\u603b\u7ed3<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\u6458\u8981<\/h3>\n
\u8fd9\u9053\u9898\u7ed9\u4e00\u4e2a\u6b63\u6574\u6570 n，\u6bcf\u6b21\u53ef\u4ee5：\u82e5 n \u662f\u5076\u6570\u5219\u7528 n\/2 \u66ff\u6362；\u82e5 n \u662f\u5947\u6570\u5219\u7528 n+1 \u6216 n-1 \u66ff\u6362\u3002\u95ee\u6700\u5c11\u51e0\u6b65\u80fd\u628a n \u53d8\u6210 1\u3002<\/p>\n
\u66b4\u529b\u53ef\u4ee5\u505a BFS \u6216\u8bb0\u5fc6\u5316\u641c\u7d22，\u4f46 n \u6700\u5927\u5230 2^31-1，\u72b6\u6001\u592a\u591a\u3002\u7528\u8d2a\u5fc3：\u5076\u6570\u4e00\u5b9a\u9664\u4ee5 2；\u5947\u6570\u65f6，\u5e0c\u671b\u4e0b\u4e00\u6b65\u80fd\u591a\u9664\u51e0\u6b21 2，\u6240\u4ee5\u770b n \u6a21 4\u2014\u2014\u82e5 n=4k+1 \u9009 n-1 \u5f97\u5230 2k \u80fd\u518d\u9664\u4e00\u6b21 2，\u82e5 n=4k+3 \u9009 n+1 \u5f97\u5230 2k+2 \u80fd\u518d\u9664\u4e00\u6b21 2\u3002\u7279\u4f8b\u662f n=3：3\u21922\u21921 \u4e24\u6b65，3\u21924\u21922\u21921 \u4e09\u6b65，\u6240\u4ee5 3 \u8981\u9009 n-1\u3002\u6309\u8fd9\u4e2a\u89c4\u5219\u8fed\u4ee3\u6216\u9012\u5f52\u5373\u53ef\u5728 O(log n) \u5185\u5f97\u5230\u6700\u5c11\u6b65\u6570\u3002\u4e0b\u9762\u7528 Swift \u5b9e\u73b0\u5e76\u8bf4\u660e\u8d2a\u5fc3\u4f9d\u636e\u3002<\/p>\n
![\"\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304114200-69a81a88b60d9.png\")
<\/p>\n
\u63cf\u8ff0<\/h3>\n
\u7ed9\u5b9a\u6b63\u6574\u6570 n，\u53ef\u4ee5\u505a\u4e24\u79cd\u64cd\u4f5c：\u82e5 n \u4e3a\u5076\u6570，\u7528 n\/2 \u66ff\u6362 n；\u82e5 n \u4e3a\u5947\u6570，\u7528 n+1 \u6216 n-1 \u66ff\u6362 n\u3002\u8fd4\u56de n \u53d8\u4e3a 1 \u6240\u9700\u7684\u6700\u5c0f\u66ff\u6362\u6b21\u6570\u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
\u8f93\u5165： n = 8
\n\u8f93\u51fa： 3
\n\u89e3\u91ca： 8 -> 4 -> 2 -> 1<\/p>\n
\u793a\u4f8b 2：<\/p>\n
\u8f93\u5165： n = 7
\n\u8f93\u51fa： 4
\n\u89e3\u91ca： 7 -> 8 -> 4 -> 2 -> 1 \u6216 7 -> 6 -> 3 -> 2 -> 1<\/p>\n
\u793a\u4f8b 3：<\/p>\n
\u8f93\u5165： n = 4
\n\u8f93\u51fa： 2<\/p>\n
\u63d0\u793a： 1 <= n <= 2^31 – 1<\/p>\n
\u6838\u5fc3\u601d\u8def：\u5076\u6570\u4e00\u5f8b\u9664\u4ee5 2；\u5947\u6570\u65f6\u7528\u300c\u4e0b\u4e00\u6b65\u80fd\u591a\u9664 2\u300d\u7684\u8d2a\u5fc3\u9009 +1 \u6216 -1，\u5e76\u5355\u72ec\u5904\u7406 n=3\u3002<\/p>\n
![\"\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304114201-69a81a89057ed.png\")
<\/p>\n
\u9898\u89e3\u7b54\u6848<\/h3>\n
class<\/span> Solution<\/span> {<\/span>
\n func<\/span> integerReplacement<\/span>(<\/span>_<\/span> n:<\/span> Int<\/span>)<\/span> -><\/span> Int<\/span> {<\/span>
\n var<\/span> num =<\/span> n
