{"id":237,"date":"2016-12-21T11:40:03","date_gmt":"2016-12-21T03:40:03","guid":{"rendered":"http:\/\/ayonel.me\/?p=237"},"modified":"2016-12-21T15:03:46","modified_gmt":"2016-12-21T07:03:46","slug":"largest_subvector","status":"publish","type":"post","link":"https:\/\/ayonel.malash.net\/index.php\/2016\/12\/21\/largest_subvector\/","title":{"rendered":"\u8ba1\u7b97\u6700\u5927\u8fde\u7eed\u5b50\u5411\u91cf"},"content":{"rendered":"

\u95ee\u9898\u63cf\u8ff0\uff1a<\/strong>\u8f93\u5165\u5177\u6709n\u4e2a\u6d6e\u70b9\u6570\u7684\u5411\u91cfx\uff0c\u8f93\u51fa\u5411\u91cfx\u4e2d\u4efb\u4f55\u8fde\u7eed\u5b50\u5411\u91cf\u4e2d\u7684\u6700\u5927\u548c\u3002\u4f8b\u5982\uff1a
\n\u5982\u679cx={1,2,3}\uff0c\u5219output=6
\n\u5982\u679cx={1,-2,3}\uff0c\u5219output=3
\n\u5982\u679cx={31,-41,59,26,-53,58,97,-93,-23,84},\u5219output=187
\n\u5f53\u6240\u6709\u8f93\u5165\u4e3a\u8d1f\u6570\u65f6\uff0c\u6700\u5927\u8fde\u7eed\u5b50\u5411\u91cf\u4e3a\u7a7a\u5411\u91cf\uff0c\u8f93\u51fa\u4e3a0<\/p>\n

\u95ee\u9898\u6765\u6e90\uff1a<\/strong>\u300a\u7f16\u7a0b\u73e0\u7391 \u7b2c2\u7248\u300b\u7b2c8\u7ae0<\/p>\n

\u5bf9\u4e8e\u8be5\u95ee\u9898\uff0c\u5e73\u65b9\u7b97\u6cd5\u4e66\u4e2d\u7ed9\u51fa\u4e86\u4e24\u79cd\uff0c\u90fd\u6bd4\u8f83\u76f4\u89c2\u3002<\/p>\n

\u4f5c\u8005\u63d0\u51fa\u4e86\u4e00\u79cdO(nlogn)\u7684\u7b97\u6cd5<\/strong>\uff0c\u4e3b\u8981\u5229\u7528\u5206\u6cbb\u548c\u9012\u5f52\u3002\u5c06\u539f\u5411\u91cf\u4ece\u4e2d\u95f4\u5206\u5f00\uff0c\u5206\u4e3a\u5de6\u5411\u91cf\u548c\u53f3\u5411\u91cf\u3002\u9012\u5f52\u5bfb\u627e\u5de6\u5411\u91cf\uff0c\u53f3\u5411\u91cf\uff0c\u4ee5\u53ca\u4ee5\u5206\u5f00\u70b9\u4e3a\u8d77\u70b9\u7684\u5411\u5de6\u6700\u5927\u5411\u91cf+\u5411\u53f3\u6700\u5927\u5411\u91cf\u3002
\n\u4e66\u4e2d\u4e5f\u7ed9\u51fa\u4e86\u7b97\u6cd5\u3002\u5982\u4e0b\uff1a<\/p>\n

