From e7d2414f9b7fe860f4d3ea52944425daf2d323c3 Mon Sep 17 00:00:00 2001 From: GitHub Date: Fri, 31 May 2024 16:22:27 +0000 Subject: [PATCH] [auto-verifier] docs commit 9151361bc2d2995ec5a3a85ce1f0b8413fb35ec4 --- index.md | 8 +- notebook.html | 104 ++++++++++++------ notebook.pdf | Bin 538365 -> 561118 bytes src/math/{FastGCD.hpp.md => BinaryGCD.hpp.md} | 26 +++-- src/modint/BarrettReduction.hpp.md | 3 +- src/modint/modint.hpp.md | 1 + test/math/BinaryGCD.test.cpp.md | 54 +++++++++ test/math/FastGCD.test.cpp.md | 54 --------- test/template.hpp.md | 6 +- 9 files changed, 152 insertions(+), 104 deletions(-) rename src/math/{FastGCD.hpp.md => BinaryGCD.hpp.md} (66%) create mode 100644 test/math/BinaryGCD.test.cpp.md delete mode 100644 test/math/FastGCD.test.cpp.md diff --git a/index.md b/index.md index 2bd3bb5..70107ba 100644 --- a/index.md +++ b/index.md @@ -27,8 +27,8 @@ data: - name: src/math pages: - icon: ':heavy_check_mark:' - path: src/math/FastGCD.hpp - title: src/math/FastGCD.hpp + path: src/math/BinaryGCD.hpp + title: Binary GCD - name: src/modint pages: - icon: ':heavy_check_mark:' @@ -84,8 +84,8 @@ data: - name: test/math pages: - icon: ':heavy_check_mark:' - path: test/math/FastGCD.test.cpp - title: test/math/FastGCD.test.cpp + path: test/math/BinaryGCD.test.cpp + title: test/math/BinaryGCD.test.cpp - name: test/modint pages: - icon: ':heavy_check_mark:' diff --git a/notebook.html b/notebook.html index 7dd8abe..75e82f8 100644 --- a/notebook.html +++ b/notebook.html @@ -37,6 +37,7 @@

ICPC Notebook

  • math
    1. +
    2. BinaryGCD.hpp
  • modint
    1. @@ -223,6 +224,26 @@

      FastSet.hpp

      math

      +
      +

      BinaryGCD.hpp

      + md5: f3ab31 + +
      +
      +
      u64 ctz(u64 x) { return countr_zero(x); }
      +u64 binary_gcd(u64 x, u64 y) {
      +   if(!x || !y) return x | y;
      +   u64 n = ctz(x), m = ctz(y);
      +   x >>= n, y >>= m;
      +   while(x != y) {
      +      if(x > y) x = (x - y) >> ctz(x - y);
      +      else y = (y - x) >> ctz(y - x);
      +   }
      +   return x << min(n, m);
      +}
      +
      +
      +

      modint

      @@ -663,16 +684,6 @@

      高度合成数

      768 1344 - -factor -3111 -3311 -33111 -421111 -631111 -5311111 -6321111 - @@ -684,6 +695,9 @@

      高度合成数

      + + + @@ -694,37 +708,65 @@

      高度合成数

      - - - - - - - - - + + +
      $10^{13}$ $10^{14}$ $10^{15}$$10^{16}$$10^{17}$$10^{18}$
      10752 17280 26880
      factor532111116322111164211111163211111115422111111642111111114147264512103680
      +

      素数階乗

      - - - - + + + + + + + + + + + - - - - + + + + + + + + + + + +
      $≤n$$10^{16}$$10^{17}$$10^{18}$$n$$2$$3$$5$$7$$11$$13$$17$$19$$23$$29$
      $d^0(x)$4147264512103680$n\#$26302102310300305105109699690$2.2 \times 10^8$$6.5 \times 10^9$
      +

