From 721dffde94dadda61f02e0491f8824b1ae5bdf48 Mon Sep 17 00:00:00 2001 From: SGColin Date: Sun, 17 Jul 2022 15:01:12 +0800 Subject: [PATCH] 0.0.1 --- .DS_Store | Bin 0 -> 8196 bytes cg/.DS_Store | Bin 0 -> 6148 bytes cg/polygon.cpp | 81 ++++++++++++++++++++++++++++++++++++++++++ cg/seg.cpp | 32 +++++++++++++++++ cg/vec.cpp | 31 ++++++++++++++++ graph/scc.cpp | 40 +++++++++++++++++++++ math/.DS_Store | Bin 0 -> 6148 bytes math/comb.cpp | 22 ++++++++++++ math/linear_sieve.cpp | 22 ++++++++++++ 9 files changed, 228 insertions(+) create mode 100644 .DS_Store create mode 100644 cg/.DS_Store create mode 100644 cg/polygon.cpp create mode 100644 cg/seg.cpp create mode 100644 cg/vec.cpp create mode 100644 graph/scc.cpp create mode 100644 math/.DS_Store create mode 100644 math/comb.cpp create mode 100644 math/linear_sieve.cpp diff --git a/.DS_Store b/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..ce02307ad8bdc20bfd4eb9ab32bf660daf86059d GIT binary patch literal 8196 zcmeHMPm9w)6rbsKZQ>#nbYVRR0ohy8wA8wyV77J-dNiU3m727r4JMh;r1nq>x$AfF zD0}xacgJgPGrS-g}wM@7E@IDItV*XTv5TM}!a!8prwpbS1|9 zyj`-2nmGidkWXBnxiGFnJ5@deWB?gJ29N<{02%nZ7=U{=H*L#(UwW}e29SaOk^z2w zFraa?6s8izr2{%q0svNFS{RJ^<3Ggo6DOI)U1$21e|p83@2>5UWDWGZ)fpSA;Lz) zg%srxC4%Jg3$j#60HP#CQRtn5C|TT9OVU0$X&7zu;h+8%vJI68lKJv-+`Rteg_0xZ zzYwF$Um``8yD0?T|KSUVh79b0fjzm#5wHKxw!i=1!I|I^$N(~MRSeK-&+c_$_4PAz y@kDs7Z9w|~jT?_kC5ja2HeLk4=j;zd7#k4Eb1a3aM3@1?7Xg9>?2v(-GVmMyaxj3*B_-M#vWw{DWBP!nHpjy^5QQw@?(^<&XM_^~^)D?cFLOGmxBV za%OIFph*UREMFh5fjNLFo1&;QVmdrJbr$4vqF9b+40yo;9X2D0{^F3Xea6)e=<$y4 z>)+hi>8GU^$YfK5Ofz6RKH1SZPhf0(f z;^7=G!K;DI(ZeB8d`Nuxvv?8vI`bE!L#ku;sX!`lsDReKw7K5@xBSbD7WqcWE)_@x z{;L8qS>3Oe++EzQC;Qa9wy-_0sVT3iL!*E22;dJrM=ovB=ZpH})xhScS#;dOiTMyP LL9$B)enEi`mohW7 literal 0 HcmV?d00001 diff --git a/cg/polygon.cpp b/cg/polygon.cpp new file mode 100644 index 0000000..56c9ee6 --- /dev/null +++ b/cg/polygon.cpp @@ -0,0 +1,81 @@ +#define nxt(x) ((x + 1) >= n ? x + 1 - n : x + 1) +struct polygon { + vector s; + polygon () {s.clear();} + ld circ () const { // 多边形的周长 + if (s.size() <= 1) return 0.0; + ld ans = 0.0; + for (int i = 0, n = s.size(); i < n; ++i) + ans += s[i].dis(s[nxt(i)]); + return ans; + } + ld area () const { // 多边形的面积 + if (s.size() <= 1) return 0.0; + ld ans = 0.0; + for (int i = 0, n = s.size(); i < n; ++i) + ans += s[i].cross(s[nxt(i)]); + return ans / 2; + } + void polar_angle_sort_origin() { // 关于原点极角排序 + auto cmp = [&](const vec &a, const vec &b) { + if (a.up() != b.up()) return a.up() > b.up(); + ld d = a.cross(b); // 叉积判断方向 + return d == 