refactor: simplify

Tiphereth-A · May 15, 2024 · cbd71da · cbd71da
1 parent 7c79a3f
commit cbd71da
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diff --git a/ICPCnotebook.cls b/ICPCnotebook.cls
@@ -51,7 +51,6 @@
 
 % User defined command
 \newcommand{\lcm}{\operatorname{lcm}}
-\newcommand{\subjectto}{~s.t.~}
 \DeclareMathOperator*{\argmin}{arg\,min}
 \DeclareMathOperator*{\argmax}{arg\,max}
 

diff --git a/config.yml b/config.yml
@@ -255,10 +255,10 @@ notebook:
     - max_area_t: 凸包内面积最大的三角形
       code_ext: hpp
       test_ext: cpp
-    - coverage_rect_with_min_area: 最小面积覆盖矩形
+    - coverage_rect_min_area: 最小面积覆盖矩形
       code_ext: hpp
       test_ext: cpp
-    - coverage_rect_with_min_circum: 最小周长覆盖矩形
+    - coverage_rect_min_circum: 最小周长覆盖矩形
       code_ext: hpp
       test_ext: cpp
     - max_dis_cvh: 两凸包中的点的最远距离
@@ -282,16 +282,16 @@ notebook:
     - extan_cc: 两圆的外切线
       code_ext: hpp
       test_ext: cpp
-    - inv_c2c: 未经过反演中心的圆的几何反演
+    - inv_p2p: 点的反演
       code_ext: hpp
       test_ext: cpp
-    - inv_c2l: 经过反演中心的圆的几何反演
+    - inv_l2c: 直线的反演
       code_ext: hpp
       test_ext: cpp
-    - inv_l2c: 直线的几何反演
+    - inv_c2c: 圆的反演(未经过反演中心)
       code_ext: hpp
       test_ext: cpp
-    - inv_p2p: 点的几何反演
+    - inv_c2l: 圆的反演(经过反演中心)
       code_ext: hpp
       test_ext: cpp
     - dist_pl: 点与直线距离
@@ -306,7 +306,13 @@ notebook:
     - ins_ll: 直线交点
       code_ext: hpp
       test_ext: cpp
-    - is_ins_ss: 判断线段是否相交
+    - is_ins_sl: 判断线段与直线是否相交
+      code_ext: hpp
+      test_ext: cpp
+    - is_ins_ss: 判断两线段是否相交
+      code_ext: hpp
+      test_ext: cpp
+    - any_ins_ss: 判断多条线段是否相交
       code_ext: hpp
       test_ext: cpp
     - is_on_s: 判断点是否在直线上
@@ -318,19 +324,22 @@ notebook:
     - proj: 点在直线上的投影与对称点
       code_ext: hpp
       test_ext: cpp
-    - make_c_ppp: 根据三点构造圆
+    - make_c_ppp: 构造圆(经过的三点)
       code_ext: hpp
       test_ext: cpp
-    - make_c_rcc_ex: 根据半径和两外切圆构造圆
+    - make_c_rpp: 构造圆(半径和经过的两点)
       code_ext: hpp
       test_ext: cpp
-    - make_c_rll: 根据半径和两切线构造圆
+    - make_c_rpl: 构造圆(半径,切线和经过的一点)
       code_ext: hpp
       test_ext: cpp
-    - make_c_rpl: 根据半径,切线和经过的一点构造圆
+    - make_c_rll: 构造圆(半径和两切线)
       code_ext: hpp
       test_ext: cpp
-    - make_c_rpp: 根据半径和经过的两点构造圆
+    - make_c_rcc_ex: 构造圆(半径和两外切圆)
+      code_ext: hpp
+      test_ext: cpp
+    - make_c_pcc_ex: 构造圆(经过的一点和两外切圆)
       code_ext: hpp
       test_ext: cpp
     - min_cover_c: 最小覆盖圆
@@ -414,6 +423,12 @@ notebook:
     - tcenter_x: 三角形 Fermat 点
       code_ext: hpp
       test_ext: cpp
+    - aunion_cs: 圆的面积并
+      code_ext: hpp
+      test_ext: cpp
+    - aunion_pos: 多边形的面积并
+      code_ext: hpp
+      test_ext: cpp
     geo3d:
     - point3d: 三维点
       code_ext: hpp
@@ -841,28 +856,19 @@ notebook:
     - mint_2e61n1: 模整数类(固定,61-1)
       code_ext: hpp
       test_ext: cpp
-    - mint_ss: 模整数类(静态,简单实现)
-      code_ext: hpp
-      test_ext: cpp
     - mint_s30: 模整数类(静态,30)
       code_ext: hpp
       test_ext: cpp
     - mint_s63: 模整数类(静态,63)
       code_ext: hpp
       test_ext: cpp
-    - mint_ds: 模整数类(动态,简单实现)
-      code_ext: hpp
-      test_ext: cpp
     - mint_d31: 模整数类(动态,31)
       code_ext: hpp
       test_ext: cpp
     - mint_d63: 模整数类(动态,63)
       code_ext: hpp
       test_ext: cpp
-    - mul_mod_s: 有符号模乘法
-      code_ext: hpp
-      test_ext: cpp
-    - mul_mod_u: 无符号模乘法
+    - mul_mod: 模乘法
       code_ext: hpp
       test_ext: cpp
     - qpow_mod: 模快速幂