      階乗

      + + - - - - + + + + + + + + + + + + + + + + + + +
      factor83221111111632211111111842211111111$5!$$6!$$7!$$8!$$9!$$10!$$11!$$12!$
      1207205040403203628803628800$4.0 \times 10^7$$4.8 \times 10^8$
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zT88nhuQK)Gqn_pm`>hq*`G)^4f2UhM*l=#=RQ7iEYH_t$jLL|7Lq@>n(RFF;3l)+f oGUwRr8?5zz4jwz6zRz**KHt6DcMQ{BsH>&5XxNMy%Pg1wKh%SNV*mgE diff --git a/src/math/FastGCD.hpp.md b/src/math/BinaryGCD.hpp.md similarity index 66% rename from src/math/FastGCD.hpp.md rename to src/math/BinaryGCD.hpp.md index 51cb237..5040607 100644 --- a/src/math/FastGCD.hpp.md +++ b/src/math/BinaryGCD.hpp.md @@ -4,14 +4,14 @@ data: _extendedRequiredBy: [] _extendedVerifiedWith: - icon: ':heavy_check_mark:' - path: test/math/FastGCD.test.cpp - title: test/math/FastGCD.test.cpp + path: test/math/BinaryGCD.test.cpp + title: test/math/BinaryGCD.test.cpp _isVerificationFailed: false _pathExtension: hpp _verificationStatusIcon: ':heavy_check_mark:' attributes: links: [] - bundledCode: "#line 1 \"src/math/FastGCD.hpp\"\nu64 ctz(u64 x) { return countr_zero(x);\ + bundledCode: "#line 1 \"src/math/BinaryGCD.hpp\"\nu64 ctz(u64 x) { return countr_zero(x);\ \ }\nu64 binary_gcd(u64 x, u64 y) {\n if(!x || !y) return x | y;\n u64 n =\ \ ctz(x), m = ctz(y);\n x >>= n, y >>= m;\n while(x != y) {\n if(x >\ \ y) x = (x - y) >> ctz(x - y);\n else y = (y - x) >> ctz(y - x);\n }\n\ @@ -22,16 +22,20 @@ data: \ else y = (y - x) >> ctz(y - x);\n }\n return x << min(n, m);\n}\n" dependsOn: [] isVerificationFile: false - path: src/math/FastGCD.hpp + path: src/math/BinaryGCD.hpp requiredBy: [] - timestamp: '2024-05-31 23:58:41+09:00' + timestamp: '2024-06-01 01:21:46+09:00' verificationStatus: LIBRARY_ALL_AC verifiedWith: - - test/math/FastGCD.test.cpp -documentation_of: src/math/FastGCD.hpp + - test/math/BinaryGCD.test.cpp +documentation_of: src/math/BinaryGCD.hpp layout: document -redirect_from: -- /library/src/math/FastGCD.hpp -- /library/src/math/FastGCD.hpp.html -title: src/math/FastGCD.hpp +title: Binary GCD --- + +割り算を使わない高速な GCD + +## 使い方 + +- `u64 binary_gcd(u64 x, u64 y)`:$x$ と $y$ の最大公約数を計算する. + - $O(\log(x + y))$ 時間 diff --git a/src/modint/BarrettReduction.hpp.md b/src/modint/BarrettReduction.hpp.md index 59dc105..e42b3af 100644 --- a/src/modint/BarrettReduction.hpp.md +++ b/src/modint/BarrettReduction.hpp.md @@ -34,6 +34,7 @@ documentation_of: src/modint/BarrettReduction.hpp layout: document title: Barrett Reduction --- +- 参考実装:[AC Library](https://github.com/atcoder/ac-library/blob/master/atcoder/internal_math.hpp) 同じ mod でたくさん計算するとき,剰余算を掛け算に変換して高速化する. @@ -41,7 +42,7 @@ title: Barrett Reduction - `Barrett br(mod)`:Barrett Reduction を準備する. - 制約:`mod < 2^32` -- `br.mul(u64 a, u64 b)`:`a * b % mod` を計算する. +- `u64 br.mul(u64 a, u64 b)`:`a * b % mod` を計算する. - 制約:`a * b < 2^64` ## 仕組み diff --git a/src/modint/modint.hpp.md b/src/modint/modint.hpp.md index 0830782..1d5ad64 100644 --- a/src/modint/modint.hpp.md +++ b/src/modint/modint.hpp.md @@ -53,6 +53,7 @@ documentation_of: src/modint/modint.hpp layout: document title: Modint --- +- 参考実装:[AC Library (初期実装)](https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/atcoder/convolution.hpp) - タイプ速度重視の簡易 