library_for_cpp

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:heavy_check_mark: verify/original/Functional_Graph.test.cpp

Depends on

Code

#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A"

#include"../../../library_for_cpp/template/template.hpp"
#include"../../../library_for_cpp/Functional_Graph/Functional_Graph.hpp"

void verify() {
    vector<int> f = {77, 0, 39, 33, 1, 87, 20, 88, 75, 49, 58, 48, 78, 24, 60, 90, 26, 55, 31, 7, 18, 14, 77, 25, 75, 89, 99, 44, 72, 92, 64, 33, 91, 64, 19, 14, 37, 7, 0, 26, 35, 0, 45, 3, 89, 29, 16, 12, 53, 17, 8, 91, 97, 60, 65, 42, 3, 4, 48, 72, 57, 61, 74, 75, 2, 76, 67, 21, 91, 15, 52, 97, 13, 12, 60, 41, 81, 79, 41, 12, 64, 65, 48, 14, 82, 45, 85, 87, 7, 59, 27, 15, 0, 37, 15, 36, 38, 11, 51, 16};

    Functional_Graph F(f);

    int n = 100, k_max = 100000;
    for (int v = 0; v < n; v++) {
        int w = v;
        for (int k = 0; k <= k_max; k++) {
            if (F.calculate(v, k) == w) {
                w = f[w];
                continue;
            } 

            cerr << "Error" << endl;
            cerr << "v = " << v << ", k = " << k << endl;
            cerr << "expect: " << w << endl;
            cerr << "returns: " << F.calculate(v, k) << endl;
            assert(false);
        }
    }
}

int main() {
    verify();
    cout << "Hello World" << endl;
}
#line 1 "verify/original/Functional_Graph.test.cpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A"

#line 2 "template/template.hpp"

using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <concepts>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
#line 2 "template/utility.hpp"

using ll = long long;

// a ← max(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmax(T &a, const U b){
    return (a < b ? a = b, 1: 0);
}

// a ← min(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmin(T &a, const U b){
    return (a > b ? a = b, 1: 0);
}

// a の最大値を取得する.
template<typename T>
inline T max(const vector<T> &a){
    if (a.empty()) throw invalid_argument("vector is empty.");

    return *max_element(a.begin(), a.end());
}

// vector<T> a の最小値を取得する.
template<typename T>
inline T min(const vector<T> &a){
    if (a.empty()) throw invalid_argument("vector is empty.");

    return *min_element(a.begin(), a.end());
}

// vector<T> a の最大値のインデックスを取得する.
template<typename T>
inline size_t argmax(const vector<T> &a){
    if (a.empty()) throw std::invalid_argument("vector is empty.");

    return distance(a.begin(), max_element(a.begin(), a.end()));
}

// vector<T> a の最小値のインデックスを取得する.
template<typename T>
inline size_t argmin(const vector<T> &a){
    if (a.empty()) throw invalid_argument("vector is empty.");

    return distance(a.begin(), min_element(a.begin(), a.end()));
}
#line 61 "template/template.hpp"

// math
#line 2 "template/math.hpp"

// 演算子
template<typename T>
T add(const T &x, const T &y) { return x + y; }

template<typename T>
T sub(const T &x, const T &y) { return x - y; }

template<typename T>
T mul(const T &x, const T &y) { return x * y; }

template<typename T>
T neg(const T &x) { return -x; }

template<integral T>
T bitwise_and(const T &x, const T &y) { return x & y; }

template<integral T>
T bitwise_or(const T &x, const T &y) { return x | y; }

template<integral T>
T bitwise_xor(const T &x, const T &y) { return x ^ y; }

// 除算に関する関数

// floor(x / y) を求める.
template<integral T, integral U>
auto div_floor(T x, U y){
    return x / y - ((x % y != 0) && ((x < 0) != (y < 0)));
}

// ceil(x / y) を求める.
template<integral T, integral U>
auto div_ceil(T x, U y){
    return x / y + ((x % y != 0) && ((x < 0) == (y < 0)));
}

// x を y で割った余りを求める.
template<integral T, integral U>
auto safe_mod(T x, U y){
    auto q = div_floor(x, y);
    return x - q * y ;
}

// x を y で割った商と余りを求める.
template<integral T, integral U>
auto divmod(T x, U y){
    auto q = div_floor(x, y);
    return make_pair(q, x - q * y);
}