diff --git a/src/cheatsheet/nt-const.tex b/src/cheatsheet/nt-const.tex
@@ -31,16 +31,16 @@ \subsection{本质不同质因子数, 因子数, 素数个数}
 
 \begin{tabular}{llll|llll}
     \hline
-    \(n\)    & \(\max\{\omega(n)\}\) & \(\max\{d(n)\}\) & \(\pi(n)\)   & \(n\)       & \(\max\{\omega(n)\}\) & \(\max\{d(n)\}\) & \(\pi(n)\)     \\
+    \(n\)    & \(\max\{\omega(n)\}\) & \(\max\{d(n)\}\) & \(\pi(n)\)     & \(n\)       & \(\max\{\omega(n)\}\) & \(\max\{d(n)\}\)  & \(\pi(n)\)        \\
     \hline
-    \(10^1\) & \(2\)                 & \(4\)            & \(4\)        & \(10^{10}\) & \(10\)                & \(2304\)         & \(455052511\)  \\
-    \(10^2\) & \(3\)                 & \(12\)           & \(25\)       & \(10^{11}\) & \(10\)                & \(4032\)         & \(4118054813\) \\
-    \(10^3\) & \(4\)                 & \(32\)           & \(168\)      & \(10^{12}\) & \(11\)                & \(6720\)         &                \\
-    \(10^4\) & \(5\)                 & \(64\)           & \(1229\)     & \(10^{13}\) & \(12\)                & \(10752\)        &                \\
-    \(10^5\) & \(6\)                 & \(128\)          & \(9592\)     & \(10^{14}\) & \(12\)                & \(17280\)        &                \\
-    \(10^6\) & \(7\)                 & \(240\)          & \(78498\)    & \(10^{15}\) & \(13\)                & \(26880\)        &                \\
-    \(10^7\) & \(8\)                 & \(448\)          & \(664579\)   & \(10^{16}\) & \(13\)                & \(41472\)        &                \\
-    \(10^8\) & \(8\)                 & \(768\)          & \(5761455\)  & \(10^{17}\) & \(14\)                & \(64512\)        &                \\
-    \(10^9\) & \(9\)                 & \(1344\)         & \(50847534\) & \(10^{18}\) & \(15\)                & \(103680\)       &                \\
+    \(10^1\) & \(2\)                 & \(4\)            & \(4\)          & \(10^{10}\) & \(10\)                & \(2~304\)         & \(455~052~511\)   \\
+    \(10^2\) & \(3\)                 & \(12\)           & \(25\)         & \(10^{11}\) & \(10\)                & \(4~032\)         & \(4~118~054~813\) \\
+    \(10^3\) & \(4\)                 & \(32\)           & \(168\)        & \(10^{12}\) & \(11\)                & \(6~720\)         &                   \\
+    \(10^4\) & \(5\)                 & \(64\)           & \(1~229\)      & \(10^{13}\) & \(12\)                & \(10~752\)        &                   \\
+    \(10^5\) & \(6\)                 & \(128\)          & \(9~592\)      & \(10^{14}\) & \(12\)                & \(17~280\)        &                   \\
+    \(10^6\) & \(7\)                 & \(240\)          & \(78~498\)     & \(10^{15}\) & \(13\)                & \(26~880\)        &                   \\
+    \(10^7\) & \(8\)                 & \(448\)          & \(664~579\)    & \(10^{16}\) & \(13\)                & \(41~472\)        &                   \\
+    \(10^8\) & \(8\)                 & \(768\)          & \(5~761~455\)  & \(10^{17}\) & \(14\)                & \(64~512\)        &                   \\
+    \(10^9\) & \(9\)                 & \(1~344\)        & \(50~847~534\) & \(10^{18}\) & \(15\)                & \(103~680\)       &                   \\
     \hline
 \end{tabular}
diff --git a/src/code/comb/binom.hpp b/src/code/comb/binom.hpp
@@ -15,24 +15,24 @@ struct Binom {
 
