{"id":136183,"date":"2020-07-21T15:34:29","date_gmt":"2020-07-21T07:34:29","guid":{"rendered":"http:\/\/4563.org\/?p=136183"},"modified":"2020-07-21T15:34:29","modified_gmt":"2020-07-21T07:34:29","slug":"10-9-8-1-%e7%9a%84%e6%97%b6%e9%97%b4%e5%a4%8d%e6%9d%82%e5%ba%a6%e6%98%af%e5%a4%9a%e5%b0%91%ef%bc%9f","status":"publish","type":"post","link":"http:\/\/4563.org\/?p=136183","title":{"rendered":"10 + 9 + 8 + … + 1 \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f\u591a\u5c11\uff1f"},"content":{"rendered":"
\n
\n
\n

10 + 9 + 8 + … + 1 \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f\u591a\u5c11\uff1f <\/h1>\n

<\/p>\n

\n
\u8cc7\u6df1\u5927\u4f6c : smallyu <\/span> <\/i> 7<\/span> <\/div>\n
<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/p><\/div>\n
<\/p>\n

\u6bd4\u5982\u6709\u4e00\u4e2a\u4e24\u5c42\u7684\u5faa\u73af\uff0c\u5982\u679c\u662f<\/p>\n

n = 0   for i in range(10):       for j in range(10):       n += 1        print(n)  \/\/ 100 <\/code><\/pre>\n
\u590d\u6742\u5ea6\u5e94\u8be5\u662f n^2 \u5427\uff0c\u90a3\u8fd9\u6837\u5462\uff1a<\/p>\n
n = 0 for i in range(10):  for j in range(i, 10):   n += 1              print(n)   \/\/ 55 <\/code><\/pre>\n
\u76f8\u5f53\u4e8e 10 + 9 + 8 + … + 1 = 55\uff0c\u8fd9\u4e2a\u590d\u6742\u5ea6\u5e94\u8be5\u600e\u4e48\u63cf\u8ff0\uff1f<\/p>\n
\u4e24\u4e2a\u5faa\u73af\u8fd8\u597d\u7406\u89e3\uff0c\u5982\u679c\u662f\u4e09\u5c42\u5faa\u73af\u5462\uff1a<\/p>\n
 n = 0   for i in range(10):    for j in range(i, 10):     for k in range(j, 10):      n += 1               print(n)   \/\/ 220 <\/code><\/pre>\n
\u4e3b\u8981\u662f\u4e09\u5c42\u5faa\u73af\u5c31\u60f3\u4e0d\u660e\u767d\u4e86\uff0c\u6c42\u6559\u8fd9\u600e\u4e48\u7406\u89e3\u5462\uff1f<\/p>\n<\/p><\/div>\n
 \u5927\u4f6c\u6709\u8a71\u8aaa<\/b> (24<\/span>)        <\/div>\n
 <\/div>\n<\/p><\/div>\n<\/p><\/div>\n
    \n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : Mistwave <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 https:\/\/www.cs.cmu.edu\/~adamchik\/15-121\/lectures\/Algorithmic%20Complexity\/complexity.html                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : sivacohan <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u4f60\u8fd9\u4e09\u4e2a\u4f8b\u5b50\u90fd\u662f O(1)
    \u56e0\u4e3a\uff0c\u8f93\u5165\u4e0e\u8f93\u51fa\u65e0\u5173\u3002<\/p>\n
    \u4f60\u91cd\u65b0\u770b\u4e00\u4e0b\u5b9a\u4e49\u5427\uff0c\u4f60\u6982\u5ff5\u90fd\u7406\u89e3\u9519\u4e86\u3002                                                            <\/p><\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : ChanKc <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u5728\u6211\u770b\u6765\u90fd\u662f O(1)                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : Mutoo <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u5927 O \u8868\u793a\u6cd5\u53ea\u53d6\u4e0e\u5f53\u95ee\u9898\u89c4\u6a21 n \u8d8b\u4e8e\u65e0\u7a77\u5927\u7684\u65f6\u5019\uff0c\u4e0e n \u76f8\u5173\u7684\u6700\u9ad8\u6b21\u5e42\u9879\u3002\u5e38\u6570\u548c\u4f4e\u6b21\u9879\u90fd\u53ef\u4ee5\u5ffd\u7565\u3002                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : kilasuelika <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u8003\u8651\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u5faa\u73af\u8303\u56f4\u4e00\u822c\u662f\u4e2a\u53d8\u91cf\u3002\u6bd4\u5982\uff1a
    for i in range(n):
     ….<\/p>\n
    \u590d\u6742\u5ea6\u4e3a O(n)\u3002
    for i in range(n):
     for j in range(i,n):
     …
    \u590d\u6742\u5ea6\u4e3a O \uff09                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : kilasuelika <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u8003\u8651\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u5faa\u73af\u8303\u56f4\u4e00\u822c\u662f\u4e2a\u53d8\u91cf\u3002\u6bd4\u5982\uff1a
    for i in range(n):
     ….<\/p>\n
    \u590d\u6742\u5ea6\u4e3a O(n)\u3002
    for i in range(n):