modint - 速度が欲しいとき:[32 bit で加減算をちゃんと書いた Modint](../extra/modint_fast.hpp) diff --git a/test/math/BinaryGCD.test.cpp.md b/test/math/BinaryGCD.test.cpp.md new file mode 100644 index 0000000..809da05 --- /dev/null +++ b/test/math/BinaryGCD.test.cpp.md @@ -0,0 +1,54 @@ +--- +data: + _extendedDependsOn: + - icon: ':heavy_check_mark:' + path: src/math/BinaryGCD.hpp + title: Binary GCD + - icon: ':heavy_check_mark:' + path: test/template.hpp + title: test/template.hpp + _extendedRequiredBy: [] + _extendedVerifiedWith: [] + _isVerificationFailed: false + _pathExtension: cpp + _verificationStatusIcon: ':heavy_check_mark:' + attributes: + '*NOT_SPECIAL_COMMENTS*': '' + PROBLEM: https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A + links: + - https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A + bundledCode: "#line 1 \"test/math/BinaryGCD.test.cpp\"\n#define PROBLEM \"https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A\"\ + \n#line 1 \"test/template.hpp\"\n#include \nusing namespace std;\n\ + using ll = long long;\nconst ll INF = LLONG_MAX / 4;\n#define rep(i, a, b) for(ll\ + \ i = a; i < (b); i++)\n#define all(a) begin(a), end(a)\n#define sz(a) ssize(a)\n\ + bool chmin(auto& a, auto b) { return a > b ? a = b, 1 : 0; }\nbool chmax(auto&\ + \ a, auto b) { return a < b ? a = b, 1 : 0; }\n#line 3 \"test/math/BinaryGCD.test.cpp\"\ + \nusing u64 = uint64_t;\n#line 1 \"src/math/BinaryGCD.hpp\"\nu64 ctz(u64 x) {\ + \ return countr_zero(x); }\nu64 binary_gcd(u64 x, u64 y) {\n if(!x || !y) return\ + \ x | y;\n u64 n = ctz(x), m = ctz(y);\n x >>= n, y >>= m;\n while(x !=\ + \ y) {\n if(x > y) x = (x - y) >> ctz(x - y);\n else y = (y - x) >>\ + \ ctz(y - x);\n }\n return x << min(n, m);\n}\n#line 5 \"test/math/BinaryGCD.test.cpp\"\ + \n\nint main() {\n mt19937_64 rnd;\n rep(shift, 0, 64) {\n rep(i, 0,\ + \ (ll)1e5) {\n u64 a = rnd() >> shift, b = rnd() >> shift;\n assert(gcd(a,\ + \ b) == binary_gcd(a, b));\n }\n }\n puts(\"Hello World\");\n}\n" + code: "#define PROBLEM \"https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A\"\ + \n#include \"test/template.hpp\"\nusing u64 = uint64_t;\n#include \"src/math/BinaryGCD.hpp\"\ + \n\nint main() {\n mt19937_64 rnd;\n rep(shift, 0, 64) {\n rep(i, 0,\ + \ (ll)1e5) {\n u64 a = rnd() >> shift, b = rnd() >> shift;\n assert(gcd(a,\ + \ b) == binary_gcd(a, b));\n }\n }\n puts(\"Hello World\");\n}\n" + dependsOn: + - test/template.hpp + - src/math/BinaryGCD.hpp + isVerificationFile: true + path: test/math/BinaryGCD.test.cpp + requiredBy: [] + timestamp: '2024-06-01 01:21:46+09:00' + verificationStatus: TEST_ACCEPTED + verifiedWith: [] +documentation_of: test/math/BinaryGCD.test.cpp +layout: document +redirect_from: +- /verify/test/math/BinaryGCD.test.cpp +- /verify/test/math/BinaryGCD.test.cpp.html +title: test/math/BinaryGCD.test.cpp +--- diff --git a/test/math/FastGCD.test.cpp.md b/test/math/FastGCD.test.cpp.md deleted file mode 100644 index fc1e56a..0000000 --- a/test/math/FastGCD.test.cpp.md +++ /dev/null @@ -1,54 +0,0 @@ ---- -data: - _extendedDependsOn: - - icon: ':heavy_check_mark:' - path: src/math/FastGCD.hpp - title: src/math/FastGCD.hpp - - icon: ':heavy_check_mark:' - path: test/template.hpp - title: test/template.hpp - _extendedRequiredBy: [] - _extendedVerifiedWith: [] - _isVerificationFailed: false - _pathExtension: cpp - _verificationStatusIcon: ':heavy_check_mark:' - attributes: - '*NOT_SPECIAL_COMMENTS*': '' - PROBLEM: https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A - links: - - https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A - bundledCode: "#line 1 \"test/math/FastGCD.test.cpp\"\n#define PROBLEM \"https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A\"\ - \n#line 1 \"test/template.hpp\"\n#include \nusing namespace std;\n\ - using ll = long long;\nconst ll INF = LLONG_MAX / 4;\n#define rep(i, a, b) for(ll\ - \ i = a; i < (b); i++)\n#define all(a) begin(a), end(a)\n#define sz(a) ssize(a)\n\ - bool chmin(auto& a, auto b) { return a > b ? a = b, 1 : 0; }\nbool chmax(auto&\ - \ a, auto b) { return a < b ? a = b, 1 : 0; }\n#line 3 \"test/math/FastGCD.test.cpp\"\ - \nusing u64 = uint64_t;\n#line 1 \"src/math/FastGCD.hpp\"\nu64 ctz(u64 x) { return\ - \ countr_zero(x); }\nu64 binary_gcd(u64 x, u64 y) {\n if(!x || !y) return x\ - \ | y;\n u64 n = ctz(x), m = ctz(y);\n x >>= n, y >>= m;\n while(x != y)\ - \ {\n if(x > y) x = (x - y) >> ctz(x - y);\n else y = (y - x) >> ctz(y\ - \ - x);\n }\n return x << min(n, m);\n}\n#line 5 \"test/math/FastGCD.test.cpp\"\ - \n\nint main() {\n mt19937_64 rnd;\n rep(i, 0, (ll)1e7) {\n u64 a = rnd(),\ - \ b = rnd();\n assert(gcd(a, b) == binary_gcd(a, b));\n }\n puts(\"Hello\ - \ World\");\n}\n" - code: "#define PROBLEM \"https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A\"\ - \n#include \"test/template.hpp\"\nusing u64 = uint64_t;\n#include \"src/math/FastGCD.hpp\"\ - \n\nint main() {\n mt19937_64 rnd;\n rep(i, 0, (ll)1e7) {\n u64 a = rnd(),\ - \ b = rnd();\n assert(gcd(a, b) == binary_gcd(a, b));\n }\n puts(\"Hello\ - \ World\");\n}\n" - dependsOn: - - test/template.hpp - - src/math/FastGCD.hpp - isVerificationFile: true - path: test/math/FastGCD.test.cpp - requiredBy: [] - timestamp: '2024-05-31 23:58:41+09:00' - verificationStatus: TEST_ACCEPTED - verifiedWith: [] -documentation_of: test/math/FastGCD.test.cpp -layout: document -redirect_from: -- /verify/test/math/FastGCD.test.cpp -- /verify/test/math/FastGCD.test.cpp.html -title: test/math/FastGCD.test.cpp ---- diff --git a/test/template.hpp.md b/test/template.hpp.md index 95de172..2c7a335 100644 --- a/test/template.hpp.md +++ b/test/template.hpp.md @@ -16,8 +16,8 @@ data: path: test/data-structure/FastSet.test.cpp title: test/data-structure/FastSet.test.cpp - icon: ':heavy_check_mark:' - path: test/math/FastGCD.test.cpp - title: test/math/FastGCD.test.cpp + path: test/math/BinaryGCD.test.cpp + title: test/math/BinaryGCD.test.cpp - icon: ':heavy_check_mark:' path: test/modint/BarrettReduction.test.cpp title: test/modint/BarrettReduction.test.cpp @@ -108,7 +108,7 @@ data: - test/string/SuffixArray.test.cpp - test/string/RollingHash.test.cpp - test/string/Manacher.test.cpp - - test/math/FastGCD.test.cpp + - test/math/BinaryGCD.test.cpp - test/modint/BarrettReduction.test.cpp - test/modint/modint.test.cpp documentation_of: test/template.hpp