{"action":"created","comment":{"url":"https://api.github.com/repos/g4s1k/Al/pulls/comments/215504468","pull_request_review_id":152780473,"id":215504468,"node_id":"MDI0OlB1bGxSZXF1ZXN0UmV2aWV3Q29tbWVudDIxNTUwNDQ2OA==","diff_hunk":"@@ -0,0 +1,188 @@\n+# Написать два алгоритма нахождения i-го по счёту простого числа.\r\n+# Первый - использовать алгоритм решето Эратосфена.\r\n+# Второй - без использования \"решета\".\r\n+# Проанализировать скорость и сложность алгоритмов.\r\n+\r\n+# Я сначала неправильно понял задачу и написал 3 функции нахождения простых чисел в последовательности из n целых чисел.\r\n+# Некоторый комментарий относительно моих соображений приведен после секции с данными функциями\r\n+\r\n+\r\n+from cProfile import run\r\n+\r\n+\r\n+def erat_alh_power(n):\r\n+    num_list = [num for num in range(2, n + 1)]              # < - Выписываем на дощечку все целые числа от 2 до n\r\n+    p = 2                                                    # < - первое простое число\r\n+    while True:                                              # < - пока не дойдем до последнего числа в качестве делителя\r\n+        for index in range(2*p - 2, n - 1, p):\r\n+            num = num_list[index]\r\n+            if (num > p) and (num != 0) and (num % p == 0):  # Протыкаем числа на каждый p-й шаг, начиная с 2p\r\n+                num_list[index] = 0\r\n+        if 2*p > n:\r\n+            break\r\n+        for index in range(p-2, n - 1):\r\n+            num = num_list[index]\r\n+            if (num > p) and (num != 0):                     # Все числа до p включительно или обведены, или проткнуты.\r\n+                p = num                                      # Мы видим первое непроткнутое число после p и берем его\r\n+                break                                        # в качестве нового делителя.\r\n+\r\n+    return num_list                                          # На выходе дощечка с простыми числами\r\n+\r\n+\r\n+# Строка вызова timeit: python -m timeit -n 100 -s \"from simpleanalyse import erat_alh_power\" \"erat_alh_power(100)\"\r\n+# результат 100 loops, best of 5: 26.8 usec per loop\r\n+# Строка вызова timeit: python -m timeit -n 100 -s \"from simpleanalyse import erat_alh_power\" \"erat_alh_power(1000)\"\r\n+# результат 100 loops, best of 5: 286 usec per loop\r\n+# Строка вызова timeit: python -m timeit -n 100 -s \"from simpleanalyse import erat_alh_power\" \"erat_alh_power(10000)\"\r\n+# результат 100 loops, best of 5: 2.94 msec per loop\r\n+\r\n+# Линейная сложность\r\n+\r\n+\r\n+def upgraded_erat_alh(n):\r\n+    num_list = [num for num in range(2, n + 1)]\r\n+    p = 2\r\n+    while True:\r\n+\r\n+        if p == 2:\r\n+            inc = p\r\n+        else:\r\n+            inc = 2*p\r\n+\r\n+        for index in range(p**2 - 2, n - 1, inc):\r\n+            num = num_list[index]\r\n+            if (num != 0) and (num % p == 0):\r\n+                num_list[index] = 0\r\n+\r\n+        index = p - 2\r\n+\r\n+        if p == 2:\r\n+            inc = 1\r\n+        else:\r\n+            inc = 2\r\n+\r\n+        while (index < n - 1):\r\n+            index += inc\r\n+            num = num_list[index]\r\n+            if num != 0:\r\n+                p = num\r\n+                break\r\n+\r\n+        if p**2 > n:\r\n+            break\r\n+    return num_list\r\n+\r\n+\r\n+# Строка вызова timeit: python -m timeit -n 100 -s \"from simpleanalyse import upgraded_erat_alh\" \"upgraded_erat_alh(100)\"\r\n+# результат 100 loops, best of 5: 12.9 usec per loop\r\n+# Строка вызова timeit: python -m timeit -n 100 -s \"from simpleanalyse import upgraded_erat_alh\" \"upgraded_erat_alh(1000)\"\r\n+# результат 100 loops, best of 5: 131 usec per loop\r\n+# Строка вызова timeit: python -m timeit -n 100 -s \"from simpleanalyse import upgraded_erat_alh\" \"upgraded_erat_alh(10000)\"\r\n+# результат 100 loops, best of 5: 1.35 msec per loop\r\n+\r\n+# Линейная сложность, примерно в 2 раза быстрее\r\n+\r\n+\r\n+def