{"id":6034,"date":"2024-04-21T01:34:20","date_gmt":"2024-04-20T16:34:20","guid":{"rendered":"https:\/\/k.foolslab.net\/dailyreport\/?p=6034"},"modified":"2024-04-21T01:34:20","modified_gmt":"2024-04-20T16:34:20","slug":"2024-4-20","status":"publish","type":"post","link":"https:\/\/k.foolslab.net\/dailyreport\/2024-4-20\/","title":{"rendered":"2024\/4\/20(\u571f)"},"content":{"rendered":"\n

ABC350\u306b\u51fa\u305f\u3002<\/p>\n\n\n\n

A: \u3084\u308b\u3060\u3051<\/p>\n\n\n\n

B: \u3084\u308b\u3060\u3051<\/p>\n\n\n\n

C: \u5148\u982d\u304b\u3089\u666e\u901a\u306b\u9078\u629e\u30bd\u30fc\u30c8\u3057\u3066\u3044\u3051\u3070\u6700\u5f8c\u306f\u5fc5\u305a\u63c3\u3046\u306e\u3067N-1\u56de\u306e\u5236\u9650\u306f\u30af\u30ea\u30a2\u3059\u308b\u304c\u3001\u8a08\u7b97\u6642\u9593\u304c$O(N^2)$\u306b\u306a\u3063\u3066\u3057\u307e\u3046\u3002permutation\u3067\u3042\u308b\u3053\u3068\u3092\u5229\u7528\u3057\u9006\u7f6e\u63db\u3092\u6301\u3063\u3066\u304a\u304f\u3068\u5404O(1)\u3067\u6b32\u3057\u3044\u6570\u5b57\u306e\u5834\u6240\u304c\u53d6\u308c\u308b\u306e\u3067$O(N)$\u3067\u89e3\u3051\u308b\u3002<\/p>\n\n\n\n

D: \u5927\u304d\u3055X\u306e\u9023\u7d50\u6210\u5206\u306b\u306f\u53cb\u9054\u95a2\u4fc2\u304c\u6700\u5927$_XC_2=X(X-1)\/2$\u307e\u3067\u4f5c\u308c\u308b\u306e\u3067\u3001UF\u3067\u9023\u7d50\u6210\u5206\u3092\u8a08\u7b97\u3057\u6700\u5927\u306e\u95a2\u4fc2\u6570\u3092\u51fa\u3059\u3002\u65e2\u306b\u3042\u308b\u53cb\u9054\u95a2\u4fc2\u306e\u6570M\u3092\u5f15\u3051\u3070\u7b54\u3048\u304c\u51fa\u308b\u3002<\/p>\n\n\n\n

E: \u3061\u3087\u3063\u3068\u6642\u9593\u3092\u304b\u3051\u3059\u304e\u305f\u3002$10^{18}<2^{60}$\u306a\u306e\u3067\u3001\u3069\u306e\u6570\u3067\u5272\u3063\u3066\u3082\u6700\u592760\u56de\u307e\u3067\u3057\u304b\u5272\u308b\u3053\u3068\u306f\u306a\u3044\u3002\u30b5\u30a4\u30b3\u30ed\u306e\u51fa\u76ee\u306b\u542b\u307e\u308c\u308b\u7d20\u56e0\u6570\u306f2,3,5\u3057\u304b\u306a\u3044\u306e\u3067$60^3$\u901a\u308a\u7a0b\u5ea6\u306e\u6570\u3057\u304b\u8003\u3048\u306a\u304f\u3066\u3088\u3044\u3053\u3068\u304c\u5206\u304b\u308b\u30026\u3067\u5272\u308b\u306e\u30682\u30683\u30671\u56de\u305a\u3064\u5272\u308b\u306e\u3092\u533a\u5225\u3057\u306a\u304f\u3066\u3044\u3044\u306e\u304b\u8ff7\u3063\u305f\u304c\u3001\u30b0\u30b0\u3063\u305f\u3089\u3069\u3046\u3084\u3089$\\lfloor \\lfloor a\/b \\rfloor \/c \\rfloor=\\lfloor a\/(bc) \\rfloor$\u3089\u3057\u3044\u3002<\/p>\n\n\n\n

https:\/\/math.stackexchange.com\/questions\/4718508\/can-floorfloora-b-c-ever-be-different-to-floora-bc<\/a><\/p>\n\n\n\n

\u671f\u5f85\u5024DP\u306b\u3061\u3087\u3063\u3068\u624b\u9593\u53d6\u3063\u305f\u3002\u51b7\u9759\u306b\u306a\u3063\u3066\u6570\u5f0f\u3092\u7acb\u3066\u3066\u6574\u7406\u3057\u305f\u3089\u666e\u901a\u306b\u89e3\u3051\u305f\u3002\u89aa\u306e\u9854\u3088\u308a\u898b\u305f\u554f\u984c\u306b\u306a\u308a\u3064\u3064\u3042\u308b\u304b\u3089\u305d\u308d\u305d\u308d\u6163\u308c\u306a\u3044\u3068\u3044\u3051\u306a\u3044\u3002\u4eca\u56de\u306e\u5834\u5408$DP[i] = (\u6570\u5b57i\u30920\u306b\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u304a\u91d1\u306e\u671f\u5f85\u5024)$\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n

A\u3067\u5272\u3063\u305f\u5834\u5408<\/p>\n\n\n\n

$DP[i] = DP[\\lfloor i\/A \\rfloor]+X$<\/p>\n\n\n\n

\u30b5\u30a4\u30b3\u30ed\u306e\u51fa\u76ee\u3067\u5272\u3063\u305f\u5834\u5408<\/p>\n\n\n\n

