Submission #680116

#	Time	Username	Problem	Language	Result	Execution time	Memory
680116		badont	Osmosmjerka (COCI17_osmosmjerka)	C++17	140 / 160	1234 ms	44748 KiB

osmosmjerka

#include<bits/stdc++.h>
using namespace std;

void dbg_out() { cout << endl; }
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cout << ' ' << H; dbg_out(T...); }

#ifdef LOCAL
#define debug(...) cout << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define debug(...) "zzz"
#endif

using LL = long long;
using LD = long double;
using pii = pair<LL,LL>;

#define FOR(i, n) for(int i = 1; i<=n; i++)
#define F0R(i, n) for(int i = 0; i<n; i++)
#define all(x) x.begin(), x.end()
#define mp make_pair
#define pb push_back
#define f first
#define s second

template<typename T, typename = void> struct is_iterable : false_type {};
template<typename T> struct is_iterable<T, void_t<decltype(begin(declval<T>())),decltype(end(declval<T>()))>> : true_type {};
template<typename T> typename enable_if<is_iterable<T>::value&&!is_same<T, string>::value,ostream&>::type operator<<(ostream &cout, T const &v);
template<typename A, typename B> ostream& operator<<(ostream &cout, pair<A, B> const &p) { return cout << "(" << p.f << ", " << p.s << ")"; }
template<typename T> typename enable_if<is_iterable<T>::value&&!is_same<T, string>::value,ostream&>::type operator<<(ostream &cout, T const &v) {
	cout << "["; 
	for (auto it = v.begin(); it != v.end();) {
		cout << *it;
		if (++it != v.end()) cout << ", ";
	}
	return cout << "]";
}

using hash_t = uint64_t;
template<const unsigned &MOD>
struct _m_uint {
    unsigned val;

    _m_uint(int64_t v = 0) {
        if (v < 0) v = v % MOD + MOD;
        if (v >= MOD) v %= MOD;
        val = unsigned(v);
    }

    _m_uint(uint64_t v) {
        if (v >= MOD) v %= MOD;
        val = unsigned(v);
    }

    _m_uint(int v) : _m_uint(int64_t(v)) {}
    _m_uint(unsigned v) : _m_uint(uint64_t(v)) {}

    explicit operator unsigned() const { return val; }
    explicit operator int64_t() const { return val; }
    explicit operator uint64_t() const { return val; }
    explicit operator double() const { return val; }
    explicit operator long double() const { return val; }

    _m_uint& operator+=(const _m_uint &other) {
        val = val < MOD - other.val ? val + other.val : val - (MOD - other.val);
        return *this;
    }

    _m_uint& operator-=(const _m_uint &other) {
        val = val < other.val ? val + (MOD - other.val) : val - other.val;
        return *this;
    }

    static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
#if !defined(_WIN32) || defined(_WIN64)
        return unsigned(x % m);
#endif
        // Optimized mod for Codeforces 32-bit machines.
        // x must be less than 2^32 * m for this to work, so that x / m fits in an unsigned 32-bit int.
        unsigned x_high = unsigned(x >> 32), x_low = unsigned(x);
        unsigned quot, rem;
        asm("divl %4\n"
            : "=a" (quot), "=d" (rem)
            : "d" (x_high), "a" (x_low), "r" (m));
        return rem;
    }

    _m_uint& operator*=(const _m_uint &other) {
        val = fast_mod(uint64_t(val) * other.val);
        return *this;
    }

    _m_uint& operator/=(const _m_uint &other) {
        return *this *= other.inv();
    }

    friend _m_uint operator+(const _m_uint &a, const _m_uint &b) { return _m_uint(a) += b; }
    friend _m_uint operator-(const _m_uint &a, const _m_uint &b) { return _m_uint(a) -= b; }
    friend _m_uint operator*(const _m_uint &a, const _m_uint &b) { return _m_uint(a) *= b; }
    friend _m_uint operator/(const _m_uint &a, const _m_uint &b) { return _m_uint(a) /= b; }

    _m_uint& operator++() {
        val = val == MOD - 1 ? 0 : val + 1;
        return *this;
    }

    _m_uint& operator--() {
        val = val == 0 ? MOD - 1 : val - 1;
        return *this;
    }

