結果

問題 No.1797 永遠のグリッド
ユーザー hitonanodehitonanode
提出日時 2022-01-01 21:22:04
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 8,261 bytes
コンパイル時間 2,064 ms
コンパイル使用メモリ 182,024 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-10-10 14:55:24
合計ジャッジ時間 3,076 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
このコードへのチャレンジ
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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
5,248 KB
testcase_01 AC 3 ms
5,248 KB
testcase_02 AC 2 ms
5,248 KB
testcase_03 AC 2 ms
5,248 KB
testcase_04 AC 1 ms
5,248 KB
testcase_05 AC 1 ms
5,248 KB
testcase_06 AC 2 ms
5,248 KB
testcase_07 AC 2 ms
5,248 KB
testcase_08 AC 2 ms
5,248 KB
testcase_09 AC 2 ms
5,248 KB
testcase_10 AC 2 ms
5,248 KB
testcase_11 AC 2 ms
5,248 KB
testcase_12 AC 1 ms
5,248 KB
testcase_13 AC 2 ms
5,248 KB
testcase_14 AC 2 ms
5,248 KB
testcase_15 AC 2 ms
5,248 KB
testcase_16 AC 2 ms
5,248 KB
testcase_17 AC 1 ms
5,248 KB
testcase_18 AC 2 ms
5,248 KB
testcase_19 AC 1 ms
5,248 KB
testcase_20 AC 2 ms
5,248 KB
testcase_21 AC 1 ms
5,248 KB
testcase_22 AC 2 ms
5,248 KB
testcase_23 AC 2 ms
5,248 KB
testcase_24 AC 2 ms
5,248 KB
testcase_25 AC 2 ms
5,248 KB
testcase_26 AC 2 ms
5,248 KB
testcase_27 AC 2 ms
5,248 KB
testcase_28 AC 2 ms
5,248 KB
testcase_29 AC 2 ms
5,248 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif

struct GridUnionFind {
    int H, W;
    std::vector<int> par, cou;
    using P = std::pair<int, int>;
    GridUnionFind(int H_, int W_) : H(H_), W(W_), par(H * W), cou(H * W, 1) {
        std::iota(par.begin(), par.end(), 0);
    }
    inline int id_(int h, int w) { return h * W + w; }
    inline bool coordinate_valid(int h, int w) { return h >= 0 and h < H and w >= 0 and w < W; }
    int _find(int x) { return (par[x] == x) ? x : (par[x] = _find(par[x])); }
    bool _unite(int x, int y) {
        x = _find(x), y = _find(y);
        if (x == y) return false;
        if (cou[x] < cou[y]) std::swap(x, y);
        par[y] = x, cou[x] += cou[y];
        return true;
    }
    int find(int h, int w) {
        assert(coordinate_valid(h, w));
        return _find(id_(h, w));
    }
    bool unite(int h, int w, int h2, int w2) {
        assert(coordinate_valid(h, w) and coordinate_valid(h2, w2));
        return _unite(id_(h, w), id_(h2, w2));
    }
    int count(int h, int w) { return cou[find(h, w)]; }
    bool same(int h, int w, int h2, int w2) { return find(h, w) == find(h2, w2); }

    int find(P p) { return find(p.first, p.second); }
    bool unite(P p, P p2) { return unite(p.first, p.second, p2.first, p2.second); }
    int count(P p) { return count(p.first, p.second); }
    bool same(P p, P p2) { return same(p.first, p.second, p2.first, p2.second); }

    void merge_outer() {
        for (int h = 0; h < H - 1; h++) unite(h, 0, h + 1, 0), unite(h, W - 1, h + 1, W - 1);
        for (int w = 0; w < W - 1; w++) unite(0, w, 0, w + 1), unite(H - 1, w, H - 1, w + 1);
    }
    template <typename OStream> friend OStream &operator<<(OStream &os, GridUnionFind &g) {
        constexpr int WW = 3;
        os << "[(" << g.H << " * " << g.W << " grid)\n";
        for (int i = 0; i < g.H; i++) {
            for (int j = 0; j < g.W - 1; j++) {
                os << std::setw(WW) << g.find(i, j) << (g.same(i, j, i, j + 1) ? '-' : ' ');
            }
            os << std::setw(WW) << g.find(i, g.W - 1) << '\n';
            if (i < g.H - 1) {
                for (int j = 0; j < g.W; j++)
                    os << std::setw(WW + 1) << (g.same(i, j, i + 1, j) ? "| " : "  ");
                os << "\n";
            }
        }
        os << "]\n";
        return os;
    }
};


lint solve(int H, int W, int K) {
    lint ret = 0;
    REP(dx, H) REP(dy, W) {
        GridUnionFind uf(H, W);
        REP(i, H) REP(j, W) {
            uf.unite(i, j, (i + dx) % H, (j + dy) % W);
        }
        vector<int> roots;
        REP(i, H) REP(j, W) {
            roots.push_back(uf.find(i, j));
        }
        roots = sort_unique(roots);
        dbg((vector<int>{dx, dy, int(roots.size())}));
        lint t = 1;
        for (auto _ : roots) t *= K;
        ret += t;
    }
    return ret / (H * W);
}

int main() {
    int H, W, K;
    cin >> H >> W >> K;
    if (K == 1) {
        puts("1");
    } else if (K == 2) {
        cout << solve(H, W, K) - 2 << endl;
    } else {
        cout << solve(H, W, 3) - solve(H, W, 2) * 3 + 3 << endl;
    }
}
0