\n var<\/span> steps =<\/span> 0<\/span>
\n while<\/span> num !=<\/span> 1<\/span> {<\/span>
\n if<\/span> num %<\/span> 2<\/span> ==<\/span> 0<\/span> {<\/span>
\n num \/=<\/span> 2<\/span>
\n steps +=<\/span> 1<\/span>
\n }<\/span> else<\/span> {<\/span>
\n if<\/span> num ==<\/span> 3<\/span> {<\/span>
\n num =<\/span> 2<\/span>
\n steps +=<\/span> 1<\/span>
\n }<\/span> else<\/span> if<\/span> num %<\/span> 4<\/span> ==<\/span> 1<\/span> {<\/span>
\n num -=<\/span> 1<\/span>
\n steps +=<\/span> 1<\/span>
\n }<\/span> else<\/span> {<\/span>
\n num +=<\/span> 1<\/span>
\n steps +=<\/span> 1<\/span>
\n }<\/span>
\n }<\/span>
\n }<\/span>
\n return<\/span> steps
\n }<\/span>
\n}<\/span><\/p>\n\u9898\u89e3\u4ee3\u7801\u5206\u6790<\/h3>\n\u4e3a\u4ec0\u4e48\u5076\u6570\u76f4\u63a5\u9664\u4ee5 2<\/h4>\n
\u5076\u6570\u65f6\u53ea\u6709\u4e00\u79cd\u64cd\u4f5c：n\/2\u3002\u9664\u4ee5 2 \u80fd\u8ba9\u6570\u5c3d\u5feb\u53d8\u5c0f，\u4e14\u4e0d\u4f1a\u300c\u6d6a\u8d39\u300d\u4e00\u6b65\u53bb\u505a +1\/-1 \u518d\u7b49\u4e0b\u6b21\u9664 2，\u6240\u4ee5\u5076\u6570\u65f6\u4e00\u5b9a\u9009 n\/2\u3002<\/p>\n
\u5947\u6570\u65f6\u4e3a\u4ec0\u4e48\u770b n % 4<\/h4>\n
\u5947\u6570\u53ea\u80fd +1 \u6216 -1，\u53d8\u6210\u5076\u6570\u540e\u518d\u9664 2\u3002\u6211\u4eec\u5e0c\u671b\u300c\u4e0b\u4e00\u6b65\u80fd\u8fde\u7eed\u9664 2 \u7684\u6b21\u6570\u5c3d\u91cf\u591a\u300d，\u8fd9\u6837\u66f4\u5feb\u63a5\u8fd1 1\u3002\u8bbe n=2k+1，\u5219 n-1=2k\u3001n+1=2k+2\u3002\u518d\u9664\u4e00\u6b21 2 \u5f97\u5230 k \u548c k+1\u3002\u82e5 k \u662f\u5076\u6570，\u5219 (n-1)\/2 \u8fd8\u80fd\u518d\u9664 2；\u82e5 k+1 \u662f\u5076\u6570，\u5219 (n+1)\/2 \u8fd8\u80fd\u518d\u9664 2\u3002n=4k+1 \u65f6：(n-1)\/2=2k \u4e3a\u5076，(n+1)\/2=2k+1 \u4e3a\u5947，\u9009 n-1 \u66f4\u6709\u5229\u3002n=4k+3 \u65f6：(n-1)\/2=2k+1 \u4e3a\u5947，(n+1)\/2=2k+2 \u4e3a\u5076，\u9009 n+1 \u66f4\u6709\u5229\u3002\u6240\u4ee5\u89c4\u5219\u662f：n % 4 == 1 \u7528 n-1，n % 4 == 3 \u7528 n+1\u3002<\/p>\n
\u4e3a\u4ec0\u4e48 n=3 \u8981\u7279\u6b8a\u5904\u7406<\/h4>\n
n=3 \u65f6 3 % 4 == 3，\u6309\u4e0a\u9762\u4f1a\u9009 n+1 \u5f97\u5230 4，\u8def\u5f84 3\u21924\u21922\u21921 \u5171 3 \u6b65\u3002\u4f46\u82e5\u9009 n-1 \u5f97\u5230 2，\u8def\u5f84 3\u21922\u21921 \u53ea\u8981 2 \u6b65\u3002\u539f\u56e0\u662f 3 \u79bb 1 \u5df2\u7ecf\u5f88\u8fd1，+1 \u53cd\u800c\u591a\u7ed5\u4e00\u6b65\u3002\u6240\u4ee5\u5355\u72ec\u5224\u65ad：\u82e5 n == 3 \u5219\u7528 n-1\u3002<\/p>\n
\u7528\u5faa\u73af\u800c\u4e0d\u662f\u9012\u5f52<\/h4>\n