   static CEXP u64 mod() { return mint::mod(); }
 
-  // \binom{m}{n}
+  // $\binom{m}{n}$
   template <uint_c T>
   CEXP mint mCn(T m, T n) const { return m < n ? 0 : mPn(m, n) * ifact[(usz)n]; }
-  // \binom{m}{n}
+  // $\binom{m}{n}$
   template <sint_c T>
   CEXP mint mCn(T m, T n) const { return m < n || n < 0 ? 0 : mCn(to_uint_t<T>(m), to_uint_t<T>(n)); }
 
-  // \binom{m}{n} * n!
+  // $\binom{m}{n} \cdot n!$
   template <uint_c T>
   CEXP mint mPn(T m, T n) const { return m < n ? 0 : fact[(usz)m] * ifact[(usz)(m - n)]; }
-  // \binom{m}{n} * n!
+  // $\binom{m}{n} \cdot n!$
   template <sint_c T>
   CEXP mint mPn(T m, T n) const { return m < n || n < 0 ? 0 : mPn(to_uint_t<T>(m), to_uint_t<T>(n)); }
 
-  // [x^n] 1 / (1-x)^m
+  // $[x^n] \frac{1}{(1-x)^m}$
   template <uint_c T>
   CEXP mint mHn(T m, T n) const { return n <= 0 ? n == 0 : mCn(m + n - 1, n); }
-  // [x^n] 1 / (1-x)^m
+  // $[x^n] \frac{1}{(1-x)^m}$
   template <sint_c T>
   CEXP mint mHn(T m, T n) const { return m < 0 || n <= 0 ? n == 0 : mHn(to_uint_t<T>(m), to_uint_t<T>(n)); }
 };

diff --git a/src/code/comb/gen_derange.hpp b/src/code/comb/gen_derange.hpp
@@ -1,7 +1,7 @@
 #ifndef TIFALIBS_COMB_GEN_DERANGE
 #define TIFALIBS_COMB_GEN_DERANGE
 
-#include "../math/mul_mod_u.hpp"
+#include "../math/mul_mod.hpp"
 
 namespace tifa_libs::math {
 

diff --git a/src/code/comb/gen_fact.hpp b/src/code/comb/gen_fact.hpp
@@ -1,7 +1,7 @@
 #ifndef TIFALIBS_COMB_GEN_FACT
 #define TIFALIBS_COMB_GEN_FACT
 
-#include "../math/mul_mod_u.hpp"
+#include "../math/mul_mod.hpp"
 
 namespace tifa_libs::math {
 

diff --git a/src/code/comb/gen_ifact.hpp b/src/code/comb/gen_ifact.hpp
@@ -1,7 +1,7 @@
 #ifndef TIFALIBS_COMB_GEN_IFACT
 #define TIFALIBS_COMB_GEN_IFACT
 
-#include "../math/mul_mod_u.hpp"
+#include "../math/mul_mod.hpp"
 #include "gen_inv.hpp"
 
 namespace tifa_libs::math {

diff --git a/src/code/comb/gen_inv.hpp b/src/code/comb/gen_inv.hpp
@@ -1,7 +1,7 @@
 #ifndef TIFALIBS_COMB_GEN_INV
 #define TIFALIBS_COMB_GEN_INV
 