    _m_uint operator++(int) { _m_uint before = *this; ++*this; return before; }
    _m_uint operator--(int) { _m_uint before = *this; --*this; return before; }

    _m_uint operator-() const {
        return val == 0 ? 0 : MOD - val;
    }

    friend bool operator==(const _m_uint &a, const _m_uint &b) { return a.val == b.val; }
    friend bool operator!=(const _m_uint &a, const _m_uint &b) { return a.val != b.val; }
    friend bool operator<(const _m_uint &a, const _m_uint &b) { return a.val < b.val; }
    friend bool operator>(const _m_uint &a, const _m_uint &b) { return a.val > b.val; }
    friend bool operator<=(const _m_uint &a, const _m_uint &b) { return a.val <= b.val; }
    friend bool operator>=(const _m_uint &a, const _m_uint &b) { return a.val >= b.val; }

    static const int SAVE_INV = int(1e6) + 5;
    static _m_uint save_inv[SAVE_INV];

    static void prepare_inv() {
        // Ensures that MOD is prime, which is necessary for the inverse algorithm below.
        for (int64_t p = 2; p * p <= MOD; p += p % 2 + 1)
            assert(MOD % p != 0);

        save_inv[0] = 0;
        save_inv[1] = 1;

        for (int i = 2; i < SAVE_INV; i++)
            save_inv[i] = save_inv[MOD % i] * (MOD - MOD / i);
    }

    _m_uint inv() const {
        if (save_inv[1] == 0)
            prepare_inv();

        if (val < SAVE_INV)
            return save_inv[val];

        _m_uint product = 1;
        unsigned v = val;

        do {
            product *= MOD - MOD / v;
            v = MOD % v;
        } while (v >= SAVE_INV);

        return product * save_inv[v];
    }

    _m_uint pow(int64_t p) const {
        if (p < 0)
            return inv().pow(-p);

        _m_uint a = *this, result = 1;

        while (p > 0) {
            if (p & 1)
                result *= a;

            p >>= 1;

            if (p > 0)
                a *= a;
        }

        return result;
    }

    friend ostream& operator<<(ostream &os, const _m_uint &m) {
        return os << m.val;
    }
};

template<const unsigned &MOD> _m_uint<MOD> _m_uint<MOD>::save_inv[_m_uint<MOD>::SAVE_INV];

uint64_t random_address() { char *p = new char; delete p; return uint64_t(p); }
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count() * (random_address() | 1));

// P = 2^32 - 13337 is a safe prime: both P and (P - 1) / 2 are prime.
const unsigned HASH_P = unsigned(-13337);
using hash_int = _m_uint<HASH_P>;

const uint64_t HASH_P2 = uint64_t(HASH_P) * HASH_P;
const int HASH_COUNT = 2;

// Avoid multiplication bases near 0 or P - 1.
uniform_int_distribution<unsigned> MULT_DIST(unsigned(0.1 * HASH_P), unsigned(0.9 * HASH_P));
const hash_int HASH_MULT[] = {MULT_DIST(rng), MULT_DIST(rng)};
const hash_int HASH_INV[] = {1 / HASH_MULT[0], 1 / HASH_MULT[1]};

vector<hash_int> hash_pow[] = {{1}, {1}};

const int INF = int(1e9) + 5;

template<typename T_string = string>
struct string_hash {
    // TODO: decide whether BUILD_REVERSE = true is needed.
    static const bool BUILD_REVERSE = true;

    static uint64_t hash(const T_string &str) {
        uint64_t result = 0;

        for (int h = 0; h < HASH_COUNT; h++) {
            uint64_t value = 1;

            for (const auto &x : str)
                value = (uint64_t(HASH_MULT[h]) * value + x) % HASH_P;

            result += value << (32 * h);
        }

        return result;
    }

    T_string str;
    vector<hash_int> _prefix[HASH_COUNT];
    vector<hash_int> _inv_prefix[HASH_COUNT];

    string_hash() {
        build({});
    }

    string_hash(const T_string &_str) {
        build(_str);
    }

    int length() const {
        return int(_prefix[0].size()) - 1;
    }

    template<typename T_char>
    void add_char(const T_char &c) {
        str.push_back(c);

        for (int h = 0; h < HASH_COUNT; h++) {
            _prefix[h].push_back(HASH_MULT[h] * _prefix[h].back() + c);

