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Merge pull request #110 from NyaanNyaan/add_misc
add misc
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| #pragma once | ||
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| #include <vector> | ||
| using namespace std; | ||
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| template <typename mint> | ||
| vector<vector<mint>> binomial_table(int n) { | ||
| n += 10; | ||
| vector dp(n, vector(n, mint{0})); | ||
| dp[0][0] = 1; | ||
| for (int i = 0; i + 1 < n; i++) { | ||
| for (int j = 0; j <= i; j++) { | ||
| dp[i + 1][j + 0] += dp[i][j]; | ||
| dp[i + 1][j + 1] += dp[i][j]; | ||
| } | ||
| } | ||
| return dp; | ||
| } |
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| #pragma once | ||
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| #include <vector> | ||
| using namespace std; | ||
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| #include "../math/primitive-root-ll.hpp" | ||
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| template <typename mint> | ||
| struct NTT_64bit { | ||
| unsigned long long mod, pr; | ||
| int level; | ||
| mint dw[64], dy[64]; | ||
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| void setwy(int k) { | ||
| mint w[64], y[64]; | ||
| w[k - 1] = mint(pr).pow((mod - 1) / (1LL << k)); | ||
| y[k - 1] = w[k - 1].inverse(); | ||
| for (int i = k - 2; i > 0; --i) | ||
| w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1]; | ||
| dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2]; | ||
| for (int i = 3; i < k; ++i) { | ||
| dw[i] = dw[i - 1] * y[i - 2] * w[i]; | ||
| dy[i] = dy[i - 1] * w[i - 2] * y[i]; | ||
| } | ||
| } | ||
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| NTT_64bit() { | ||
| mod = mint::get_mod(); | ||
| if (mod >= 2) { | ||
| pr = primitive_root_ll(mod); | ||
| level = __builtin_ctzll(mod - 1); | ||
| setwy(level); | ||
| } | ||
| } | ||
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| void fft4(vector<mint> &a, int k) { | ||
| if ((int)a.size() <= 1) return; | ||
| if (k == 1) { | ||
| mint a1 = a[1]; | ||
| a[1] = a[0] - a[1]; | ||
| a[0] = a[0] + a1; | ||
| return; | ||
| } | ||
| if (k & 1) { | ||
| int v = 1 << (k - 1); | ||
| for (int j = 0; j < v; ++j) { | ||
| mint ajv = a[j + v]; | ||
| a[j + v] = a[j] - ajv; | ||
| a[j] += ajv; | ||
| } | ||
| } | ||
| int u = 1 << (2 + (k & 1)); | ||
| int v = 1 << (k - 2 - (k & 1)); | ||
| mint one = mint(1); | ||
| mint imag = dw[1]; | ||
| while (v) { | ||
| // jh = 0 | ||
| { | ||
| int j0 = 0; | ||
| int j1 = v; | ||
| int j2 = j1 + v; | ||
| int j3 = j2 + v; | ||
| for (; j0 < v; ++j0, ++j1, ++j2, ++j3) { | ||
| mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3]; | ||
| mint t0p2 = t0 + t2, t1p3 = t1 + t3; | ||
| mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag; | ||
| a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3; | ||
| a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3; | ||
| } | ||
| } | ||
| // jh >= 1 | ||
| mint ww = one, xx = one * dw[2], wx = one; | ||
| for (int jh = 4; jh < u;) { | ||
| ww = xx * xx, wx = ww * xx; | ||
| int j0 = jh * v; | ||
| int je = j0 + v; | ||
| int j2 = je + v; | ||
| for (; j0 < je; ++j0, ++j2) { | ||
| mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww, | ||
| t3 = a[j2 + v] * wx; | ||
| mint t0p2 = t0 + t2, t1p3 = t1 + t3; | ||
| mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag; | ||
| a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3; | ||
| a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3; | ||
| } | ||
| xx *= dw[__builtin_ctzll((jh += 4))]; | ||
| } | ||
| u <<= 2; | ||
| v >>= 2; | ||
| } | ||
| } | ||
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| void ifft4(vector<mint> &a, int k) { | ||
| if ((int)a.size() <= 1) return; | ||
| if (k == 1) { | ||
| mint a1 = a[1]; | ||
| a[1] = a[0] - a[1]; | ||
| a[0] = a[0] + a1; | ||
| return; | ||
| } | ||
| int u = 1 << (k - 2); | ||
| int v = 1; | ||
| mint one = mint(1); | ||
| mint imag = dy[1]; | ||
| while (u) { | ||
| // jh = 0 | ||
| { | ||
| int j0 = 0; | ||
| int j1 = v; | ||
| int j2 = v + v; | ||
| int j3 = j2 + v; | ||
| for (; j0 < v; ++j0, ++j1, ++j2, ++j3) { | ||
| mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3]; | ||
| mint t0p1 = t0 + t1, t2p3 = t2 + t3; | ||
| mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag; | ||
| a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3; | ||
| a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3; | ||
| } | ||
| } | ||
| // jh >= 1 | ||
| mint ww = one, xx = one * dy[2], yy = one; | ||
| u <<= 2; | ||
| for (int jh = 4; jh < u;) { | ||
| ww = xx * xx, yy = xx * imag; | ||
| int j0 = jh * v; | ||
| int je = j0 + v; | ||
| int j2 = je + v; | ||
| for (; j0 < je; ++j0, ++j2) { | ||
| mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v]; | ||
| mint t0p1 = t0 + t1, t2p3 = t2 + t3; | ||
| mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy; | ||
| a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww; | ||
