{"url":"https://info.atcoder.jp/entry/algorithm_lectures/cycle_lemma","published":"2026-04-10 14:16:53","image_url":"https://cdn.user.blog.st-hatena.com/default_entry_og_image/158934417/1702097020779738","blog_title":"AtCoderInfo","author_url":"https://blog.hatena.ne.jp/atcoder/","categories":["\u6570\u3048\u4e0a\u3052","Cycle Lemma","Catalan \u6570","\u62ec\u5f27\u5217","Narayana \u6570"],"height":"190","title":"Cycle Lemma","author_name":"atcoder","type":"rich","provider_url":"https://hatena.blog","blog_url":"https://info.atcoder.jp/","description":"\u89e3\u8aac\u52d5\u753b\u306f\u3053\u3061\u3089\u3067\u3059\uff0e 1. \u6982\u8981 \u672c\u8a18\u4e8b\u3067\u306f\uff0c\u6570\u3048\u4e0a\u3052\u306b\u95a2\u3059\u308b Cycle Lemma \u3068\u547c\u3070\u308c\u308b\u5b9a\u7406\u3092\u7d39\u4ecb\u3057\u307e\u3059\uff0e \u3053\u308c\u306f\u3042\u308b\u7a2e\u306e\u6574\u6570\u5217\u306b\u3064\u3044\u3066\uff0c\u5217\u306e\u5de1\u56de\u30b7\u30d5\u30c8\u306e\u3046\u3061\uff0c\u7d2f\u7a4d\u548c\u304c\u5e38\u306b\u6b63\u306b\u306a\u308b\u3082\u306e\u306e\u500b\u6570\u3092\u6c7a\u5b9a\u3059\u308b\u3082\u306e\u3067\uff0c\u4e3b\u5f35\u3082\u8a3c\u660e\u3082\u6613\u3057\u3044\u3067\u3059\uff0e\u672c\u8a18\u4e8b\u3067\u306f Cycle Lemma \u3092\u8a3c\u660e\u3057\uff0c\u305d\u3053\u304b\u3089\u591a\u304f\u306e\u6709\u540d\u306a\u6570\u3048\u4e0a\u3052\u516c\u5f0f\u304c\u5c0e\u51fa\u3055\u308c\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u307e\u3059\uff0e 2. \u524d\u63d0\u77e5\u8b58 \u4e8c\u9805\u4fc2\u6570\u306e\u7406\u89e3\u3092\u4eee\u5b9a\u3057\u307e\u3059\uff0e 3. Cycle Lemma 3.1. \u4e3b\u5f35 \u3010\u5b9a\u7fa9 1\u3011\uff08\u7d2f\u7a4d\u548c\uff09 \u6574\u6570\u5217 $A=(A_0,A_1,\\ldots,A_{N-1})$ \u306b\u5bfe\u3057\u3066\uff0c\u305d\u306e\u7d2f\u7a4d\u548c\uff08prefix sum\uff09$S=(S_0,S_\u2026","provider_name":"Hatena Blog","version":"1.0","width":"100%","html":""}