            if (hash_pow[h].size() < _prefix[h].size())
                hash_pow[h].push_back(HASH_MULT[h] * hash_pow[h].back());

            if (BUILD_REVERSE)
                _inv_prefix[h].push_back((_inv_prefix[h].back() + c) * HASH_INV[h]);
        }
    }

    void pop_char() {
        str.pop_back();

        for (int h = 0; h < HASH_COUNT; h++) {
            _prefix[h].pop_back();

            if (BUILD_REVERSE)
                _inv_prefix[h].pop_back();
        }
    }

    void build(const T_string &_str) {
        str = {};
        str.reserve(_str.size());

        for (int h = 0; h < HASH_COUNT; h++) {
            hash_pow[h].reserve(_str.size() + 1);
            _prefix[h] = {0};
            _prefix[h].reserve(_str.size() + 1);

            if (BUILD_REVERSE) {
                _inv_prefix[h] = {0};
                _inv_prefix[h].reserve(_str.size() + 1);
            }
        }

        for (auto &c : _str)
            add_char(c);
    }

    uint64_t _single_hash(int h, int start, int end) const {
        // Convert everything to `uint64_t` for speed. Note: we add hash_pow[length] to fix strings that start with 0.
        uint64_t power = uint64_t(hash_pow[h][end - start]);
        return (power + uint64_t(_prefix[h][end]) + HASH_P2 - uint64_t(_prefix[h][start]) * power) % HASH_P;
    }

    uint64_t substring_hash(int start, int end) const {
        assert(0 <= start && start <= end && end <= length());
        return _single_hash(0, start, end) + (HASH_COUNT > 1 ? _single_hash(1, start, end) << 32 : 0);
    }

    uint64_t complete_hash() const {
        return substring_hash(0, length());
    }

    uint64_t _reverse_single_hash(int h, int start, int end) const {
        // Convert everything to `uint64_t` for speed. Note: we add hash_pow[length] to fix strings that start with 0.
        uint64_t power = uint64_t(hash_pow[h][end - start]);
        return (power + uint64_t(_inv_prefix[h][end]) * power + HASH_P - uint64_t(_inv_prefix[h][start])) % HASH_P;
    }

    uint64_t reverse_substring_hash(int start, int end) const {
        assert(0 <= start && start <= end && end <= length());
        return _reverse_single_hash(0, start, end) + (HASH_COUNT > 1 ? _reverse_single_hash(1, start, end) << 32 : 0);
    }

    uint64_t reverse_complete_hash() const {
        return reverse_substring_hash(0, length());
    }

    bool equal(int start1, int start2, int length) const {
        return substring_hash(start1, start1 + length) == substring_hash(start2, start2 + length);
    }

    bool is_palindrome(int start, int end) const {
        return substring_hash(start, end) == reverse_substring_hash(start, end);
    }

    int compare(int start1, int start2, int max_length = INF) const;
};

uint64_t concat_hashes(uint64_t hash1, uint64_t hash2, int len2) {
    if (len2 == 0) return hash1;
    uint64_t hash1_low = hash1 & unsigned(-1);
    uint64_t hash2_low = hash2 & unsigned(-1);
    uint64_t power = uint64_t(hash_pow[0][len2]);
    uint64_t combined = (hash1_low * power + hash2_low + HASH_P - power) % HASH_P;

    if (HASH_COUNT > 1) {
        hash1 >>= 32;
        hash2 >>= 32;
        power = uint64_t(hash_pow[1][len2]);
        combined += (hash1 * power + hash2 + HASH_P - power) % HASH_P << 32;
    }

    return combined;
}

template<typename T_string>
int first_mismatch(const string_hash<T_string> &hash1, int start1,
                   const string_hash<T_string> &hash2, int start2, int max_length = INF) {
    max_length = min({max_length, hash1.length() - start1, hash2.length() - start2});

    static const int FIRST = 5;
    int first = min(max_length, FIRST);

    for (int i = 0; i < first; i++)
        if (hash1.str[start1 + i] != hash2.str[start2 + i])
            return i;

    if (hash1.substring_hash(start1, start1 + max_length) == hash2.substring_hash(start2, start2 + max_length))
        return max_length;

    static const int MANUAL = 15;
    int low = first, high = max_length - 1;

