{"author_name":"atcoder","provider_url":"https://hatena.blog","image_url":"https://cdn.user.blog.st-hatena.com/default_entry_og_image/158934417/1702097020779738","version":"1.0","blog_url":"https://info.atcoder.jp/","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Finfo.atcoder.jp%2Fentry%2Falgorithm_lectures%2Fsqrt_tree\" title=\"Sqrt Tree - AtCoderInfo\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","url":"https://info.atcoder.jp/entry/algorithm_lectures/sqrt_tree","height":"190","provider_name":"Hatena Blog","blog_title":"AtCoderInfo","width":"100%","published":"2026-04-10 14:10:06","title":"Sqrt Tree","categories":["\u30c7\u30fc\u30bf\u69cb\u9020","\u533a\u9593\u30af\u30a8\u30ea","Sqrt Tree","Disjoint Sparse Table","\u30e2\u30ce\u30a4\u30c9"],"type":"rich","author_url":"https://blog.hatena.ne.jp/atcoder/","description":"1. \u6982\u8981 \u672c\u8a18\u4e8b\u3067\u306f\uff0cSqrt Tree \u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\uff0e Sqrt Tree \u306f\u5217\u306e\u5e73\u65b9\u5206\u5272\u3092\u518d\u5e30\u7684\u306b\u884c\u3046\u3053\u3068\u3067\u3067\u304d\u308b\u6728\u69cb\u9020\u3067\u3059\uff0e\u7279\u306b\u9759\u7684\u306a\u30e2\u30ce\u30a4\u30c9\u5217\u306b\u5bfe\u3059\u308b\u533a\u9593\u7a4d\u30af\u30a8\u30ea\u3092\u9ad8\u901f\u306b\u51e6\u7406\u3067\u304d\u307e\u3059\uff0e\u5177\u4f53\u7684\u306b\u306f\uff0c\u5217\u306e\u9577\u3055\u3092 $N$ \u3068\u3059\u308b\u3068\u304d\uff0c\u4e8b\u524d\u8a08\u7b97 $\\mathrm{O}(N\\log \\log N)$ \u6642\u9593\u306e\u3082\u3068\uff0c\u30af\u30a8\u30ea\u3042\u305f\u308a $\\mathrm{O}(1)$ \u6642\u9593\u3067\u533a\u9593\u7a4d\u3092\u51e6\u7406\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e \u533a\u9593\u7a4d\u30af\u30a8\u30ea\u306e\u89e3\u6cd5\u3068\u3057\u3066\u306f\u30bb\u30b0\u30e1\u30f3\u30c8\u6728\u3084 Disjoint Sparse Table\uff08\u4ee5\u4e0b DST \u3068\u3082\u7565\u8a18\u3057\u307e\u3059\uff09\u3092\u7528\u3044\u308b\u65b9\u6cd5\u3082\u6709\u540d\u3067\u3059\u304c\uff0c\u30af\u30a8\u30ea\u306e\u500b\u6570 $Q$ \u304c $N$ \u306b\u8fd1\u3044\u72b6\u6cc1\u3067\u3042\u308c\u3070\u2026"}