Algorithm_5.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Algorithm 5.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNvpyXqXvNkJmgHLvWBSS4j",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Ohgangrae/ai/blob/main/Algorithm_5.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vpiKvvO9BuZ2"
      },
      "outputs": [],
      "source": [
        "# 단순 삽입법\n",
        "\n",
        "# 삽입하려는 데이터를 변수를 따로 하나 준비하여 대입한다. \n",
        "# 변수의 데이터를 이미 정렬된 데이터와 순서대로 비교한다. \n",
        "# 변수의 데이터보다 작은 데이터가 발견되면 그 뒤의 요소에 변수의 데이터를 삽입한다. \n",
        "\n",
        "\n",
        "# 올바른 순서가 되도록 하나씩 데이터를 삽입한다. \n",
        "# 단순 삽입법은 삽입 정렬, 기본 삽입법, 삽입법이라고 한다. \n",
        "\n",
        "0 1 2 3 4 \n",
        "5 3 4 1 2\n",
        "\n",
        "\n",
        "일단 index 0 을 정렬된 공이라고 가정한다. \n",
        "\n",
        "\n",
        "5        3 4 1 2\n",
        "--   정렬된 공으로 가정\n",
        "\n",
        "정렬이 안된 공들 중 첫번째 즉3을 정렬된 공들 중 올바른 순서가 되도록 삽입한다. \n",
        "\n",
        "3 5      4 1 2\n",
        "\n",
        "0번째 칸의 앞에는 없기 때문에 5를 하나뒤로 이동하고 3인공을 0번째 칸에 넣는다. \n",
        "이제 3과 5 는 정렬된 상태가 되었다. \n",
        "\n",
        "\n",
        "다시 정렬이 안된 공들 중 첫번째 즉 4를 정렬된 공들 중 올바른 순서가 되도록 삽입한다. \n",
        "\n",
        "이 시점에서 '정렬된 공'은 0번칸의 3과 1번칸의 5 사이가 되므로 3의 뒤, 5의 앞이다. \n",
        "4를 5 앞에 삽입한다. \n",
        "\n",
        "3  4  5       1 2\n",
        "\n",
        "\n",
        "다시 정렬이 안된 공들 중 첫번째 즉 1를 정렬된 공들 중 올바른 순서가 되도록 삽입한다. \n",
        "\n",
        "정렬된 공은 0번 칸의 3 1번칸의 4 2번칸의 5이다. 여기서 올바른 위치는 3의 앞이므로 \n",
        "1을 3의 앞에 삽입한다. \n",
        "\n",
        "1  3  4  5      2\n",
        "-----------\n",
        "마지막으로 2를 정렬된 공들 중 올바른 순서가 되도록 삽입한다. \n",
        "\n",
        "1  2  3  4  5"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# 퀵 정렬 quick sort\n",
        "\n",
        "데이터를 대소 그룹의 둘로 나누어 분해하여 전체를 정렬하는 방식의 알고리즘\n",
        "실행 속도가 빠른 것이 특징이다. \n",
        "\n",
        "대량의 데이터를 정렬할 때 자주 사용되며 유명한 정렬 알고리즘 중에서도 실제로 사용되는\n",
        "빈도가 높은 가장 중요한 알고리즘의 하나이다. \n",
        "\n",
        "\n",
        "5 3 7 6 8 4 1 2 9\n",
        "--\n",
        "우선 정렬의 기준이 되는 공을 선택하자. 첫 번째 기준은 5번 공이다. \n",
        "\n",
        "기준 공 5보다 작은 공은 5의 앞으로 이동시키고 \n",
        "기준 공 5보다 콘 공은 5의 뒤로 이동 시킨다. \n",
        "            \n",
        "3 4 1 2    5    7 6 8 9\n",
        "             --                 5  는 정렬된 상태\n",
        "\n",
        "1 2       3      4       5            6      7      8  9\n",
