{"id":1563,"date":"2023-06-27T13:54:14","date_gmt":"2023-06-27T05:54:14","guid":{"rendered":"https:\/\/xinchewhd.com.cn\/?p=1563"},"modified":"2023-06-27T13:54:14","modified_gmt":"2023-06-27T05:54:14","slug":"%e3%80%90%e7%ae%97%e6%b3%95%e9%a2%98%e8%a7%a3%e3%80%914-%e6%af%94%e7%89%b9%e4%bd%8d%e8%ae%a1%e6%95%b0","status":"publish","type":"post","link":"https:\/\/xinchewhd.com.cn\/index.php\/%e7%ae%97%e6%b3%95\/%e3%80%90%e7%ae%97%e6%b3%95%e9%a2%98%e8%a7%a3%e3%80%914-%e6%af%94%e7%89%b9%e4%bd%8d%e8%ae%a1%e6%95%b0\/","title":{"rendered":"\u3010\u7b97\u6cd5\u9898\u89e3\u30114. \u6bd4\u7279\u4f4d\u8ba1\u6570"},"content":{"rendered":"
\n

\u9898\u76ee<\/span><\/span><\/h2>\n

<\/figure>\n
\n
\n
\u7ed9\u4f60\u4e00\u4e2a\u6574\u6570 n \uff0c\u5bf9\u4e8e 0 <= i <= n \u4e2d\u7684\u6bcf\u4e2a i \uff0c\u8ba1\u7b97\u5176\u4e8c\u8fdb\u5236\u8868\u793a\u4e2d 1 \u7684\u4e2a\u6570 \uff0c\u8fd4\u56de\u4e00\u4e2a\u957f\u5ea6\u4e3a n + 1 \u7684\u6570\u7ec4 ans \u4f5c\u4e3a\u7b54\u6848\u3002<\/span><\/section>\n<\/section>\n
https:\/\/leet<\/span>code.cn\/problems\/counting-bits\/description\/<\/span><\/section>\n<\/blockquote>\n
<\/span><\/section>\n

\u89e3\u6cd5\uff1a\u52a8\u6001\u89c4\u5212<\/span><\/span><\/h2>\n
\u89e3\u9898\u601d\u8def<\/span><\/section>\n

\u9996\u5148\u53ef\u4ee5\u786e\u5b9a\u7684\u662f <\/span>ans[0] = 0<\/span>\u3002<\/span><\/p>\n

\u5f53 <\/span>1 <= i <= n<\/span> \u65f6\uff0c\u5047\u8bbe <\/span>j = i & (i - 1)<\/span>\uff0c\u5373 <\/span>j<\/span> \u4e3a <\/span>i<\/span> \u5220\u9664\u6700\u4f4e\u4f4d\u540e\u7684\u503c\uff0c\u5982\u4e0b\u8868\u6240\u793a\uff1a<\/span><\/p>\n

<\/span><\/section>\n\n\n\n\n\n\n\n\n\n\n\n
i<\/span><\/th>\nj = i & (i - 1) <\/span><\/th>\n<\/tr>\n
0001
<\/span><\/td>\n		0000
<\/span><\/td>\n<\/tr>\n
0010
<\/span><\/td>\n		0000
<\/span><\/td>\n<\/tr>\n
0011<\/span><\/td>\n0010<\/span><\/td>\n<\/tr>\n
0100<\/span><\/td>\n0000
<\/span><\/td>\n<\/tr>\n
0101<\/span><\/td>\n0100
<\/span><\/td>\n<\/tr>\n
0110<\/span><\/td>\n0100
<\/span><\/td>\n<\/tr>\n
0111<\/span><\/td>\n0110
<\/span><\/td>\n<\/tr>\n
...
<\/td>\n		...
<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

<\/section>\n

\u7531\u4e0a\u8868\u53ef\u77e5\uff0c<\/span>ans[i] = ans[j] + 1 = ans[i & (i - 1)] + 1<\/span>\uff0c\u5373 <\/span>ans[i]<\/span> \u53ef\u4ee5\u7531 <\/span>ans[j]<\/span> \u63a8\u5bfc\u51fa\u6765\uff0c\u4e14\u56e0\u4e3a <\/span>0 <= j < i <\/span>\u6240\u4ee5\u8ba1\u7b97 <\/span>ans[i]<\/span> \u7684\u65f6\u5019 <\/span>ans[j]<\/span> \u80af\u5b9a\u5df2\u7ecf\u8ba1\u7b97\u8fc7\u4e86\uff0c\u6240\u4ee5\u53ef\u4ee5\u76f4\u63a5\u62ff\u6765\u7528\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u4ee3\u7801\u5b9e\u73b0<\/span><\/p>\n