#include <stdlib.h><\/span>
\nint<\/span> x[<\/span>10<\/span>]<\/span> =<\/span> {<\/span>31<\/span>,-<\/span>41<\/span>,<\/span>59<\/span>,<\/span>26<\/span>,-<\/span>53<\/span>,<\/span>58<\/span>,<\/span>97<\/span>,-<\/span>93<\/span>,-<\/span>23<\/span>,<\/span>84<\/span>}<\/span>;<\/span>
\nfloat<\/span> max(<\/span>float<\/span> x,<\/span> float<\/span> y)<\/span> {<\/span>
\n    return<\/span> x >=<\/span> y?<\/span> x :<\/span> y;<\/span>
\n}<\/span>
\n
\nfloat<\/span> max3(<\/span>float<\/span> x,<\/span> float<\/span> y,<\/span> float<\/span> z)<\/span> {<\/span>
\n    int<\/span> larger =<\/span> max(<\/span>x,<\/span> y)<\/span>;<\/span>
\n    return<\/span> max(<\/span>larger,<\/span> z)<\/span>;<\/span>
\n}<\/span>
\n\/\/\u6838\u5fc3\u7b97\u6cd5<\/span>
\nfloat<\/span> maxsum3(<\/span>int<\/span> l,<\/span> int<\/span> u)<\/span> {<\/span>
\n    if<\/span> (<\/span>l ><\/span> u)<\/span>
\n        return<\/span> 0<\/span>;<\/span>
\n    if<\/span> (<\/span>l ==<\/span> u)<\/span>
\n        return<\/span> max(<\/span>0<\/span>,<\/span> x[<\/span>1<\/span>]<\/span>)<\/span>;<\/span>
\n    int<\/span> m =<\/span> (<\/span>l +<\/span> u)<\/span> \/<\/span> 2<\/span>;<\/span>
\n    \/\/\u627e\u51fa\u4ee5m\u4e3a\u8d77\u70b9\u7684\u5411\u5de6\u7684\u6700\u5927\u5b50\u5411\u91cf<\/span>
\n    float<\/span> lmax  =<\/span> 0<\/span>;<\/span>
\n    float<\/span> sum =<\/span> 0<\/span>;<\/span>
\n    for<\/span> (<\/span>int<\/span> i =<\/span> m;<\/span> i >=<\/span> 1<\/span>;<\/span> i--<\/span>)<\/span> {<\/span>
\n        sum +=<\/span> x[<\/span>i]<\/span>;<\/span>
\n        lmax =<\/span> max(<\/span>lmax,<\/span> sum)<\/span>;<\/span>
\n    }<\/span>
\n    \/\/\u627e\u51fa\u4ee5m\u4e3a\u8d77\u70b9\u7684\u5411\u53f3\u7684\u6700\u5927\u5b50\u5411\u91cf<\/span>
\n    float<\/span> rmax =<\/span> 0<\/span>;<\/span>
\n    sum =<\/span> 0<\/span>;<\/span>
\n    for<\/span>(<\/span>int<\/span> i =<\/span> m +<\/span> 1<\/span>;<\/span> i <<\/span> u;<\/span> i++<\/span>)<\/span> {<\/span>
\n        sum +=<\/span> x[<\/span>i]<\/span>;<\/span>
\n        rmax =<\/span> max(<\/span>rmax,<\/span> sum)<\/span>;<\/span>
\n    }<\/span>
\n    \/\/lmax+rmax \u5c31\u662f\u7ecf\u8fc7m\u7684\u6700\u5927\u5b50\u5411\u91cf<\/span>
\n    return<\/span> max3(<\/span>lmax+<\/span>rmax,<\/span> maxsum3(<\/span>l,<\/span> m)<\/span>,<\/span> maxsum3(<\/span>m+<\/span>1<\/span>,<\/span> u)<\/span>)<\/span>;<\/span>
\n}<\/span>
\nint<\/span> main(<\/span>)<\/span>{<\/span>
\n    printf<\/span>(<\/span>"%f"<\/span>,<\/span> maxsum3_l(<\/span>0<\/span>,<\/span>9<\/span>)<\/span>)<\/span>;<\/span>
\n}<\/span><\/div><\/div>\n

\u4e66\u4e2d\u53c8\u7ed9\u51fa\u4e86\u4e00\u4e2a\u7ebf\u6027\u626b\u63cf\u7b97\u6cd5<\/strong>\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n),\u7a0b\u5e8f\u7684\u5173\u952e\u5c31\u662f\u5bf9maxendinghere\u53d8\u91cf\uff0c\u5728\u6bcf\u4e00\u6b21for\u5faa\u73af\u4e2d\u5bf9\u5176\u8d4b\u503c\u4e4b\u524d\uff0c\u5176\u662f\u7ed3\u675f\u4f4d\u7f6e\u4e3ai-1\u7684\u6700\u5927\u5b50\u5411\u91cf\u7684\u548c\u3002\u8d4b\u503c\u540e\u5176\u5b9e\u7ed3\u675f\u4f4d\u7f6e\u4e3ai\u7684\u6700\u5927\u5b50\u5411\u91cf\u7684\u548c\uff1b\u82e5\u52a0\u4e0ax[i]\u4e4b\u540e\u7ed3\u679c\u4f9d\u7136\u4e3a\u6b63\uff0c\u5219\u8be5\u8d4b\u503c\u8bed\u53e5\u5c06maxendinghere\u589e\u5927x[i];\u82e5\u52a0\u4e0ax[i]\u4e4b\u540e\u7ed3\u679c\u4e3a\u8d1f\uff0c\u5219\u8be5\u8d4b\u503c\u8bed\u53e5\u5c06maxendinghere\u7f6e\u4e3a0\uff08\u56e0\u4e3a\u7ed3\u675f\u4e3a\u6b62\u4e3ai\u7684\u6700\u5927\u5b50\u5411\u91cf\u73b0\u5728\u4e3a\u7a7a\u5411\u91cf\uff09
\n\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n