        "           --              --                  --                3과 7이 정렬된 상태가 되었다. \n",
        "\n",
        "1  2  3  4  5  6  7  8  9   더이상 정렬이 필요하지 않은 4, 6 은 그대로 확정 되었고\n",
        "                                 1,2    8,9 역시 위의 과정을 통해 정렬된 상태가 되었다. \n"
      ],
      "metadata": {
        "id": "bwoBLocCE2qe"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "에라토스테네스의 체\n",
        "# 소수를 찾아내는 알고리즘 (특정 범위의 수 중에서 소수를 찾는 알고리즘)\n",
        "# 소수는 2 이상의 정수 중 1과 그 수 자신으로만 나눌수 있는 수\n",
        "# 소수는 나열되어 있는 구간이 불규칙하므로 임의 로 찾기 어렵다. \n",
        "\n",
        "2 3 5 7 11 13 17 .....\n",
        "\n",
        "소수인지 아닌지를 구분하는 것은 의외로 아주 어렵다. \n",
        "\n",
        "예를들면 3의 배수는 3,6,9,12,15....처럼 3 간격으로 나열되면 비교적 간단하다. 하지만 소수는 \n",
        "규칙성이 없기 때문에 간격이 불규칙하고 랜덤하다. 즉 소수를 한번에 열거하기는 어렵다. \n",
        "\n",
        "하나하나 그 수보다 작은 숫자로 나누어 보고 나눌수 있으면 소수가 아닌 것으로 판단할 수 있다. \n",
        "이 방법은 비효율적이고, 수의 범위가 커지면 어마어마하게 많은 시간이 요소된다. \n",
        "\n",
        "고대 그리스의 에라토스테네스는 위와 같은 방법을 개선하여 소수를 효율적으로 발견하는 방법을\n",
        "고안했다. \n",
        "\n",
        "에라토스테네스의 체는 '그 수의 제곱근보다 작은 소수의 배수를 없애면 남은 수가 소수다'\n",
        "라는 생각을 바탕으로 소수를 찾는 방법을 말한다. \n",
        "\n",
        "예를 들면 100 이하의 소수를 모두 찾고 싶으면 가장먼저 100의 제곱근 이하의 소수를 선택한다. \n",
        "100의 제곱근은 10이므로 10 이하에서의 모든 소수는 2,3,5,7 네개이다. \n",
        "\n",
        "먼저 2부터 100까지 중 2는 남기고 2의 배수를 모두 삭제한다. \n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "6Z6GkHKgHXr6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "oWOR2I-Ygl02"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "fhgibJHngmq-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "vW-hLtJHgoOY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "나누어 지는 수는 모두 소수가 아니므로 즉, 제곱근 이하의 어느 소수로도 나누어\n",
        "떨어지지 않고 끝까지 체에 남아 있는 수가 소수이다.  "
      ],
      "metadata": {
        "id": "0iRumE1zguUA"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "에라토스 테네스의 체 알고리즘\n",
        "1. 어떤 수 이하의 모든 정수 데이터를 준비\n",
        "2. 어떤 수의 제곱근 보다 작은 소수의 배수를 제거한다. \n",
        "3. 마지막까지 남은 수를 출력한다. \n"
      ],
      "metadata": {
        "id": "_ffvdHTmgvCi"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# 유클리드 알고리즘\n",
        "\n",
        "# 최대 공약수를 구하는 알고리즘\n",
        "# 최대 공약수는 공통의 약수 중에서 가장 큰수를 말한다. \n",
        "# 반복 구조를 이용하여 해결한다는 점에서 프로그래머가 알고 있어야 할 대표적인 알고리즘이다. \n",
        "\n",
        "약수  \n",
        "3의 약수  1, 3\n",
        "4의 약수 1,2,4\n",
        "5의 약수 1,5\n",
        "6의 약수 1,2,3,6       \n",
        "8의 약수 1,2,4,8\n",
        "12의 약수 1,2,3,4,6\n",