// 四捨五入を求める.
template<integral T, integral U>
auto round(T x, U y){
    auto [q, r] = divmod(x, y);
    if (y < 0) return (r <= div_floor(y, 2)) ? q + 1 : q;
    return (r >= div_ceil(y, 2)) ? q + 1 : q;
}

// 奇数かどうか判定する.
template<integral T>
bool is_odd(const T &x) { return x % 2 != 0; }

// 偶数かどうか判定する.
template<integral T>
bool is_even(const T &x) { return x % 2 == 0; }

// m の倍数かどうか判定する.
template<integral T, integral U>
bool is_multiple(const T &x, const U &m) { return x % m == 0; }

// 正かどうか判定する.
template<typename T>
bool is_positive(const T &x) { return x > 0; }

// 負かどうか判定する.
template<typename T>
bool is_negative(const T &x) { return x < 0; }

// ゼロかどうか判定する.
template<typename T>
bool is_zero(const T &x) { return x == 0; }

// 非負かどうか判定する.
template<typename T>
bool is_non_negative(const T &x) { return x >= 0; }

// 非正かどうか判定する.
template<typename T>
bool is_non_positive(const T &x) { return x <= 0; }

// 指数に関する関数

// x の y 乗を求める.
ll intpow(ll x, ll y){
    ll a = 1;
    while (y){
        if (y & 1) { a *= x; }
        x *= x;
        y >>= 1;
    }
    return a;
}

// x の y 乗を z で割った余りを求める.
template<typename T, integral U>
T modpow(T x, U y, T z) {
    T a = 1;
    while (y) {
        if (y & 1) { (a *= x) %= z; }

        (x *= x) %= z;
        y >>= 1;
    }

    return a;
}

template<typename T>
T sum(const vector<T> &X) {
    T y = T(0);
    for (auto &&x: X) { y += x; }
    return y;
}

template<typename T>
T gcd(const T x, const T y) {
    return y == 0 ? x : gcd(y, x % y);
}

// a x + b y = gcd(a, b) を満たす整数の組 (a, b) に対して, (x, y, gcd(a, b)) を求める.
template<integral T>
tuple<T, T, T> Extended_Euclid(T a, T b) {
    T s = 1, t = 0, u = 0, v = 1;
    while (b) {
        auto [q, r] = divmod(a, b);
        a = b;
        b = r;
        tie(s, t) = make_pair(t, s - q * t);
        tie(u, v) = make_pair(v, u - q * v);
    }

    return make_tuple(s, u, a);
}

// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll isqrt(const ll &N) { 
    if (N <= 0) { return 0; }

    ll x = sqrtl(N);
    while ((x + 1) * (x + 1) <= N) { x++; }
    while (x * x > N) { x--; }

    return x;
}

// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll floor_sqrt(const ll &N) { return isqrt(N); }

// ceil(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll ceil_sqrt(const ll &N) {
    ll x = isqrt(N);
    return x * x == N ? x : x + 1;
}
#line 64 "template/template.hpp"

// inout
#line 1 "template/inout.hpp"
// 入出力
template<class... T>
void input(T&... a){ (cin >> ... >> a); }

void print(){ cout << "\n"; }

template<class T, class... Ts>
void print(const T& a, const Ts&... b){
    cout << a;
    (cout << ... << (cout << " ", b));
    cout << "\n";
}

template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &P){
    is >> P.first >> P.second;
    return is;
}

template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &P){
    os << P.first << " " << P.second;
    return os;
}

template<typename T>
vector<T> vector_input(int N, int index){
    vector<T> X(N+index);
    for (int i=index; i<index+N; i++) cin >> X[i];
    return X;
}

template<typename T>
istream &operator>>(istream &is, vector<T> &X){
    for (auto &x: X) { is >> x; }
    return is;
}

template<typename T>
ostream &operator<<(ostream &os, const vector<T> &X){
    int s = (int)X.size();
    for (int i = 0; i < s; i++) { os << (i ? " " : "") << X[i]; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &S){
    int i = 0;
    for (T a: S) {os << (i ? " ": "") << a; i++;}
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const set<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const multiset<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
std::vector<T> input_vector(size_t n, size_t offset = 0) {
    std::vector<T> res;
    // 最初に必要な全容量を確保（再確保を防ぐ）
    res.reserve(n + offset);
    // offset 分をデフォルト値で埋める（特別 indexed 用）
    res.assign(offset, T());
    
    for (size_t i = 0; i < n; ++i) {
        T el;
        if (!(std::cin >> el)) break;
        res.push_back(std::move(el));
    }
    return res;
}
#line 67 "template/template.hpp"