     for j in range(i,n):
     …
    \u590d\u6742\u5ea6\u4e3a O(n^2)\u3002                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : putaozhenhaochi <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u65f6\u95f4\u590d\u6742\u5ea6\u63cf\u8ff0\u7684\u662f\u589e\u957f\u8d8b\u52bf                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : polaa <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u90fd\u662f O(1) …
    \u628a 10 \u6362\u4e3a n \u7684\u8bdd<\/p>\n
    \u7b2c\u4e00\u4e2a O(n^2) 
    \u7b2c\u4e8c\u4e2a O(n^2) \u2211(i = 1~n) \u2211 (j = i~n) = \u222b\u222b = 1\/2 n^2 
    \u7b2c\u4e09\u4e2a \u540c\u7406<\/p>\n
    \u4e0d\u77e5\u9053\u7b97\u9519\u6ca1 QAQ                                                            <\/p><\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : optional <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u4e2d\u95f4\u7684 n += 1 \u88ab\u6267\u884c\u4e86\u51e0\u6b21\u5c31\u662f\u591a\u5c11                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : octobered <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u90fd\u662f O1\uff0c\u90fd\u786e\u5b9a\u6b21\u6570\u4e86
    ps: \u8fd9\u4e2a\u5199\u6210 c\uff0c\u653e\u5230 gcc \u91cc\u5f00 O3 \u5c31\u76f4\u63a5 print(100)\u4e86                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : allenhu <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u4f60\u7684\u8fd0\u7b97\u6b21\u6570\u6ca1\u6709\u53d7 n \u7684\u5f71\u54cd\uff0c\u662f\u5e38\u91cf\uff0c\u6240\u4ee5\u662f o1                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : allenhu <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u4e3e\u4f8b\uff1a\u5047\u8bbe\u4ece 1 \u4e00\u76f4\u52a0\u5230 n \u6c42\u548c\uff0c\u4f60\u9700\u8981\u52a0 n \u6b21\uff0c\u6b64\u65f6\u8fd0\u7b97\u6b21\u6570\u4e0e n \u76f8\u5173\u4e86\uff0c\u5b83\u662f o \uff08 n \uff09                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : necomancer <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 O(N^2), O(N^3)\uff0c\u4e0a\u9762\u89e3\u91ca\u5f88\u6e05\u695a\u4e86\uff0c\u5982\u679c\u4f60\u8fd8\u662f\u6709\u56f0\u60d1\u7684\u8bdd\uff1a<\/p>\n
    In [1]: s = 0<\/p>\n
    In [2]: for i in range(100):
     …: for j in range(i, 100):
     …: s += 1
     …:<\/p>\n
    In [3]: s
    Out[3]: 5050<\/p>\n
    In [4]: s = 0<\/p>\n
    In [5]: for i in range(1000):
     …: for j in range(i, 1000):
     …: s += 1
     …:<\/p>\n
    In [6]: s
    Out[6]: 500500<\/p>\n
    In [7]: s\/5050
    Out[7]: 99.10891089108911<\/p>\n
    In [8]: (1000\/100) **2
    Out[8]: 100.0                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : whileFalse <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u7b2c\u4e8c\u4e2a\u662f O(n^2)\uff0c\u7b2c\u4e09\u4e2a\u662f O(n^3)\u3002
    \u4f60\u5148\u8981\u7406\u89e3\u4e00\u4e2a\u6982\u5ff5\uff1aO(n\/2)\u3001O(n+100)\u7684\u6b63\u786e\u8868\u8ff0\u662f O(n)\u3002
    \u4e5f\u5c31\u662f\u8bf4\uff0c\u4ee5\u4e0b\u4e09\u4e2a\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f\u4e00\u6837\u7684\uff1a
    1. for i in range(n): dosomething(i)
    2. for i in range(n\/2): dosomething(i)
    3. for i in range(n+100): dosomething(i)
    \u65f6\u95f4\u590d\u6742\u5ea6\u53d6\u503c\u4e3a\u6574\u4e2a\u7b97\u6cd5\u5faa\u73af\u6b21\u6570\u516c\u5f0f\u4e2d\u4e2d\u6210\u957f\u901f\u5ea6\u6700\u5feb\u7684\u90a3\u4e2a\u90e8\u5206\uff0c\u6210\u957f\u901f\u5ea6\u8f83\u4f4e\u7684\u90e8\u5206\u88ab\u76f4\u63a5\u5220\u9664\uff1b\u7cfb\u6570\u5168\u90e8\u8bbe\u4e3a 1 \u3002
    \u5bf9\u4e8e\u7b2c\u4e8c\u4e2a\u7b97\u6cd5\uff0c\u5176\u5faa\u73af\u6b21\u6570\u4e3a n*(n+1)\/2=0.5 * n^2 + 0.5 * n \u3002”0.5 n^2″\u7684\u6210\u957f\u901f\u5ea6\u5927\u4e8e\u201c0.5*n\u201d\uff0c\u6240\u4ee5 0.5*n \u88ab\u5220\u9664\uff0c\u5269\u4e0b”0.5 n^2″\uff1b\u7136\u540e\u7cfb\u6570\u8bbe\u7f6e\u4e3a 1\uff0c\u5373\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n^2)                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : raysonx <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u53cd\u5bf9 13 \u548c 14 \u90fd\u7b54\u6848\u3002\u9898\u4e3b\u7684\u4ee3\u7801\u590d\u6742\u5ea6\u5747\u4e3a O \uff08 1 \uff09\u3002<\/p>\n