n \u6700\u5927 2^31-1，\u6309\u4e0a\u8ff0\u89c4\u5219\u6b65\u6570\u7ea6\u4e3a O(log n)，\u5faa\u73af\u8fed\u4ee3 log n \u6b21\u5373\u53ef，\u907f\u514d\u9012\u5f52\u6808\u3002\u7528 var num = n \u548c while num != 1 \u6bcf\u6b21\u6309\u89c4\u5219\u66f4\u65b0 num \u5e76\u7d2f\u52a0 steps，\u6700\u540e\u8fd4\u56de steps\u3002<\/p>\n
\u793a\u4f8b 2 \u7b80\u8981\u8fc7\u7a0b：n = 7<\/h4>\n
7 \u4e3a\u5947\u4e14 7 % 4 == 3，\u9009 +1 \u2192 8；8 \u4e3a\u5076 \u2192 4 \u2192 2 \u2192 1\u3002\u5171 4 \u6b65，\u4e0e\u8f93\u51fa\u4e00\u81f4\u3002<\/p>\n
\u793a\u4f8b\u6d4b\u8bd5\u53ca\u7ed3\u679c<\/h3>\n\u793a\u4f8b 1：n = 8<\/h4>\n
8\u21924\u21922\u21921，3 \u6b65，\u8f93\u51fa 3\u3002<\/p>\n
\u793a\u4f8b 2：n = 7<\/h4>\n
7\u21928\u21924\u21922\u21921，4 \u6b65，\u8f93\u51fa 4\u3002<\/p>\n
\u793a\u4f8b 3：n = 4<\/h4>\n
4\u21922\u21921，2 \u6b65，\u8f93\u51fa 2\u3002<\/p>\n
\u793a\u4f8b 4：n = 3<\/h4>\n
3\u21922\u21921，2 \u6b65（\u82e5\u6309 %4 \u9009 +1 \u4f1a\u5f97\u5230 3 \u6b65，\u7279\u4f8b\u5904\u7406\u540e\u4e3a 2）\u3002<\/p>\n
\u793a\u4f8b 5：n = 1<\/h4>\n
\u5df2\u662f 1，0 \u6b65，\u8f93\u51fa 0（\u9898\u76ee n>=1，\u82e5\u4f20\u5165 1 \u5219\u5faa\u73af\u4e0d\u6267\u884c，\u8fd4\u56de 0）\u3002<\/p>\n
\u65f6\u95f4\u590d\u6742\u5ea6<\/h3>\n
\u6bcf\u6b21\u8981\u4e48\u9664\u4ee5 2（n \u81f3\u5c11\u51cf\u534a），\u8981\u4e48 \u00b11 \u540e\u53d8\u6210\u5076\u6570\u518d\u9664，\u6574\u4f53\u89c4\u6a21\u7ea6\u6bcf\u6b21\u51cf\u534a\u6216\u63a5\u8fd1\u51cf\u534a，\u6b65\u6570 O(log n)，\u5355\u6b21\u64cd\u4f5c O(1)，\u603b\u65f6\u95f4 O(log n)\u3002<\/p>\n
\u7a7a\u95f4\u590d\u6742\u5ea6<\/h3>\n
\u53ea\u7528\u4e86\u82e5\u5e72\u53d8\u91cf，O(1)\u3002<\/p>\n
\u5b9e\u9645\u5e94\u7528\u573a\u666f<\/h3>\n
\u7c7b\u4f3c\u300c\u7528\u6700\u5c11\u6b65\u6570\u628a\u6570\u53d8\u6210 1\u300d\u7684\u89c4\u5219\u5728\u6e38\u620f\u6b65\u6570\u3001\u72b6\u6001\u673a\u6700\u7b80\u8def\u5f84\u3001\u6216\u67d0\u4e9b\u7f16\u7801\/\u89e3\u7801\u6b65\u6570\u5206\u6790\u91cc\u4f1a\u78b0\u5230\u3002\u8d2a\u5fc3\u300c\u80fd\u9664 2 \u5c31\u9664\u3001\u5947\u6570\u65f6\u9009\u4e0b\u4e00\u6b65\u66f4\u80fd\u9664\u300d\u7684\u601d\u8def，\u5728\u89c4\u5219\u7b80\u5355\u3001\u6709\u660e\u786e\u300c\u66f4\u4f18\u4e0b\u4e00\u6b65\u300d\u65f6\u5e38\u7528\u3002<\/p>\n
\u603b\u7ed3<\/h3>\n