    while (high - low > MANUAL) {
        int mid = (low + high + 1) / 2;

        if (hash1.substring_hash(start1, start1 + mid) == hash2.substring_hash(start2, start2 + mid))
            low = mid;
        else
            high = mid - 1;
    }

    for (int i = low; i < high; i++)
        if (hash1.str[start1 + i] != hash2.str[start2 + i])
            return i;

    return high;
}

template<typename T_string>
int hash_compare(const string_hash<T_string> &hash1, int start1,
                 const string_hash<T_string> &hash2, int start2, int max_length = INF) {
    int mismatch = first_mismatch(hash1, start1, hash2, start2, max_length);
    int length1 = min(hash1.length() - start1, max_length);
    int length2 = min(hash2.length() - start2, max_length);

    if (mismatch == min(length1, length2))
        return length1 == length2 ? 0 : (length1 < length2 ? -1 : +1);

    if (hash1.str[start1 + mismatch] == hash2.str[start2 + mismatch])
        return 0;

    return hash1.str[start1 + mismatch] < hash2.str[start2 + mismatch] ? -1 : +1;
}

template<typename T_string>
int string_hash<T_string>::compare(int start1, int start2, int max_length) const {
    return hash_compare(*this, start1, *this, start2, max_length);
}

#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;

//var 
const array<int, 8> dx = {-1,0,1,-1,1,-1,0,1};
const array<int, 8> dy = {-1,-1,-1,0,0,1,1,1};
LL T;

void solve() {
	LL n, m, k;
	cin >> n >> m >> k;

	k = min(k, lcm(n, m));
	while (k%n || k%m) k++;

	LL cnt = n * m * 8;
	vector a(n, vector<char>(m));
	for (auto& row : a) {
		for (auto& elem : row) 
			cin >> elem;
	}

	gp_hash_table<hash_t, LL> dp;

	auto process = [&](string s, int howMany) -> void {
		if (s.empty()) return;
		//debug(s);
		//debug(howMany, k);
		string_hash hasher(s);
		F0R (j, howMany) {
			dp[hasher.substring_hash(j, j + k)]++;
		}
		for (int j = 2 * k - 1, seen = 0; seen<howMany; j--, seen++)
			dp[hasher.reverse_substring_hash(j - k + 1, j + 1)]++;
	};


	F0R (i, n) {
		string s = "", os ="";
		F0R (j, m) os += a[i][j];
		while ((int)s.size() < k)
			s += os;
		s += s;
		process(s, m);
	}

	F0R (i, m) {
		string s = "", os = "";
		F0R (j, n) os += a[j][i];
		while ((int)s.size() < k)
			s += os;
		s += s;
		process(s, n);
		//debug(s);
	}

	vector v(n, vector<bool>(m));
	F0R (j, m) if (!v[0][j]) {
		string s = "", os = "";
		int cx = 0, cy = j;
		int how = 0;
		while (!v[cx][cy]) {
			v[cx][cy] = 1;
			os += a[cx][cy];
			cx = (cx + 1) % n;
			cy = (cy + 1) % m;
			how++;
		}
		//debug(os);
		if ((int)os.size()) while ((int)s.size() < k) s += os;
		s += s;
		process(s, how);
	}
	F0R (i, n) F0R (j, m) v[i][j] = 0;

	F0R (j, m) if (!v[0][j]){
		string s = "", os = "";
		int cx = 0, cy = j;
		int how = 0;
		while (!v[cx][cy]) {
			v[cx][cy] = 1;
			os += a[cx][cy];
			cx = (cx + 1) % n;
			cy = (cy - 1 + m) % m;
			how++;
		}
		if (!os.empty()) while ((int)s.size() < k) s += os;
		s += s;
		process(s, how);
	}

	LL numer = 0;
	//debug(dp);
	for (auto [hash, cnt] : dp) {
		numer += cnt * cnt;
	}

	LL denom = cnt * cnt;

	LL g = gcd(numer, denom);
	numer /= g;
	denom /= g;

	cout << numer << "/" << denom << '\n';



}

int main() {
	ios_base::sync_with_stdio(0); 
	cin.tie(0);

	T = 1;
	//cin >> T;
	FOR(t, T)
		solve();

	cout.flush();
	return 0;
}

• Subtask 1: 140 / 160