$DP[i]=\\{\\sum_{k=1}^6(DP[\\lfloor i\/k \\rfloor]+Y)\\}\/6$<\/p>\n\n\n\n

\u6574\u7406\u3059\u308b\u3068<\/p>\n\n\n\n

$DP[i]=\\frac{6}{5}Y+\\{\\sum_{k=2}^6 DP[\\lfloor i\/k \\rfloor]\\}\/5$<\/p>\n\n\n\n

Y\u306b6\/5\u304c\u304b\u304b\u308b\u306e\u304c\u3061\u3087\u3063\u3068\u6c17\u6301\u3061\u60aa\u3044\u30022\u8005\u3092\u6bd4\u8f03\u3057\u3066\u5c0f\u3055\u3044\u65b9\u3092\u9078\u3093\u3067\u3044\u304f\u3088\u3046\u306b\u5b9f\u88c5\u3059\u308b\u3068\u8cb0\u3046DP\u304c\u5b8c\u6210\u3059\u308b\u3002<\/p>\n\n\n\n

F: \u307e\u305a\u524d\u8a08\u7b97\u3068\u3057\u3066\u3001\u5404\u30ab\u30c3\u30b3\u306b\u3064\u3044\u3066\u5bfe\u5fdc\u3059\u308b\u76f8\u624b\u306e\u30ab\u30c3\u30b3\u3092\u3082\u3068\u3081\u3066\u3084\u308b\u3002\u3053\u3046\u3044\u3046\u30ab\u30c3\u30b3\u5217\u306e\u51e6\u7406\u306f\u30b9\u30bf\u30c3\u30af\u3092\u4f7f\u3046\u3068\u826f\u3044\u3002\u306a\u304a\u30b9\u30bf\u30c3\u30af\u3068\u30ad\u30e5\u30fc\u304c\u3054\u3063\u3061\u3083\u306b\u306a\u3063\u3066\u53d6\u308a\u9055\u3048\u3066\u30c7\u30d0\u30c3\u30b0\u306b\u624b\u9593\u53d6\u3063\u305f\u3002\u611a\u304b\u3002<\/p>\n\n\n\n

\u5148\u982d\u304b\u3089\u9806\u306b\u898b\u3066\u3044\u304d\u3001\u30ab\u30c3\u30b3\u304c\u958b\u304f\u306a\u3089\u305d\u306e\u30ab\u30c3\u30b3\u306e\u9589\u3058\u30ab\u30c3\u30b3\u3078\u79fb\u52d5\u3057\u3066\u9032\u884c\u65b9\u5411\u3092\u8ee2\u63db\u3059\u308b\u3002\u30ab\u30c3\u30b3\u304c\u9589\u3058\u308b\u306a\u3089\u305d\u306e\u30ab\u30c3\u30b3\u306e\u958b\u304d\u30ab\u30c3\u30b3\u3078\u623b\u308a\u9032\u884c\u65b9\u5411\u3092\u8ee2\u63db\u3059\u308b\u3002\u3053\u308c\u306b\u3088\u3063\u3066$O(N)$\u3067\u6700\u7d42\u6587\u5b57\u5217\u306e\u901a\u308a\u306e\u9806\u306b\u6587\u5b57\u5217\u5168\u4f53\u3092\u8d70\u67fb\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u958b\u3044\u305f\u30ab\u30c3\u30b3\u306e\u6570\u306e\u5076\u5947\u3067\u5927\u6587\u5b57\u5c0f\u6587\u5b57\u53cd\u8ee2\u3092\u3059\u308b\u304b\u3057\u306a\u3044\u304b\u3092\u5909\u3048\u308c\u3070\u3088\u3044\u3002\u3042\u307e\u308a\u3084\u3089\u306a\u3044\u3088\u3046\u306a\u5b9f\u88c5\u3060\u304c\u7d50\u69cb\u7c21\u5358\u306a\u5b9f\u88c5\u3067\u89e3\u3051\u308b\u306e\u3067\u5272\u3068\u597d\u304d\u3002<\/p>\n\n\n\n

G: \u89e3\u3051\u305a\u3002\u3044\u308d\u3044\u308d\u3084\u308a\u3088\u3046\u304c\u3042\u308b\u3089\u3057\u3044\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

ABC350\u306b\u51fa\u305f\u3002 A: \u3084\u308b\u3060\u3051 B: \u3084\u308b\u3060\u3051 C: \u5148\u982d\u304b\u3089\u666e\u901a\u306b\u9078\u629e\u30bd\u30fc\u30c8\u3057\u3066\u3044\u3051\u3070\u6700\u5f8c\u306f\u5fc5\u305a\u63c3\u3046\u306e\u3067N-1\u56de\u306e\u5236\u9650\u306f\u30af\u30ea\u30a2\u3059\u308b\u304c\u3001\u8a08\u7b97\u6642\u9593\u304c$O(N^2)$\u306b\u306a\u3063\u3066\u3057\u307e\u3046\u3002permutation\u3067\u3042\u308b\u3053\u3068\u3092\u5229 … <\/p>\n

Read more » “2024\/4\/20(\u571f)”<\/span><\/a><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-6034","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/posts\/6034","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/comments?post=6034"}],"version-history":[{"count":27,"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/posts\/6034\/revisions"}],"predecessor-version":[{"id":6061,"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/posts\/6034\/revisions\/6061"}],"wp:attachment":[{"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/media?parent=6034"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/categories?post=6034"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/tags?post=6034"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}