0 ? a.norm() < b.norm() : d > 0; + }; + sort(s.begin(), s.end(), cmp); + } + void polar_angle_sort() { // 极角排序 + auto cmp = [&](const vec &a, const vec &b) { + double d = (a - s[0]).cross(b - s[0]); + return d == 0 ? a.dis2(s[0]) < b.dis2(s[0]) : d > 0; + }; + for (int i = 1, n = s.size(); i < n; ++i) + if (s[i] < s[0]) swap(s[0], s[i]); + sort(s.begin() + 1, s.end(), cmp); // 注意不要把 s[0] 排进去 + } + void convex_hull () { // 求凸包 + if (s.size() <= 1) return; + polar_angle_sort(); // 先进行极角排序 + vector t; t.clear(); swap(s, t); + s.push_back(t[0]); s.push_back(t[1]); + for (int top = 1, i = 2, n = t.size(); i < n; ++i) { + while ((s[top] - s[top - 1]).cross(t[i] - s[top - 1]) <= 0) { + s.pop_back(); if ((--top) < 1) break; + } + s.push_back(t[i]); ++top; + } + } + void convex_hull_maxcnt() { // 上下凸壳合并版写法 + auto cmp = [&](const vec &a, const vec &b) { + return a.y == b.y ? a.x < b.x : a.y < b.y; + }; + sort(s.begin(), s.end(), cmp); + vector t; t.clear(); swap(s, t); + s.push_back(t[0]); s.push_back(t[1]); + int top = 1; + for (int i = 2, n = t.size(); i < n; ++i) { // 保留最多的点 + while ((s[top] - s[top - 1]).cross(t[i] - s[top - 1]) < 0) { + s.pop_back(); if ((--top) < 1) break; + } + s.push_back(t[i]); ++top; + } + int lim = top; + for (int i = t.size() - 2; i >= 0; --i) { + while ((s[top] - s[top - 1]).cross(t[i] - s[top - 1]) < 0) { + s.pop_back(); if ((--top) < lim) break; + } + s.push_back(t[i]); ++top; + } + s.pop_back(); + } + ld convex_diam () const { // 凸包的直径 + if (s.size() <= 1) return 0.0; + ld ans = 0; + for (int i = 0, ptr = 1, n = s.size(); i < n; ++i) { + while (s[i].dis(s[ptr]) <= s[i].dis(s[nxt(ptr)])) + ptr = nxt(ptr); + ans = max(ans, s[i].dis(s[ptr])); + } + return ans; + } +}; \ No newline at end of file diff --git a/cg/seg.cpp b/cg/seg.cpp new file mode 100644 index 0000000..798e86e --- /dev/null +++ b/cg/seg.cpp @@ -0,0 +1,32 @@ +struct seg { + vec p1, p2; + vec proj(const vec &b) {return p1 + (p2 - p1).proj(b - p1);} + vec refl(const vec &b) {return p1 + (p2 - p1).refl(b - p1);} + bool cross(const seg &b) const{ // 判断两线段是否相交 + ld w1 = (p2 - p1).cross(b.p1 - p1); + ld w2 = (p2 - p1).cross(b.p2 - p1); + ld w3 = (b.p2 - b.p1).cross(p1 - b.p1); + ld w4 = (b.p2 - b.p1).cross(p2 - b.p1); + if (w1 * w2 > 0 || w3 * w4 > 0) return 0; + if (w1 * w2 < 0 || w3 * w4 < 0) return 1; + ld v1 = (b.p1 - p1).dot(b.p1 - p2); + ld v2 = (b.p2 - p1).dot(b.p2 - p2); + ld v3 = (p1 - b.p1).dot(p1 - b.p2); + ld v4 = (p2 - b.p1).dot(p2 - b.p2); + return (v1 <= 0 || v2 <= 0 || v3 <= 0 || v4 <= 0); + } + vec