\u6574\u6570\u66ff\u6362\u7684\u6700\u5c0f\u6b65\u6570\u53ef\u4ee5\u7528\u8d2a\u5fc3：\u5076\u6570\u4e00\u5f8b n\/2；\u5947\u6570\u65f6 n % 4 == 1 \u7528 n-1，n % 4 == 3 \u7528 n+1，\u5e76\u5355\u72ec\u628a n=3 \u8bbe\u4e3a n-1\u3002\u6309\u6b64\u89c4\u5219\u8fed\u4ee3\u76f4\u5230 n \u53d8\u4e3a 1，\u6b65\u6570\u5373\u4e3a\u7b54\u6848，\u65f6\u95f4 O(log n)\u3001\u7a7a\u95f4 O(1)\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u6587\u7ae0\u76ee\u5f55\u6458\u8981\u63cf\u8ff0\u9898\u89e3\u7b54\u6848\u9898\u89e3\u4ee3\u7801\u5206\u6790\u4e3a\u4ec0\u4e48\u5076\u6570\u76f4\u63a5\u9664\u4ee5 2\u5947\u6570\u65f6\u4e3a\u4ec0\u4e48\u770b n % 4\u4e3a\u4ec0\u4e48 n3 \u8981\u7279\u6b8a\u5904\u7406\u7528\u5faa\u73af\u800c\u4e0d\u662f\u9012\u5f52\u793a\u4f8b 2 \u7b80\u8981\u8fc7\u7a0b：n 7\u793a\u4f8b\u6d4b\u8bd5\u53ca\u7ed3\u679c\u793a\u4f8b 1：n 8\u793a\u4f8b 2：n 7\u793a\u4f8b 3：n 4\u793a\u4f8b 4：n 3\u793a\u4f8b 5：n 1\u65f6\u95f4\u590d\u6742\u5ea6\u7a7a\u95f4\u590d\u6742\u5ea6\u5b9e\u9645\u5e94\u7528\u573a\u666f\u603b\u7ed3\u6458\u8981
\n\u8fd9\u9053\u9898\u7ed9\u4e00\u4e2a\u6b63\u6574\u6570 n，\u6bcf\u6b21\u53ef\u4ee5：\u82e5 n \u662f\u5076\u6570\u5219\u7528 n\/2 \u66ff\u6362&<\/p>\n","protected":false},"author":2,"featured_media":80258,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[2692,427,925],"topic":[],"class_list":["post-80262","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-leetcode","tag-427","tag-925"],"yoast_head":"\n
LeetCode 397 \u6574\u6570\u66ff\u6362 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/80262.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"LeetCode 397 \u6574\u6570\u66ff\u6362 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u6587\u7ae0\u76ee\u5f55\u6458\u8981\u63cf\u8ff0\u9898\u89e3\u7b54\u6848\u9898\u89e3\u4ee3\u7801\u5206\u6790\u4e3a\u4ec0\u4e48\u5076\u6570\u76f4\u63a5\u9664\u4ee5 2\u5947\u6570\u65f6\u4e3a\u4ec0\u4e48\u770b n % 4\u4e3a\u4ec0\u4e48 n3 \u8981\u7279\u6b8a\u5904\u7406\u7528\u5faa\u73af\u800c\u4e0d\u662f\u9012\u5f52\u793a\u4f8b 2 \u7b80\u8981\u8fc7\u7a0b：n 7\u793a\u4f8b\u6d4b\u8bd5\u53ca\u7ed3\u679c\u793a\u4f8b 1：n 8\u793a\u4f8b 2：n 7\u793a\u4f8b 3：n 4\u793a\u4f8b 4：n 3\u793a\u4f8b 5：n 1\u65f6\u95f4\u590d\u6742\u5ea6\u7a7a\u95f4\u590d\u6742\u5ea6\u5b9e\u9645\u5e94\u7528\u573a\u666f\u603b\u7ed3\u6458\u8981 \u8fd9\u9053\u9898\u7ed9\u4e00\u4e2a\u6b63\u6574\u6570 n，\u6bcf\u6b21\u53ef\u4ee5：\u82e5 n \u662f\u5076\u6570\u5219\u7528 n\/2 \u66ff\u6362&\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/80262.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-03-04T11:42:02+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304114200-69a81a8863a8e.png\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/80262.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/80262.html\",\"name\":\"LeetCode 397 \u6574\u6570\u66ff\u6362 - 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