takahashi-r/全ての組み合わせが出現するまでの回数を求める.ipynb

## 全ての組み合わせが出現するまでの回数を求める.ipynb
{
  "cells": [
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-11-21T02:38:42.239Z",
          "end_time": "2022-11-21T11:38:44.109000+09:00"
        },
        "trusted": true
      },
      "id": "4db176ee",
      "cell_type": "code",
      "source": "versioninfo()",
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": "Julia Version 1.8.0\nCommit 5544a0fab7 (2022-08-17 13:38 UTC)\nPlatform Info:\n  OS: Windows (x86_64-w64-mingw32)\n  CPU: 8 × Intel(R) Core(TM) i5-10210U CPU @ 1.60GHz\n  WORD_SIZE: 64\n  LIBM: libopenlibm\n  LLVM: libLLVM-13.0.1 (ORCJIT, skylake)\n  Threads: 1 on 8 virtual cores\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {},
      "id": "3d8a171e",
      "cell_type": "markdown",
      "source": "例えば、10個のおはじきがあるとする。ここから2個ランダムに選ぶ試行を繰り返すとき、全てのおはじきが最低1回は選ばれような試行回数を求めたい。"
    },
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-11-21T02:38:43.298Z",
          "end_time": "2022-11-21T11:39:02.327000+09:00"
        },
        "scrolled": true,
        "trusted": true
      },
      "id": "9aba2402",
      "cell_type": "code",
      "source": "using Plots\nusing Distributions\nusing StatsBase\nusing Random\npyplot()\n\nconst rng = Xoshiro(20221121)",
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 2,
          "data": {
            "text/plain": "Xoshiro(0x4f16cdc466490183, 0x25e86977b44ac0e8, 0x59f9101e471d992d, 0x7cd83307570ec348)"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-11-21T02:38:43.747Z",
          "end_time": "2022-11-21T11:39:19.418000+09:00"
        },
        "trusted": true
      },
      "id": "11bd7e42",
      "cell_type": "code",
      "source": "# 1回の試行で2個から1つ選ぶとき、両方の要素が最低1回は選ばれる試行回数を求める\nfunction plot_n2(iter)\n    ns = zeros(iter)\n    for i in 1:iter\n        n = 0\n        samples = []\n        while length(unique(samples)) != 2\n            push!(samples, rand(rng, Bernoulli(0.5)))\n            n += 1\n        end\n        ns[i] = n\n    end\n    histogram(1:max(ns...), ns, title=\"iter=$iter mean=$(mean(ns))\", label=false)\nend\nplot_n2(100)",
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 3,
          "data": {
            "image/png": 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"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-11-21T02:38:44.230Z",
          "end_time": "2022-11-21T11:39:22.234000+09:00"
        },
        "trusted": true
      },
      "id": "ca5052d7",
      "cell_type": "code",
      "source": "# 1回の試行でN個からd個をランダムで選ぶとき、全ての要素が最低1回は選ばれる試行回数を求める\n\"\"\"\niter: 試行回数\nN   : サンプル数\nd   : 抽出するサンプル数\n\"\"\"\nfunction plot_nd(iter, N, d)\n    ns = zeros(iter)\n    for i in 1:iter\n        n = 0\n        samples = []\n        while length(unique(samples)) != N\n            push!(samples, sample(rng, 1:N, d, replace=false)...)\n            n += 1\n        end\n        ns[i] = n\n    end\n    histogram(1:max(ns...), ns, title=\"iter=$iter N=$N d=$d mean=$(mean(ns))\", label=false)\nend\nplot_nd(1_000, 250, 60)",
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 4,
          "data": {
            "image/png": 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"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": false
      },
      "id": "db02fc2e",
      "cell_type": "code",
      "source": "",
      "execution_count": null,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": false
      },
      "id": "465274a4",
      "cell_type": "code",
      "source": "",
      "execution_count": null,
      "outputs": []
    }
  ],
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    "@webio": {
      "lastCommId": null,
      "lastKernelId": null
    },
    "_draft": {
      "nbviewer_url": "https://gist.github.com/155caec6a5e080dd691eee177dda9e69"
    },
    "gist": {
      "id": "155caec6a5e080dd691eee177dda9e69",
      "data": {
        "description": "public_2022_11_21_全ての組み合わせが出現するまでの回数を求める.ipynb",
        "public": true
      }
    },
    "hide_input": false,
    "kernelspec": {
      "name": "julia-1.8",
      "display_name": "Julia 1.8.0",
      "language": "julia"
    },
    "language_info": {
      "file_extension": ".jl",
      "name": "julia",
      "mimetype": "application/julia",
      "version": "1.8.0"
    },
    "toc": {
      "nav_menu": {},
      "number_sections": true,
      "sideBar": true,
      "skip_h1_title": false,
      "base_numbering": 1,
      "title_cell": "Table of Contents",
      "title_sidebar": "Contents",
      "toc_cell": false,
      "toc_position": {},
      "toc_section_display": true,
      "toc_window_display": false
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}