cross_point(const seg &b) const { // 相交且不平行的情况下求交点 + vec v = p2 - p1, u1 = b.p1 - p1, u2 = b.p2 - p1; + ld s1 = fabs(v.cross(u1)) / 2, s2 = fabs(v.cross(u2)) / 2; + return p1 + u1 * (s2 / (s1 + s2)) + u2 * (s1 / (s1 + s2)); + } + ld dis(const vec &b) const { // 点到线段距离 + if ((p2 - p1).dot(b - p1) < 0 || (p1 - p2).dot(b - p2) < 0) + return min(p1.dis(b), p2.dis(b)); // 垂足不在线段上 + return fabs((p2 - p1).cross(b - p1)) / (p2 - p1).len(); + } + ld dis(const seg &b) const { // 线段到线段距离 + if (cross(b)) return 0.0; + return min(min(dis(b.p1), dis(b.p2)), min(b.dis(p1), b.dis(p2))); + } +}; \ No newline at end of file diff --git a/cg/vec.cpp b/cg/vec.cpp new file mode 100644 index 0000000..f6e2879 --- /dev/null +++ b/cg/vec.cpp @@ -0,0 +1,31 @@ +const ld a90 = atan(1) * 2; +const ld a180 = a90 * 2, a270 = a90 * 3, a360 = a90 * 4; +const ld dlt[2][2] = {0, a180, a360, a180}; +struct vec { + ld x, y; + vec (ld _x = 0, ld _y = 0){x = _x; y = _y;} + vec operator + (const vec &b) const {return (vec){x + b.x, y + b.y};} + vec operator - (const vec &b) const {return (vec){x - b.x, y - b.y};} + vec operator * (const ld &k) const {return (vec){x * k, y * k};} + ld dot (const vec &b) const {return x * b.x + y * b.y;} + ld cross (const vec &b) const {return x * b.y - y * b.x;} + ld norm () const {return x * x + y * y;} + ld len () const {return sqrt(norm());} + ld dis (const vec &b) const {return ((*this) - b).len();} + ld dis2 (const vec &b) const {return ((*this) - b).norm();} + ld angle() const { // 与 x 正半轴夹角，逆时针旋转 + if (fabs(x) < 1e-15) return a90 * (1 + 2 * (y < 0)); + else return atan(y / x) + dlt[y < 0][x < 0]; + } + vec turn (const ld &ang) { // 逆时针旋转 ang 角度 + ld cosa = cos(ang), sina = sin(ang); + return (vec){x * cosa - y * sina, x * sina + y * cosa}; + } + vec proj (const vec &b) {return (*this) * (dot(b) / this -> norm());} + vec refl (const vec &b) {return proj(b) * 2 - b;} //对称 + //找最下的点里，最靠左的，把其他点控制在一二象限和x正半轴 + bool up() const {return (y > 0 || (y == 0 && x > 0));} + bool operator < (const vec &b) const{ + return y == b.y ? x < b.x : y < b.y; + } +}; \ No newline at end of file diff --git a/graph/scc.cpp b/graph/scc.cpp new file mode 100644 index 0000000..0588aff --- /dev/null +++ b/graph/scc.cpp @@ -0,0 +1,40 @@ +bool vis[N]; +int n, m, scc, bl[N]; +vector e[N], re[N], nodes[N], order; +void add(int u, int v) {e[u].pb(v); re[v].pb(u);} +void dfs1(int u) { + vis[u] = 1; + for (auto v : e[u]) if (!vis[v]) dfs1(v); + order.pb(u); +} +void dfs2(int u) { + nodes[bl[u] = scc].pb(u); + for (auto v : re[u]) if (!bl[v]) dfs2(v); +} +void kosaraju(int n) { + for (int u = 1; u <= n; ++u) if (!vis[u]) dfs1(u); + reverse(order.begin(), order.end()); + for (auto u : order) if (!bl[u]) {++scc; dfs2(u);} +} +// ===== shrink nodes ===== +int indeg[N], outdeg[N]; +vector source, sink; +unordered_map valid; +inline bool has_edge(int u, int v) { + ll w = 1000000000ll * u + v; + if (valid[w]) return 1; + valid[w] = 1; return 0; +} +inline void shrink(int n) { + valid.clear(); + for (int u = 1; u <= n; ++u) e[u].clear(); + for (int v = 1; v <= n; ++v) + for (auto u : re[v]) + if (bl[u] != bl[v] && !has_edge(bl[u], bl[v])) { + ++indeg[bl[v]]; ++outdeg[bl[u]]; e[bl[u]].pb(bl[v]); + } + for (int u = 1; u <= scc; ++u) if (!indeg[u]) source.pb(u); + for (int u = 1; u <= scc; ++u) if (!outdeg[u]) sink.pb(u); + for (int u = 1; u <= n; ++u) re[u].clear(); + for (int u = 1; u <= scc; ++u) for (auto v : e[u]) re[v].pb(u); +} \ No newline at end of file diff --git a/math/.DS_Store b/math/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..66591f2d7adae7b111c1394b320ccf64c4026494 GIT binary patch literal 6148 zcmeHKyH3ME5S)b+mS|E^-WNpT4~{4l)O-NokOIlzC=LrVd>((c^t z?cCW@+yj6tpYP6qIe><)h*u3$({c5Q9Ysb_Y>oxi*kXIx_3KIX;e>Ju`@pY;cPmuJOd)1~2r({I_p>n>= 1, x = 1ll * x * x % mod) + if (t & 1) res = 1ll * res * x % mod; + return res; + } + + inline void init() { + fac[0] = ifac[0] = 1; + for (int i = 1; i < N; ++i) fac[i] = 1ll * fac[i - 1] * i % mod; + ifac[N - 1] = fpow(fac[N - 1], mod - 2); + for (int i = N - 2; i; --i) ifac[i] = 1ll * ifac[i + 1] * (i + 1) % mod; + } + + inline int C(int n, int m) { + if (n < m) return 0; + return 1ll * fac[n] * ifac[m] % mod * ifac[n - m] % mod; + } +} \ No newline at end of file diff --git a/math/linear_sieve.cpp b/math/linear_sieve.cpp new file mode 100644 index 0000000..e6f803f --- /dev/null +++ b/math/linear_sieve.cpp @@ -0,0 +1,22 @@ +int mnd[N], mncnt[N], mnpw[N], prm[N], phi[N] = {0, 1}; +for (int i = 2; i < N; ++i) { + if (!mind[i]) { + prm[++prm[0]] = mnd[i] = mnpw[i] = i; mncnt[i] = 1; + phi[i] = i - 1; // cntd[i] = 2; // sumd[i] = 1 + i; + } + for (int j = 1, p = prm[1], n; j <= prm[0]; p = prm[++j]) { + if ((n = i * p) > N) break; + if (p == mind[i]) { + mind[n] = p; + pw[n] = pw[i] * p; + cnt[n] = cnt[i] + 1; + if (i == pw[i]) phi[n] = phi[i] * p; + // cntd[n] = cnt[n] + 1; + // sumd[n] = (pw[n] * p - 1) / (p - 1); + else phi[n] = phi[i / pw[i]] * phi[pw[i] * p]; + break; + } + mnd[n] = pw[n] = p; cnt[n] = 1; + phi[n] = phi[i] * phi[p]; + } +} \ No newline at end of file