#include <stdlib.h><\/span>
\nint<\/span> x[<\/span>10<\/span>]<\/span> =<\/span> {<\/span>31<\/span>,-<\/span>41<\/span>,<\/span>59<\/span>,<\/span>26<\/span>,-<\/span>53<\/span>,<\/span>58<\/span>,<\/span>97<\/span>,-<\/span>93<\/span>,-<\/span>23<\/span>,<\/span>84<\/span>}<\/span>;<\/span>
\nfloat<\/span> maxsum4(<\/span>int<\/span> n)<\/span>{<\/span>
\n    float<\/span> maxsofar =<\/span> 0<\/span>;<\/span>
\n    float<\/span> maxendinghere =<\/span> 0<\/span>;<\/span>
\n    for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> ++<\/span>i)<\/span> {<\/span>
\n        maxendinghere =<\/span> max(<\/span>maxendinghere+<\/span>x[<\/span>i]<\/span>,<\/span> 0<\/span>)<\/span>;<\/span>
\n        maxsofar =<\/span> max(<\/span>maxsofar,<\/span> maxendinghere)<\/span>;<\/span>
\n    }<\/span>
\n    return<\/span> maxsofar;<\/span>
\n}<\/span>
\n
\nint<\/span> main(<\/span>)<\/span>{<\/span>
\n    printf<\/span>(<\/span>"%f"<\/span>,<\/span> maxsum4(<\/span>10<\/span>)<\/span>)<\/span>;<\/span>
\n
\n}<\/span><\/div><\/div>\n

\u53ef\u4ee5\u8bc1\u660e\u4e0d\u4f1a\u5b58\u5728\u5feb\u4e8eO(n)\u7684\u7b97\u6cd5\u3002<\/strong>\u5728\u8bfe\u540e\u9898\u4e2d\u4f5c\u8005\u63d0\u51fa\u6539\u8fdb\u539f\u6765O(nlogn)\u7684\u9012\u5f52\u7b97\u6cd5\uff0c\u4f7f\u5176\u5728\u6700\u574f\u60c5\u51b5\u4e0b\u7684\u590d\u6742\u5ea6\u4e3aO(n),\u4e3b\u8981\u6838\u5fc3\u601d\u60f3\u662f\u4ecem\u5411\u5de6\u4ee5\u53ca\u5411\u53f3\u627e\u6700\u5927\u5b50\u5411\u91cf\u65f6\uff0c\u8981\u8bb0\u4e0b\u6700\u5927\u5b50\u5411\u91cf\u7684\u7ed3\u675f\u4f4d\u7f6e\uff0c\u4e0b\u4e00\u8f6e\u9012\u5f52\u5bfb\u627e\u65f6\uff0c\u76f4\u63a5\u4ece\u4e0a\u4e00\u6b21\u8bb0\u4e0b\u7684\u7ed3\u675f\u4f4d\u7f6e\u5f00\u59cb\uff0c\u5206\u522b\u5411\u5de6\u548c\u5411\u53f3\u627e\u3002\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n