// macro
#line 2 "template/macro.hpp"

// マクロの定義
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define unless(cond) if (!(cond))
#define until(cond) while (!(cond))
#define loop while (true)

// オーバーロードマクロ
#define overload2(_1, _2, name, ...) name
#define overload3(_1, _2, _3, name, ...) name
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload5(_1, _2, _3, _4, _5, name, ...) name

// 繰り返し系
#define rep1(n) for (ll i = 0; i < n; i++)
#define rep2(i, n) for (ll i = 0; i < n; i++)
#define rep3(i, a, b) for (ll i = a; i < b; i++)
#define rep4(i, a, b, c) for (ll i = a; i < b; i += c)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define foreach1(x, a) for (auto &&x: a)
#define foreach2(x, y, a) for (auto &&[x, y]: a)
#define foreach3(x, y, z, a) for (auto &&[x, y, z]: a)
#define foreach4(x, y, z, w, a) for (auto &&[x, y, z, w]: a)
#define foreach(...) overload5(__VA_ARGS__, foreach4, foreach3, foreach2, foreach1)(__VA_ARGS__)
#line 70 "template/template.hpp"

// bitop
#line 2 "template/bitop.hpp"

// 非負整数 x の bit legnth を求める.
ll bit_length(ll x) {
    if (x == 0) { return 0; }
    return (sizeof(long) * CHAR_BIT) - __builtin_clzll(x);
}

// 非負整数 x の popcount を求める.
ll popcount(ll x) { return __builtin_popcountll(x); }

// 正の整数 x に対して, floor(log2(x)) を求める.
ll floor_log2(ll x) { return bit_length(x) - 1; }

// 正の整数 x に対して, ceil(log2(x)) を求める.
ll ceil_log2(ll x) { return bit_length(x - 1); }

// x の第 k ビットを取得する
int get_bit(ll x, int k) { return (x >> k) & 1; }

// x のビット列を取得する.
// k はビット列の長さとする.
vector<int> get_bits(ll x, int k) {
    vector<int> bits(k);
    rep(i, k) {
        bits[i] = x & 1;
        x >>= 1;
    }

    return bits;
}

// x のビット列を取得する.
vector<int> get_bits(ll x) { return get_bits(x, bit_length(x)); }
#line 73 "template/template.hpp"

// exception
#line 2 "template/exception.hpp"

class NotExist: public exception {
    private:
    string message;

    public:
    NotExist() : message("求めようとしていたものは存在しません.") {}

    const char* what() const noexcept override {
        return message.c_str();
    }
};
#line 2 "Functional_Graph/Functional_Graph.hpp"

class Functional_Graph {
    private:
    vector<int> f;
    vector<vector<int>> f_inv;
    int N;

    vector<vector<int>> cycles;
    vector<int> cycle_ids, cycle_vertex_ids;

    vector<int> tree_ids, tree_vertex_ids, tree_depth;
    vector<vector<int>> tree_vertices;
    vector<vector<vector<int>>> tree_doubling;

    public:
    Functional_Graph(const vector<int> &f): f(f), N(f.size()) {
        f_inv.resize(N);
        for (int x = 0; x < N; x++) { f_inv[f[x]].emplace_back(x); }
        build_up();
    }

    private:
    void build_up() {
        build_cycles();
        build_branches();
    }

    // サイクル検出パート
    void build_cycles() {
        vector<int> indegree(N);
        stack<int> st;
        for (int x = 0; x < N; x++) {
            indegree[x] = f_inv[x].size();
            if (indegree[x] == 0) { st.push(x); }
        }

        vector<bool> cycle_flag(N, true);

        while (!st.empty()) {
            int x = st.top();
            st.pop();

            cycle_flag[x] = false;
            indegree[f[x]]--;
            if (indegree[f[x]] == 0) { st.push(f[x]); }
        }

        cycles.clear();
        cycle_ids.assign(N, -1);
        cycle_vertex_ids.assign(N, -1);

        for (int x = 0; x < N; x++) {
            if (!cycle_flag[x]) { continue; }

            int cycle_id = cycles.size();

            vector<int> cycle{x};
            cycle_flag[x] = false;
            int y = f[x];
            while (y != x) {
                cycle.emplace_back(y);
                cycle_flag[y] = false;
                y = f[y];
            }