\n
    \n
  • <\/li>\n
  • <\/li>\n
  • <\/li>\n
  • <\/li>\n
  • <\/li>\n
  • <\/li>\n
  • <\/li>\n
  • <\/li>\n
  • <\/li>\n<\/ul>\n
    class<\/span> Solution<\/span> {<\/span><\/code>    public<\/span> int<\/span>[] countBits<\/span>(int<\/span> n<\/span>)<\/span> {<\/span><\/code>        int<\/span>[] ans = new<\/span> int<\/span>[n + 1<\/span>];<\/span><\/code>        for<\/span>(int<\/span> i = 1<\/span>; i <= n; i++){           <\/span><\/code>            ans[i] = ans[i & (i - 1<\/span>)] + 1<\/span>;<\/span><\/code>        }<\/span><\/code>        return<\/span> ans;<\/span><\/code>    }<\/span><\/code>}<\/span><\/code><\/pre>\n<\/section>\n
    <\/span><\/p>\n
    \u590d\u6742\u5ea6\u5206\u6790<\/span>
    <\/section>\n
    \u65f6\u95f4\u590d\u6742\u5ea6O(n): \u5faa\u73afn\u6b21<\/span><\/section>\n
    \u7a7a\u95f4\u590d\u6742\u5ea6O(1)\uff1a\u989d\u5916\u5f00\u8f9f\u4e86\u4e00\u4e2aans\u6570\u7ec4\uff0c\u5927\u5c0f\u662f\u5e38\u6570\uff0c\u6240\u4ee5\u7a7a\u95f4\u590d\u6742\u5ea6\u662fO(1);<\/span><\/section>\n
    <\/mp-style-type><\/p>\n
    \n
    \u672c\u7bc7\u6587\u7ae0\u6765\u6e90\u4e8e\u5fae\u4fe1\u516c\u4f17\u53f7:                 i\u4f59\u6570              <\/p>\n<\/blockquote>\n<\/div>\n","raw":"","protected":false},"excerpt":{"rendered":"
    \u9898\u76ee \u7ed9\u4f60\u4e00\u4e2a\u6574\u6570 n \uff0c\u5bf9\u4e8e 0 <= i <= n \u4e2d\u7684\u6bcf\u4e2a i \uff0c\u8ba1\u7b97\u5176\u4e8c\u8fdb\u5236\u8868\u793a\u4e2d 1 \u7684\u4e2a\u6570 \uff0c\u8fd4\u56de\u4e00\u4e2a\u957f\u5ea6 …<\/p>\n","protected":false},"author":1,"featured_media":1562,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"emotion":"","emotion_color":"","title_style":"","license":"","footnotes":""},"categories":[22],"tags":[],"class_list":["post-1563","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-22"],"post_thumbnail_image":"https:\/\/wp-moto-1258805347.cos.ap-shanghai.myqcloud.com\/2023\/05\/20230528043709220-150x150.jpeg","content_first_image":null,"post_medium_image_300":"https:\/\/wp-moto-1258805347.cos.ap-shanghai.myqcloud.com\/2023\/05\/20230528043709220-300x128.jpeg","post_thumbnail_image_624":"https:\/\/wp-moto-1258805347.cos.ap-shanghai.myqcloud.com\/2023\/05\/20230528043709220-1024x436.jpeg","post_frist_image":null,"post_medium_image":"https:\/\/wp-moto-1258805347.cos.ap-shanghai.myqcloud.com\/2023\/05\/20230528043709220-300x128.jpeg","post_large_image":"https:\/\/wp-moto-1258805347.cos.ap-shanghai.myqcloud.com\/2023\/05\/20230528043709220-1024x436.jpeg","post_full_image":"https:\/\/wp-moto-1258805347.cos.ap-shanghai.myqcloud.com\/2023\/05\/20230528043709220.jpeg","post_all_images":[],"videoAdId":"","listAd":"0","listAdId":"","listAdEvery":6,"total_comments":0,"category_name":"\u7b97\u6cd5","post_date":"2023-06-27","like_count":"0","praiseWord":"\u9f13\u52b1","copyright_state":"","excitationAd":"0","rewardedVideoAdId":"","detailAdId":"","detailAd":"0","enterpriseMinapp":"0","audios":[],"postImageUrl":"https:\/\/wp-moto-1258805347.cos.ap-shanghai.myqcloud.com\/2023\/05\/20230519082947553.jpg","avatarurls":[],"related_posts":null,"pageviews":287,"next_post_id":2484,"next_post_title":"Java\u4e2d\u5c06 int[] \u6570\u7ec4 \u8f6c\u6362\u4e3a List\uff08ArrayList\uff09","previous_post_id":1489,"previous_post_title":"\u3010\u7b97\u6cd5\u9898\u89e3\u301114. \u6709\u6548\u7684\u62ec\u53f7","_links":{"self":[{"href":"https:\/\/xinchewhd.com.cn\/index.php\/wp-json\/wp\/v2\/posts\/1563","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/xinchewhd.com.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/xinchewhd.com.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/xinchewhd.com.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/xinchewhd.com.cn\/index.php\/wp-json\/wp\/v2\/comments?post=1563"}],"version-history":[{"count":0,"href":"https:\/\/xinchewhd.com.cn\/index.php\/wp-json\/wp\/v2\/posts\/1563\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/xinchewhd.com.cn\/index.php\/wp-json\/wp\/v2\/media\/1562"}],"wp:attachment":[{"href":"https:\/\/xinchewhd.com.cn\/index.php\/wp-json\/wp\/v2\/media?parent=1563"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/xinchewhd.com.cn\/index.php\/wp-json\/wp\/v2\/categories?post=1563"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/xinchewhd.com.cn\/index.php\/wp-json\/wp\/v2\/tags?post=1563"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}