#include <stdlib.h><\/span>
\nint<\/span> x[<\/span>10<\/span>]<\/span> =<\/span> {<\/span>31<\/span>,-<\/span>41<\/span>,<\/span>59<\/span>,<\/span>26<\/span>,-<\/span>53<\/span>,<\/span>58<\/span>,<\/span>97<\/span>,-<\/span>93<\/span>,-<\/span>23<\/span>,<\/span>84<\/span>}<\/span>;<\/span>
\nfloat<\/span> max(<\/span>float<\/span> x,<\/span> float<\/span> y)<\/span> {<\/span>
\n    return<\/span> x >=<\/span> y?<\/span> x :<\/span> y;<\/span>
\n}<\/span>
\n
\nfloat<\/span> max3(<\/span>float<\/span> x,<\/span> float<\/span> y,<\/span> float<\/span> z)<\/span> {<\/span>
\n    int<\/span> larger =<\/span> max(<\/span>x,<\/span> y)<\/span>;<\/span>
\n    return<\/span> max(<\/span>larger,<\/span> z)<\/span>;<\/span>
\n}<\/span>
\nfloat<\/span> maxsum3_l(<\/span>int<\/span> l,<\/span> int<\/span> u)<\/span> {<\/span>
\n    if<\/span> (<\/span>l ><\/span> u)<\/span>
\n        return<\/span> 0<\/span>;<\/span>
\n    if<\/span> (<\/span>l ==<\/span> u)<\/span>
\n        return<\/span> max(<\/span>0<\/span>,<\/span> x[<\/span>l]<\/span>)<\/span>;<\/span>
\n    int<\/span> m =<\/span> (<\/span>l +<\/span> u)<\/span> \/<\/span> 2<\/span>;<\/span>
\n
\n    float<\/span> lmax  =<\/span> 0<\/span>;<\/span>
\n    float<\/span> sum =<\/span> 0<\/span>;<\/span>
\n    int<\/span> last_l =<\/span> m;<\/span>  \/\/\u5411\u5de6\u627e\u65f6\u6700\u5927\u5b50\u5411\u91cf\u7684\u7ed3\u675f\u4f4d\u7f6e<\/span>
\n    for<\/span> (<\/span>int<\/span> i =<\/span> m;<\/span> i >=<\/span> 0<\/span>;<\/span> i--<\/span>)<\/span> {<\/span>
\n        sum +=<\/span> x[<\/span>i]<\/span>;<\/span>
\n        if<\/span> (<\/span>lmax<=<\/span>sum)<\/span> {<\/span>
\n            lmax =<\/span> sum;<\/span>
\n            last_l--;<\/span>
\n        }<\/span>
\n    }<\/span>
\n
\n    int<\/span> last_r =<\/span> m+<\/span>1<\/span>;<\/span> \/\/\u5411\u53f3\u627e\u65f6\u6700\u5927\u5b50\u5411\u91cf\u7684\u7ed3\u675f\u4f4d\u7f6e<\/span>
\n    float<\/span> rmax =<\/span> 0<\/span>;<\/span>
\n    sum =<\/span> 0<\/span>;<\/span>
\n    for<\/span>(<\/span>int<\/span> i =<\/span> m +<\/span> 1<\/span>;<\/span> i <=<\/span> u;<\/span> i++<\/span>)<\/span> {<\/span>
\n        sum +=<\/span> x[<\/span>i]<\/span>;<\/span>
\n        if<\/span> (<\/span>rmax<<\/span>sum)<\/span> {<\/span>
\n            rmax =<\/span> sum;<\/span>
\n            last_r++;<\/span>
\n        }<\/span>
\n    }<\/span>
\n    return<\/span> max3(<\/span>lmax+<\/span>rmax,<\/span> maxsum3_l(<\/span>l,<\/span> last_l-<\/span>1<\/span>)<\/span>,<\/span> maxsum3_l(<\/span>last_r,<\/span> u)<\/span>)<\/span>;<\/span> \/\/\u76f4\u63a5\u4ece\u7ed3\u675f\u4f4d\u7f6e\u5411\u5de6\u53ca\u5411\u53f3\u627e<\/span>
\n}<\/span>
\nint<\/span> main(<\/span>)<\/span>{<\/span>
\n    printf<\/span>(<\/span>"%f"<\/span>,<\/span> maxsum3_l(<\/span>0<\/span>,<\/span>9<\/span>)<\/span>)<\/span>;<\/span>
\n}<\/span><\/div><\/div>\n

\u4e0a\u8ff0\u7a0b\u5e8f\u7684\u8f93\u51fa\u5e94\u8be5\u5747\u4e3a187.000000<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

\u95ee\u9898\u63cf\u8ff0\uff1a\u8f93\u5165\u5177\u6709n\u4e2a\u6d6e\u70b9\u6570\u7684\u5411\u91cfx\uff0c\u8f93\u51fa\u5411\u91cfx\u4e2d\u4efb\u4f55\u8fde\u7eed\u5b50\u5411\u91cf\u4e2d\u7684\u6700\u5927\u548c\u3002\u4f8b\u5982\uff1a \u5982\u679cx={1,2,3}\uff0c\u5219 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-237","post","type-post","status-publish","format-standard","hentry","category-algorithm"],"_links":{"self":[{"href":"https:\/\/ayonel.malash.net\/index.php\/wp-json\/wp\/v2\/posts\/237","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ayonel.malash.net\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ayonel.malash.net\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ayonel.malash.net\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ayonel.malash.net\/index.php\/wp-json\/wp\/v2\/comments?post=237"}],"version-history":[{"count":4,"href":"https:\/\/ayonel.malash.net\/index.php\/wp-json\/wp\/v2\/posts\/237\/revisions"}],"predecessor-version":[{"id":241,"href":"https:\/\/ayonel.malash.net\/index.php\/wp-json\/wp\/v2\/posts\/237\/revisions\/241"}],"wp:attachment":[{"href":"https:\/\/ayonel.malash.net\/index.php\/wp-json\/wp\/v2\/media?parent=237"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ayonel.malash.net\/index.php\/wp-json\/wp\/v2\/categories?post=237"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ayonel.malash.net\/index.php\/wp-json\/wp\/v2\/tags?post=237"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}