結果

問題 No.1685 One by One
コンテスト
ユーザー hitonanode
提出日時 2021-08-14 15:15:44
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 4,709 bytes
コンパイル時間 1,426 ms
コンパイル使用メモリ 86,144 KB
最終ジャッジ日時 2025-01-23 22:06:09
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3 TLE * 1
other AC * 26 TLE * 20
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 # 

// TLE
#include <cassert>
#include <iostream>
#include <vector>
#include <atcoder/modint>
using mint = atcoder::modint1000000007;
using namespace std;

// atcoder::static_modint<P>, P: prime number
template <typename modint> struct acl_fac {
    std::vector<modint> facs, facinvs;
    acl_fac(int N) {
        assert(-1 <= N and N < modint::mod());
        facs.resize(N + 1, 1);
        for (int i = 1; i <= N; i++) facs[i] = facs[i - 1] * i;
        facinvs.assign(N + 1, facs.back().inv());
        for (int i = N; i > 0; i--) facinvs[i - 1] = facinvs[i] * i;
    }
    modint ncr(int n, int r) const {
        if (n < 0 or r < 0 or n < r) return 0;
        return facs[n] * facinvs[r] * facinvs[n - r];
    }
    modint operator[](int i) const { return facs[i]; }
    modint finv(int i) const { return facinvs[i]; }
};

mint solve_Onnm(int N, int M) {
    acl_fac<mint> fac(N + M);
    mint ret = 0;

    // 中央値がゼロ
    for (int nneg = 0; nneg <= (N - 1) / 2; nneg++) {
        for (int npos = 0; npos <= N / 2; npos++) {
            if (nneg == 0 and npos == 0) {
                if (M % 2 == 0) ret++;
                continue;
            }
            for (int m = M - npos - nneg; m >= 0; m -= 2) {
                ret += fac.ncr(N, nneg) * fac.ncr(N - nneg, npos) * fac.ncr(npos + nneg - 1 + m, m);
            }
        }
    }

    if (N % 2) {
        // 中央値が 1 または -1
        for (int nneg = 0; nneg <= N / 2; nneg++) {
            for (int npos = 0; npos <= N / 2; npos++) {
                if (npos == 0 and nneg == 0) {
                    if (M >= N and (M - N) % 2 == 0) ret++;
                    continue;
                }
                const int n1 = N - nneg - npos;
                for (int m = M - npos * 2 - n1; m >= 0; m -= 2) {
                    ret += fac.ncr(N, nneg) * fac.ncr(N - nneg, npos) * fac.ncr(npos + nneg - 1 + m, m) * 2;
                }

                // ダブルカウントを消す
                int rem = M - n1 - max(nneg, npos) * 2;
                for (int m = rem; m >= 0; m -= 2) {
                    ret -= fac.ncr(N, nneg) * fac.ncr(N - nneg, npos) * fac.ncr(npos + nneg - 1 + m, m);
                }
            }
        }
    }
    return ret;
}

mint solve_Onm(int N, int M) {
    acl_fac<mint> fac(N + M);
    vector precalc(N + 1, vector<mint>(M + 1));
    precalc[0][0] = 1;
    for (int n = 0; n <= N; n++) {
        for (int m = 0; m <= M; m++) {
            if (n + m - 1 >= 0) precalc[n][m] = fac.ncr(n + m - 1, n - 1);
            if (m >= 2) precalc[n][m] += precalc[n][m - 2];
        }
    }

    mint ret = 0;
    if (N % 2 == 0) {
        int half = (N - 1) / 2;
        for (int nnonzero = 0; nnonzero <= half * 2; nnonzero++) {
            mint coeff = 0;
            for (int npos = 0; npos <= half; npos++) {
                int nneg = nnonzero - npos;
                if (nneg < 0 or nneg > half) continue;
                coeff += fac.ncr(N - 1, npos) * fac.ncr(N - 1 - npos, nneg);
            }
            mint tmp = 0;
            for (int b0 = 0; b0 <= M; b0++) {
                if (M - nnonzero - b0 < 0) continue;
                tmp += precalc.at(nnonzero).at(M - nnonzero - b0) * (b0 == 0 ? 1 : 2);
            }
            ret += tmp * coeff;
        }
    } else {
        for (int npos = 0; npos <= N / 2; npos++) {
            for (int nneg = 0; nneg <= N / 2; nneg++) {
                int nnonzero = npos + nneg;
                if (M - nnonzero < 0) continue;
                ret += fac.ncr(N, nnonzero) * fac.ncr(nnonzero, npos) * precalc[nnonzero][M - nnonzero];
            }
        }

        for (int npos = 0; npos <= N / 2; npos++) {
            for (int nneg = 0; nneg <= N / 2; nneg++) {
                int nnonzero = npos + nneg;
                int m = M - npos - (N - nneg);
                if (m < 0) continue;
                ret += fac.ncr(N, nnonzero) * fac.ncr(nnonzero, npos) * precalc[nnonzero][m] * 2;
            }
        }

        for (int npos = 0; npos <= N / 2; npos++) {
            for (int nneg = 0; nneg <= N / 2; nneg++) {
                const int nnonzero = npos + nneg;
                int m = M - (N - nnonzero) - max(npos, nneg) * 2;
                if (m < 0) continue;
                ret -= fac.ncr(N, nnonzero) * fac.ncr(nnonzero, npos) * precalc[nnonzero][m];
            }
        }
    }
    return ret;
}

int main() {
    for (int n = 2; n <= 50; n++) {
        for (int m = 0; m <= 50; m++) {
            if (solve_Onm(n, m) != solve_Onnm(n, m)) {
                cerr << n << ' ' << m << endl;
                throw;
            }
        }
    }
    int N, M;
    cin >> N >> M;
    cout << solve_Onnm(N, M).val() << '\n';
}
0