            cycles.emplace_back(cycle);
            for (int j = 0; j < cycle.size(); j++) {
                int y = cycle[j];
                cycle_ids[y] = cycle_id;
                cycle_vertex_ids[y] = j;
            }
        }
    }

    void build_branches() {
        tree_ids.assign(N, -1);
        tree_vertex_ids.assign(N, -1);
        tree_depth.assign(N, 0);

        for (int x = 0; x < N; x++) {
            if (cycle_ids[x] == -1) { continue; }

            int tree_id = tree_vertices.size();
            vector<int> tree_vertex{x};

            int vertex_id = 0;
            tree_ids[x] = tree_id;
            tree_vertex_ids[x] = vertex_id;

            stack<int> st;
            st.push(x);

            int max_depth = 0;

            while (!st.empty()) {
                int y = st.top(); st.pop();

                for (int z: f_inv[y]) {
                    if (cycle_ids[z] != -1) { continue; }

                    vertex_id++;
                    tree_ids[z] = tree_id;
                    tree_vertex_ids[z] = vertex_id;

                    tree_depth[z] = tree_depth[y] + 1;
                    chmax(max_depth, tree_depth[z]);

                    st.push(z);
                    tree_vertex.emplace_back(z);
                }
            }

            tree_vertices.emplace_back(tree_vertex);
            int m = tree_vertex.size();
            vector<vector<int>> doubling(max<int>(1, bit_length(max_depth)), vector<int>(m, -1));

            for (int j = 1; j < m; j++) {
                doubling[0][j] = tree_vertex_ids[f[tree_vertex[j]]];
            }

            for (int b = 1; b < max<int>(1, bit_length(max_depth)); b++) {
                for (int j = 0; j < m; j++) {
                    doubling[b][j] = doubling[b - 1][doubling[b - 1][j]];
                }
            }

            tree_doubling.emplace_back(doubling);
        }
    }

    int upper(int x, ll k) {
        int tree_id = tree_ids[x];
        int vertex_id = tree_vertex_ids[x];

        vector<vector<int>> doubling = tree_doubling[tree_id];
        for (int b = 0; k; k >>= 1, b++) {
            if (k & 1) { vertex_id = doubling[b][vertex_id]; }
        }

        return tree_vertices[tree_id][vertex_id];
    }

    int jump_on_cycle(int cycle_id, int vertex_id, ll k) {
        auto &cycle = cycles[cycle_id];
        int m = cycle.size();
        k = safe_mod(k, m);
        return cycle[(vertex_id + k) % m];
    }

    public:
    inline int root(int x) const { return tree_vertices[tree_ids[x]][0]; }

    int calculate(int x, ll k) {
        if ( k < tree_depth[x]) { return upper(x, k); }

        k -= tree_depth[x];
        x = root(x);

        int cycle_id = cycle_ids[x];
        int vertex_id = cycle_vertex_ids[x];
        return jump_on_cycle(cycle_id, vertex_id, k);
    }

    vector<vector<int>> &get_cycles() { return cycles; }
};
#line 5 "verify/original/Functional_Graph.test.cpp"

void verify() {
    vector<int> f = {77, 0, 39, 33, 1, 87, 20, 88, 75, 49, 58, 48, 78, 24, 60, 90, 26, 55, 31, 7, 18, 14, 77, 25, 75, 89, 99, 44, 72, 92, 64, 33, 91, 64, 19, 14, 37, 7, 0, 26, 35, 0, 45, 3, 89, 29, 16, 12, 53, 17, 8, 91, 97, 60, 65, 42, 3, 4, 48, 72, 57, 61, 74, 75, 2, 76, 67, 21, 91, 15, 52, 97, 13, 12, 60, 41, 81, 79, 41, 12, 64, 65, 48, 14, 82, 45, 85, 87, 7, 59, 27, 15, 0, 37, 15, 36, 38, 11, 51, 16};

    Functional_Graph F(f);

    int n = 100, k_max = 100000;
    for (int v = 0; v < n; v++) {
        int w = v;
        for (int k = 0; k <= k_max; k++) {
            if (F.calculate(v, k) == w) {
                w = f[w];
                continue;
            } 

            cerr << "Error" << endl;
            cerr << "v = " << v << ", k = " << k << endl;
            cerr << "expect: " << w << endl;
            cerr << "returns: " << F.calculate(v, k) << endl;
            assert(false);
        }
    }
}

int main() {
    verify();
    cout << "Hello World" << endl;
}
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