        "\n",
        "공약수 : 공통된 약수\n",
        "4,6 의 공약수  1,2\n",
        "8,12의 공약수 1.2.4\n",
        "6, 12의 공약수 1,2,3,6\n",
        "최대공약수 : 공통된 약수들 중 제일 큰 숫자.\n",
        "4,6의 최대공약수는 2\n",
        "8,12의 최대공약수는 4\n",
        "6,12의 최대공약수는 6\n"
      ],
      "metadata": {
        "id": "A1DMhP2bgwZy"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "유클리드 알고리즘이란? 두수의 나눗셈을 반복하여 최대 공약수를 구한다. \n",
        "\n",
        "12 와 6의 최대 공약수\n",
        "\n",
        "12   %   6    =   0  # 나머지가 없이 딱 나누어 떨어지는데 사용된 수가 최대 공약수\n",
        "\n",
        "\n",
        "221 % 143 = 78\n",
        "         143 % 78 = 65\n",
        "                  78 % 65 = 13\n",
        "                          65 % 13 = 0    # 0이 나올때의 나누어준 수 13 이 바로 최대 공약수"
      ],
      "metadata": {
        "id": "IN2DvkV1onzs"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# 나머지를 구하는 나눗셈의 산수 연산자 %를 사용한다. \n",
        "# 딱 나누어 떨어지지 않을 때에 나눗셈을 반복하는 처리를 반복 구조로 표현한다. \n",
        "# 반복 구조에는 선판정형과 후판정형이 있다.  \n",
        "# 선 판정형 구조는 반복 처리에 들어 가기 전에 조건식으로 판정을 실시한다. \n",
        "# 후 판정형 구조는 반복 처리 후에 조건식으로 판정을 실시한다.  do ~ while 자바"
      ],
      "metadata": {
        "id": "TlWPFNpcgyrK"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "빅오 표기법\n",
        "\n",
        "알고리즘이 얼마 빠른지를 표시하는 특별한 방법\n",
        "\n",
        "탐색\n",
        "                  단순 탐색                       이진 탐색\n",
        "100개            100밀리초                       7밀리 초\n",
        "10000개          10초                            14밀리 초\n",
        "1000000000개   11일                            32밀리 초\n",
        "\n",
        "원소의 개수가 증가해도 이진탐색 시간은 얼마 늘어나지 않는다. \n",
        "하지만 단순탐색의 시간은 어마어마하게 증가 된다. \n",
        "원소의 갯수가 커질수록 이진캄색은 훨씬 빨라지게 된다. \n",
        "\n",
        "빅오 표기법은 알고리즘이 얼마나 빠른지만 말해준다. \n",
        "\n",
        "단순 탐색은 원소를 하나하나 확인하기 때문에 n번 연산을 해야한다. \n",
        "빅오 표기법으로는 O(n) 이다. 빅오 표기법은 속도를 시간단위로 세지 않는다. \n",
        "빅오 표기법은 연산 횟수를 비교하기 위한 개념이다. \n",
        "단순 탐색의 실행시간은 O(n) 로 나타낸다. \n",
        "\n",
        "O(log n) 이진 탐색\n",
        "\n",
        "O(n) 선형 시간 , 단순 탐색\n",
        "\n",
        "O(n * log n) \n",
        "\n",
        "O(n^2) 선택 정렬, 느린 정렬 알고리즘\n",
        "\n",
        "O(n!) 외판원 문제, 정말 느린 알고리즘\n",
        "\n",
        "알고리즘의 속도는 시간으로 측정하지 않는다. \n",
        "알고리즘의 시간은 어떻게 증가하는가로 측정한다. \n",
        "알고리즘의 시간은 빅오표기법으로 나타낸다. \n"
      ],
      "metadata": {
        "id": "Qx8-vWHtoqQq"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}