| a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww; | ||
| } | ||
| xx *= dy[__builtin_ctzll(jh += 4)]; | ||
| } | ||
| u >>= 4; | ||
| v <<= 2; | ||
| } | ||
| if (k & 1) { | ||
| u = 1 << (k - 1); | ||
| for (int j = 0; j < u; ++j) { | ||
| mint ajv = a[j] - a[j + u]; | ||
| a[j] += a[j + u]; | ||
| a[j + u] = ajv; | ||
| } | ||
| } | ||
| } | ||
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| void ntt(vector<mint> &a) { | ||
| if ((int)a.size() <= 1) return; | ||
| fft4(a, __builtin_ctz(a.size())); | ||
| } | ||
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| void intt(vector<mint> &a) { | ||
| if ((int)a.size() <= 1) return; | ||
| ifft4(a, __builtin_ctz(a.size())); | ||
| mint iv = mint(a.size()).inverse(); | ||
| for (auto &x : a) x *= iv; | ||
| } | ||
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| vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) { | ||
| int l = a.size() + b.size() - 1; | ||
| if (min<int>(a.size(), b.size()) <= 40) { | ||
| vector<mint> s(l); | ||
| for (int i = 0; i < (int)a.size(); ++i) | ||
| for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j]; | ||
| return s; | ||
| } | ||
| int k = 2, M = 4; | ||
| while (M < l) M <<= 1, ++k; | ||
| setwy(k); | ||
| vector<mint> s(M); | ||
| for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i]; | ||
| fft4(s, k); | ||
| if (a.size() == b.size() && a == b) { | ||
| for (int i = 0; i < M; ++i) s[i] *= s[i]; | ||
| } else { | ||
| vector<mint> t(M); | ||
| for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i]; | ||
| fft4(t, k); | ||
| for (int i = 0; i < M; ++i) s[i] *= t[i]; | ||
| } | ||
| ifft4(s, k); | ||
| s.resize(l); | ||
| mint invm = mint(M).inverse(); | ||
| for (int i = 0; i < l; ++i) s[i] *= invm; | ||
| return s; | ||
| } | ||
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| void ntt_doubling(vector<mint> &a) { | ||
| int M = (int)a.size(); | ||
| auto b = a; | ||
| intt(b); | ||
| mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1)); | ||
| for (int i = 0; i < M; i++) b[i] *= r, r *= zeta; | ||
| ntt(b); | ||
| copy(begin(b), end(b), back_inserter(a)); | ||
| } | ||
| }; |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,39 @@ | ||
| #pragma once | ||
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| #include <utility> | ||
| #include <vector> | ||
| using namespace std; | ||
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| template <typename G> | ||
| vector<int> centroid(const G &g) { | ||
| const int N = (int)g.size(); | ||
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| vector<pair<int, int> > st; | ||
| st.emplace_back(0, -1); | ||
| vector<int> sz(N), par(N); | ||
| while (!st.empty()) { | ||
| auto p = st.back(); | ||
| if (sz[p.first] == 0) { | ||
| sz[p.first] = 1; | ||
| for (auto &to : g[p.first]) | ||
| if (to != p.second) st.emplace_back(to, p.first); | ||
| } else { | ||
| for (auto &to : g[p.first]) | ||
| if (to != p.second) sz[p.first] += sz[to]; | ||
| par[p.first] = p.second; | ||
| st.pop_back(); | ||
| } | ||
| } | ||
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| vector<int> ret; | ||
| int size = N; | ||
| for (int i = 0; i < N; i++) { | ||
| int val = N - sz[i]; | ||
| for (auto &to : g[i]) | ||
| if (to != par[i]) val = max(val, sz[to]); | ||
| if (val < size) size = val, ret.clear(); | ||
| if (val == size) ret.emplace_back(i); | ||
| } | ||
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| return ret; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,49 @@ | ||
| #pragma once | ||
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| #include <array> | ||
| #include <chrono> | ||
| #include <random> | ||
| #include <vector> | ||
| using namespace std; | ||
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| #include "../internal/internal-hash.hpp" | ||
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| template <typename G> | ||
| struct RootedTreeHash { | ||
| using Hash = internal::Hash<1>; | ||
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| const G& g; | ||
| int n; | ||
| vector<Hash> hash; | ||
| vector<int> depth; | ||
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| static vector<Hash>& xs() { | ||
| static vector<Hash> _xs; | ||
| return _xs; | ||
| } | ||
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| RootedTreeHash(const G& _g, int root = 0) : g(_g), n(g.size()) { | ||
| hash.resize(n); | ||
| depth.resize(n, 0); | ||
| while ((int)xs().size() <= n) xs().push_back(Hash::get_basis()); | ||
| dfs(root, -1); | ||
| } | ||
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| private: | ||
| int dfs(int c, int p) { | ||
| int dep = 0; | ||
| for (auto& d : g[c]) { | ||
| if (d != p) dep = max(dep, dfs(d, c) + 1); | ||
| } | ||
| Hash x = xs()[dep], h = Hash::set(1); | ||
| for (auto& d : g[c]) { | ||
| if (d != p) h = h * (x + hash[d]); | ||
| } | ||
| hash[c] = h; | ||
| return depth[c] = dep; | ||
| } | ||
| }; | ||
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| /** | ||
| * @brief 根付き木のハッシュ | ||
| */ |
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