simple_power(n):\r\n+    num_list = [num for num in range(2, n + 1)]\r\n+    begin = 1\r\n+    end = n - 1\r\n+    while begin <= end:\r\n+        p = num_list[begin - 1]\r\n+        index = begin\r\n+        while index < end:\r\n+            if num_list[index] % p == 0:\r\n+                del(num_list[index])\r\n+                end -= 1\r\n+            else:\r\n+                index += 1\r\n+        begin += 1\r\n+\r\n+    return num_list\r\n+\r\n+# Строка вызова timeit: python -m timeit -n 100 -s \"from simpleanalyse import simple_power\" \"simple_power(100)\"\r\n+# результат 100 loops, best of 5: 44.8 usec per loop\r\n+# Строка вызова timeit: python -m timeit -n 100 -s \"from simpleanalyse import simple_power\" \"simple_power(1000)\"\r\n+# результат 100 loops, best of 5: 1.47 msec per loop\r\n+# Строка вызова timeit: python -m timeit -n 100 -s \"from simpleanalyse import simple_power\" \"simple_power(10000)\"\r\n+# результат 100 loops, best of 5: 83.1 msec per loop\r\n+\r\n+# Сложность явно не линейная на мое удивление, я думал, что так будет быстрее....Короткое - не всегда быстрое\r\n+\r\n+\r\n+# И вот тут я понял, что делаю немного не то........\r\n+# Согласно Википедии \"Решето́ Эратосфе́на — алгоритм нахождения всех простых чисел до некоторого целого числа n\"\r\n+# И лично мне совершенно непонятно, как можно реализовать с помощью этого алгоритма задачу вычисления i-го простого числа,\r\n+# так как необходимо знать, сколько конкретно нужно перебрать целых чисел, чтобы получить i-е простое число.\r\n+# Однако, если отступить от метода решета Эратосфена в чистом виде, то можно реализовать данную задачу, хотя и не очень\r\n+# эффективно.\r\n+\r\n+# Первый приходящий на ум алгоритм, не похожий на решето:\r\n+\r\n+def find_i_simple_num(i):\r\n+    count = 1\r\n+    num = 2\r\n+    simple_list = [2]\r\n+    while count < i:\r\n+        num += 1\r\n+        flag = True\r\n+        for item in simple_list:\r\n+            if num % item == 0:\r\n+                flag = False\r\n+        if flag:\r\n+            simple_list.append(num)\r\n+            count += 1\r\n+    return simple_list[i - 1]\r\n+\r\n+# Строка вызова timeit: python -m timeit -n 100 -s \"from simpleanalyse import find_i_simple_num\" \"find_i_simple_num(10)\"\r\n+# результат 100 loops, best of 5: 9.8 usec per loop\r\n+# Строка вызова timeit: python -m timeit -n 100 -s \"from simpleanalyse import find_i_simple_num\" \"find_i_simple_num(100)\"\r\n+# результат 100 loops, best of 5: 1.2 msec per loop\r\n+# Строка вызова timeit: python -m timeit -n 100 -s \"from simpleanalyse import find_i_simple_num\" \"find_i_simple_num(1000)\"\r\n+# результат 100 loops, best of 5: 192 msec per loop\r\n+\r\n+# Естественно, сложность нелинейная. Я думал при последнем запуске я не дождусь ответа.\r","path":"simpleanalyse.py","position":144,"original_position":144,"commit_id":"3a18747be8cbd21b40eb22f2cf63fe72368c209f","original_commit_id":"3a18747be8cbd21b40eb22f2cf63fe72368c209f","user":{"login":"Dzhoker1","id":31956448,"node_id":"MDQ6VXNlcjMxOTU2NDQ4","avatar_url":"https://avatars2.githubusercontent.com/u/31956448?v=4","gravatar_id":"","url":"https://api.github.com/users/Dzhoker1","html_url":"https://github.com/Dzhoker1","followers_url":"https://api.github.com/users/Dzhoker1/followers","following_url":"https://api.github.com/users/Dzhoker1/following{/other_user}","gists_url":"https://api.github.com/users/Dzhoker1/gists{/gist_id}","starred_url":"https://api.github.com/users/Dzhoker1/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dzhoker1/subscriptions","organizations_url":"https://api.github.com/users/Dzhoker1/orgs","repos_url":"https://api.github.com/users/Dzhoker1/repos","events_url":"https://api.github.com/users/Dzhoker1/events{/privacy}","received_events_url":"https://api.github.com/users/Dzhoker1/received_events","type":"User","site_admin":false},"body":"Два цикла и много проверок составных чисел. 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