-#include "../math/mul_mod_u.hpp"
+#include "../math/mul_mod.hpp"
 
 namespace tifa_libs::math {
 

diff --git a/src/code/comb/gen_invseq.hpp b/src/code/comb/gen_invseq.hpp
@@ -1,7 +1,7 @@
 #ifndef TIFALIBS_COMB_GEN_INVSEQ
 #define TIFALIBS_COMB_GEN_INVSEQ
 
-#include "../math/mul_mod_u.hpp"
+#include "../math/mul_mod.hpp"
 #include "../nt/inverse.hpp"
 
 namespace tifa_libs::math {

diff --git a/src/code/conv/conv_3ntt.hpp b/src/code/conv/conv_3ntt.hpp
@@ -1,7 +1,7 @@
 #ifndef TIFALIBS_CONV_CONV_3NTT
 #define TIFALIBS_CONV_CONV_3NTT
 
-#include "../math/mul_mod_u.hpp"
+#include "../math/mul_mod.hpp"
 #include "conv_dft.hpp"
 #include "ntt.hpp"
 
@@ -10,8 +10,8 @@ namespace tifa_libs::math {
 // 167772161, 469762049, 754974721
 template <class mint0, class mint1, class mint2>
 CEXP vecu64 conv_3ntt_u64(std::tuple<NTT<mint0>, NTT<mint1>, NTT<mint2>> &ntt3, vecu64 CR l, vecu64 CR r, u64 mod, u32 ans_size = 0) {
-  CEXP u32 m0 = mint0::mod(), m1 = mint1::mod(), m2 = mint2::mod();
-  const u32 r01 = mint1(m0).inv().val(), r02 = mint2(m0).inv().val(), r12 = mint2(m1).inv().val(), r02r12 = (u32)mul_mod_u(r02, r12, m2);
+  CEXP u64 m0 = mint0::mod(), m1 = mint1::mod(), m2 = mint2::mod();
+  const u64 r01 = mint1(m0).inv().val(), r02 = mint2(m0).inv().val(), r12 = mint2(m1).inv().val(), r02r12 = (u32)mul_mod_u(r02, r12, m2);
   const u64 w1 = m0 % mod, w2 = mul_mod_u(m0, m1, mod);
 
   if (!ans_size) ans_size = u32(l.size() + r.size() - 1);

diff --git a/src/code/ds/skew_heap.hpp b/src/code/ds/skew_heap.hpp
@@ -6,7 +6,7 @@
 namespace tifa_libs::ds {
 
 template <class T, class C = std::less<T>>
-class SkewHeap {
+class skew_heap {
   static CEXP C comp_{};
   struct TIFA {
     T k, lz;

diff --git a/src/code/fast/str2uint_mod.hpp b/src/code/fast/str2uint_mod.hpp
@@ -1,7 +1,7 @@
 #ifndef TIFALIBS_FAST_STR2UINT_MOD
 #define TIFALIBS_FAST_STR2UINT_MOD
 
-#include "../math/mul_mod_u.hpp"
+#include "../math/mul_mod.hpp"
 #include "str2uint_si64.hpp"
 
 namespace tifa_libs {

diff --git a/src/code/geo2d/ang2pi_pp.hpp b/src/code/geo2d/ang2pi_pp.hpp
@@ -9,7 +9,7 @@ namespace tifa_libs::geo {
 template <class FP>
 CEXP FP ang2pi_PP(point<FP> CR p1, point<FP> CR p2) {
   FP res = ang_PP(p1, p2);
-  return is_neg(res) ? res + 2 * std::numbers::pi_v<FP> : res;
+  return is_neg(res) ? res + 2 * pi_v<FP> : res;
 }
 
