From 9151361bc2d2995ec5a3a85ce1f0b8413fb35ec4 Mon Sep 17 00:00:00 2001 From: tatyam Date: Sat, 1 Jun 2024 01:21:46 +0900 Subject: [PATCH] add BinaryGCD.md --- .verify-helper/docs/static/notebook.html | 104 ++++++++++++------ .verify-helper/docs/static/notebook.pdf | Bin 538365 -> 561118 bytes build/notebook.html | 21 ++++ docs/math/BinaryGCD.md | 11 ++ docs/modint/BarrettReduction.md | 3 +- docs/modint/modint.md | 1 + notebook.pdf | Bin 540996 -> 561118 bytes src/math/{FastGCD.hpp => BinaryGCD.hpp} | 0 .../{FastGCD.test.cpp => BinaryGCD.test.cpp} | 10 +- 9 files changed, 114 insertions(+), 36 deletions(-) create mode 100644 docs/math/BinaryGCD.md rename src/math/{FastGCD.hpp => BinaryGCD.hpp} (100%) rename test/math/{FastGCD.test.cpp => BinaryGCD.test.cpp} (50%) diff --git a/.verify-helper/docs/static/notebook.html b/.verify-helper/docs/static/notebook.html index 7dd8abe..75e82f8 100644 --- a/.verify-helper/docs/static/notebook.html +++ b/.verify-helper/docs/static/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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      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

      diff --git a/docs/math/BinaryGCD.md b/docs/math/BinaryGCD.md new file mode 100644 index 0000000..1c152c3 --- /dev/null +++ b/docs/math/BinaryGCD.md @@ -0,0 +1,11 @@ +--- +title: Binary GCD +documentation_of: //src/math/BinaryGCD.hpp +--- + +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/docs/modint/BarrettReduction.md b/docs/modint/BarrettReduction.md index d5ab9a9..ffe4a3b 100644 --- a/docs/modint/BarrettReduction.md +++ b/docs/modint/BarrettReduction.md @@ -2,6 +2,7 @@ title: Barrett Reduction documentation_of: //src/modint/BarrettReduction.hpp --- +- 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. @@ -9,7 +10,7 @@ documentation_of: //src/modint/BarrettReduction.hpp - `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/docs/modint/modint.md b/docs/modint/modint.md index ad52253..bafb6c0 100644 --- a/docs/modint/modint.md +++ b/docs/modint/modint.md @@ -2,6 +2,7 @@ title: Modint documentation_of: //src/modint/modint.hpp --- +- 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/notebook.pdf b/notebook.pdf index 5a5d08f08f0537bb19b7c41293bc5bec42cdb94c..da23effa4aa5a239ee9cf946b3e73b011f78df23 100644 GIT binary patch delta 401433 zcma&NWmKJQk~RE9NFcbo2e;r3!QI{AKp;qPw>u%YoZv3O-8E=}9o!D??jGFo9q8_v zo_=Q5_wpx;{Hawp``Wduc2%bz`C~Qb(Y<2h;(W); z6D8cqm9Y{dmYxyYJ$G-UJh_*@J}u1af6W^~PPkM>Aa)gfuH0(o6s|XEJ)n3&dXhh- z`sc+%_()6)?=#jHGkrHZ{yXOeTc*(UR#11lPI8|9WQ zaxiA12Ik#c-o`c8CpAAc*|Tf&y`6w~Z%X^L-leUT{1tvZ zo}`MA+U+hGUg_~3;@+O_0e`=(geQob`*B=rC(j|)!dd>uEVVHE)cm~mbx7^HoTaDZ 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