結果
問題 | No.1685 One by One |
ユーザー |
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提出日時 | 2021-08-07 15:17:01 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 251 ms / 3,000 ms |
コード長 | 3,074 bytes |
コンパイル時間 | 1,145 ms |
コンパイル使用メモリ | 84,124 KB |
最終ジャッジ日時 | 2025-01-23 16:40:18 |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 46 |
ソースコード
#include <cassert> #include <iostream> #include <vector> #include <atcoder/modint> using namespace std; using mint = atcoder::modint1000000007; // 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]; } }; int main() { int N, M; cin >> N >> 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]; } } } cout << ret.val() << '\n'; }