Submission #1335726

#TimeUsernameProblemLanguageResultExecution timeMemory
1335726mamabearLego Wall (EGOI22_legowall)C++20
50 / 100
3095 ms13216 KiB
#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

const int MOD = 1000000007;

long long power(long long base, long long exp) {
    long long res = 1;
    base %= MOD;
    while (exp > 0) {
        if (exp % 2 == 1) res = (res * base) % MOD;
        base = (base * base) % MOD;
        exp /= 2;
    }
    return res;
}

vector<long long> berlekamp_massey(const vector<long long>& s) {
    vector<long long> C = {1}, B = {1};
    int L = 0;
    long long m = 1;
    for (int i = 0; i < s.size(); i++) {
        long long d = 0;
        for (int j = 0; j <= L; j++) {
            d = (d + C[j] * s[i - j]) % MOD;
        }
        if (d == 0) {
            B.insert(B.begin(), 0);
            continue;
        }
        vector<long long> temp = C;
        long long c = (d * power(m, MOD - 2)) % MOD;
        while (C.size() <= B.size() + 1) C.push_back(0);
        for (int j = 0; j < B.size(); j++) {
            C[j + 1] = (C[j + 1] - c * B[j]) % MOD;
            if (C[j + 1] < 0) C[j + 1] += MOD;
        }
        if (2 * L <= i) {
            L = i + 1 - L;
            B = temp;
            m = d;
        } else {
            B.insert(B.begin(), 0);
        }
    }
    return C;
}

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

    int w, h;
    if (!(cin >> w >> h)) return 0;

    vector<long long> row(max(w, 2 * h + 5) + 1, 0);
    row[0] = 1;
    row[1] = 1;
    for (int i = 2; i < row.size(); i++) {
        row[i] = (row[i - 1] + row[i - 2]) % MOD;
    }

    vector<long long> total(row.size(), 0);
    for (int i = 0; i < total.size(); i++) {
        total[i] = power(row[i], h);
    }

    int bm_limit = min((int)total.size() - 1, 2 * h + 2);
    vector<long long> bm_input(total.begin(), total.begin() + bm_limit + 1);
    vector<long long> C = berlekamp_massey(bm_input);

    vector<long long> P(h + 2, 0);
    for (int k = 0; k <= min(h + 1, (int)C.size() - 1); k++) {
        for (int j = 0; j <= k; j++) {
            if (j < C.size()) {
                P[k] = (P[k] + total[k - j] * C[j]) % MOD;
            }
        }
    }

    vector<long long> dp(w + 1, 0);
    int limit = min(w, h + 1);
    
    if (w >= 1) dp[1] = total[1];
    for (int i = 2; i <= limit; i++) {
        long long bad = 0;
        for (int j = 1; j < i; j++) {
            bad = (bad + dp[j] * total[i - j]) % MOD;
        }
        dp[i] = (total[i] - bad + MOD) % MOD;
    }

    for (int i = limit + 1; i <= w; i++) {
        long long val = 0;
        for (int j = 1; j <= h + 1; j++) {
            if (i - j < 1) break;
            val = (val + P[j] * dp[i - j]) % MOD;
        }
        dp[i] = (-val % MOD + MOD) % MOD;
    }

    cout << dp[w] << "\n";
    return 0;
}
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