (a != b) ans[a] = min(ans[a], vt.distance(a, b));
            }
        }
        for (int v : vs) is_target[v] = 0;
    }

    for (auto &&x : ans) pr.println(x);
    return 0;
}

Back to top page