    \u6309\u7167\u5faa\u73af\u5c42\u6570\u731c\u6d4b\u590d\u6742\u5ea6\u662f\u5178\u578b\u7684\u6c11\u79d1\u3002\u4e3b\u53ef\u4ee5\u770b\u4e00\u4e0b\u5806\u6392\u5e8f\u7b97\u6cd5\u4e2d\u5efa\u5806\u7684\u590d\u6742\u5ea6\u4e3a\u4ec0\u4e48\u662f O \uff08 n \uff09\u3002                                                            <\/p><\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : w99w <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 O(n)                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : w99w <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u53e6\u5916\uff0c\u4e3b\u4f60\u7684\u5199\u6cd5\u5c31\u4e0d\u592a\u5bf9\u3002
    \u4e00\u822c\u4e0d\u662f n+=1,\u800c\u662f n+=i
    1~n \u76f8\u52a0\u6574\u4e2a\u8fd0\u7b97\u8fc7\u7a0b\u9700\u8981\u8ba1\u7b97 n \u6b21\u52a0\u6cd5\u3002
    \u6240\u4ee5\u662f O(n)                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : wellsc <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u5e38\u91cf 1                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : iseki <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u6211\u8bb0\u5f97\u4ed6\u4eec\u8bb2\u5927 O \u7b26\u53f7\u7684\u65f6\u5019\u8bb2\u4e86\u4e0b\u03b8\u6e10\u8fdb\u7b26\u53f7 emmm\uff0c\u53d6\u6700\u9ad8\u6b21\u9879\u5e42\uff1f                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : newtype0092 <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u5982\u679c\u4f60\u662f\u60f3\u6c42\u7b49\u5dee\u6570\u5217\u7684\u590d\u6742\u5ea6\uff0c
    (1+n)*n\/2 = n^2\/2 + n\/2
    \u590d\u6742\u5ea6\u53ea\u770b n^2                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : newtype0092 <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u6211\u4e5f\u88ab\u81ea\u5df1\u7ed5\u660f\u4e86\uff0c\u770b\u8d77\u6765\u786e\u5b9e\u662f O(1)\u554a                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : SiliusMo <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u4ece 1 \u52a0\u5230 10 \u8fd9\u4e2a\u4ee3\u7801\u91cc\u90fd\u6ca1\u6709 n. \u54ea\u91cc\u6765\u7684 O(n)?
    \u65e0\u8bba\u4f60\u5957\u51e0\u5c42\u5faa\u73af\uff0c\u9700\u8981\u7684\u6b65\u9aa4\u90fd\u662f\u5e38\u91cf, \u6240\u4ee5\u7ed3\u679c\u662f O(A). A \u4ee3\u8868\u4e00\u4e2a\u5e38\u6570. \u5176\u5b9e\u4e5f\u5c31\u662f O(1).                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : ourFEer <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 O(1)                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
     \u8cc7\u6df1\u5927\u4f6c : wnpllrzodiac <\/span>  <\/div>\n
     <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                 \u590d\u6742\u5ea6\u548c \u6307\u4ee4\u4f18\u5316\u662f\u4e24\u4e2a\u6982\u5ff5\u3002\u867d\u7136\u73b0\u5728\u7f16\u8bd1\u5668\u667a\u80fd\u4e86\uff0c\u800c\u4e14\u673a\u5668\u6027\u80fd\u9ad8\u4e86\uff0c\u5f88\u591a\u4e1c\u897f\u90fd\u4e0d\u9700\u8981\u4eba\u8003\u8651\u4e86                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n","protected":false},"excerpt":{"rendered":"
    10 + 9 + 8 + &#82…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[],"tags":[],"_links":{"self":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts\/136183"}],"collection":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=136183"}],"version-history":[{"count":0,"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts\/136183\/revisions"}],"wp:attachment":[{"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=136183"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=136183"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=136183"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}