 }  // namespace tifa_libs::geo

diff --git a/src/code/geo2d/any_ins_ss.hpp b/src/code/geo2d/any_ins_ss.hpp
@@ -0,0 +1,49 @@
+#ifndef TIFALIBS_GEO2D_ANY_INS_SS
+#define TIFALIBS_GEO2D_ANY_INS_SS
+
+#include "ins_ll.hpp"
+#include "is_ins_sl.hpp"
+
+namespace tifa_libs::geo {
+
+// judge if any two segments are intersected
+template <class FP>
+CEXP bool any_ins_Ss(vec<line<FP>> CR ss) {
+  if (ss.empty()) return false;
+  using seq_t = std::tuple<FP, int, line<FP>>;
+  const auto seqcmp = [](seq_t CR u, seq_t CR v) {
+    auto [u0, u1, u2] = u;
+    auto [v0, v1, v2] = v;
+    if (is_eq(u0, v0)) return u1 == v1 ? u2 < v2 : u1 < v1;
+    return is_lt(u0, v0);
+  };
+  vec<seq_t> seq;
+  for (auto seg : ss) {
+    if (is_gt(seg.l.x, seg.r.x)) swap(seg.l, seg.r);
+    seq.emplace_back(seg.l.x, 0, seg), seq.emplace_back(seg.r.x, 1, seg);
+  }
+  std::ranges::sort(seq, seqcmp);
+  FP x_now;
+  auto cmp = [&](line<FP> CR u, line<FP> CR v) {
+    if (is_eq(u.l.x, u.r.x) || is_eq(v.l.x, v.r.x)) return is_lt(u.l.y, v.l.y);
+    return is_lt(((x_now - u.l.x) * (u.r.y - u.l.y) + u.l.y * (u.r.x - u.l.x)) * (v.r.x - v.l.x), ((x_now - v.l.x) * (v.r.y - v.l.y) + v.l.y * (v.r.x - v.l.x)) * (u.r.x - u.l.x));
+  };
+  std::multiset<line<FP>, decltype(cmp)> s{cmp};
+  for (auto CR[x, o, seg] : seq) {
+    x_now = x;
+    auto it = s.lower_bound(seg);
+    if (!o) {
+      if (it != s.end() && is_ins_SL(seg, *it)) return 1;
+      if (it != s.begin() && is_ins_SL(seg, *prev(it))) return 1;
+      s.insert(seg);
+    } else {
+      if (next(it) != s.end() && it != s.begin() && is_ins_LL(*prev(it), *next(it))) return 1;
+      s.erase(it);
+    }
+  }
+  return 0;
+}
+
+}  // namespace tifa_libs::geo
+
+#endif
diff --git a/src/code/geo2d/area_cc.hpp b/src/code/geo2d/area_cc.hpp
@@ -9,8 +9,8 @@ namespace tifa_libs::geo {
 template <class FP>
 CEXP FP area_CC(circle<FP> CR c1, circle<FP> CR c2) {
   auto relation = relation_CC(c1, c2);
-  if (relation == RELCC::lyingout_cc || relation == RELCC::touchex_cc) return FP{};
-  if (relation == RELCC::lyingin_cc || relation == RELCC::touchin_cc) return min(c1.area(), c2.area());
+  if (relation == lyingout_cc || relation == touchex_cc) return FP{};
+  if (relation == lyingin_cc || relation == touchin_cc) return min(c1.area(), c2.area());
   FP d = dist_PP(c1.o, c2.o);
   return c1.crown_area(std::acos((c1.r * c1.r - c2.r * c2.r + d * d) / (2 * c1.r * d)) * 2) + c2.crown_area(std::acos((c2.r * c2.r - c1.r * c1.r + d * d) / (2 * c2.r * d)) * 2);
 }

diff --git a/src/code/geo2d/area_poc.hpp b/src/code/geo2d/area_poc.hpp
@@ -11,7 +11,7 @@ namespace tifa_libs::geo {
 template <class FP>
 CEXP FP area_PoC(polygon<FP> CR po, circle<FP> CR c) {
   math::kahan<FP> ans{};
-  u32 sz = (u32)po.vs.size();
+  u32 sz = po.size();
   if (sz < 3) return ans;
   flt_ (u32, i, 0, sz) ans += sarea_CT(c, po[i], po[po.next(i)]);
   return abs<FP>(ans);