{"id":4034,"date":"2023-01-23T00:53:22","date_gmt":"2023-01-22T15:53:22","guid":{"rendered":"https:\/\/k.foolslab.net\/dailyreport\/?p=4034"},"modified":"2023-01-23T00:53:23","modified_gmt":"2023-01-22T15:53:23","slug":"2023-1-22","status":"publish","type":"post","link":"https:\/\/k.foolslab.net\/dailyreport\/2023-1-22\/","title":{"rendered":"2023\/1\/22(\u65e5)"},"content":{"rendered":"\n

ARC154\u306b\u51fa\u305f\u3002<\/p>\n\n\n\n

A: \u9811\u5f35\u3063\u3066\u8003\u5bdf\u3059\u308b\u3068\u3001\u3068\u306b\u304b\u304f\u7247\u4e00\u65b9\u3092\u3067\u304b\u304f\u3057\u3066\u7247\u4e00\u65b9\u3092\u5c0f\u3055\u304f\u3059\u308b\u3068\u6700\u5c0f\u306b\u306a\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u3002\u3042\u3068\u306fA\u3068B\u306emod 998244353\u3092\u8a08\u7b97\u3057\u3066\u639b\u3051\u5408\u308f\u305b\u308b\u3060\u3051\u3002<\/p>\n\n\n\n

B: \u9006\u306e\u64cd\u4f5c\u3092\u8003\u3048\u308b\u3068\u300c\u4efb\u610f\u306e\u5834\u6240\u304b\u3089\u629c\u304d\u53d6\u3063\u3066\u5148\u982d\u306b\u5165\u308c\u308b\u300d\u306b\u306a\u308b\u3002T\u3092\u3053\u306e\u9006\u64cd\u4f5c\u3067S\u306b\u5909\u63db\u3067\u304d\u308b\u304b\u3092\u8003\u3048\u308b\u3002<\/p>\n\n\n\n

T\u306b\u3053\u306e\u64cd\u4f5c\u3092k\u56de\u3084\u308b\u3068\u3001\u629c\u304d\u53d6\u3063\u305f\u6587\u5b57\u3092\u4e26\u3079\u305fk\u6587\u5b57\u306e\u6587\u5b57\u5217+\u6b8b\u3063\u305fN-k\u6587\u5b57\u306e\u6587\u5b57\u5217\u306b\u306a\u308b\u3002k=N\u3068\u3059\u308c\u3070\u4efb\u610f\u306b\u4e26\u3079\u66ff\u3048\u308b\u3053\u3068\u304c\u51fa\u6765\u308b\u306e\u3067\u3001S\u3068T\u304c\u30bd\u30fc\u30c8\u3057\u3066\u4e00\u81f4\u3059\u308b\u306a\u3089\u5fc5\u305a\u5909\u63db\u53ef\u80fd\u3067\u3042\u308b\u3068\u8a00\u3048\u308b\u3002\u3042\u3068\u306fk\u3092\u6700\u5c0f\u5316\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u308b\u3002<\/p>\n\n\n\n

S\u306e\u5f8c\u308d\u306eN-k\u6587\u5b57\u304cT\u306e\u90e8\u5206\u5217\u3067\u3042\u308b\u306a\u3089\u3070k\u56de\u3067\u5909\u63db\u53ef\u80fd\u3067\u3042\u308b\u3068\u8a00\u3048\u308b\u3002\u3053\u306e\u5224\u5b9a\u306f$O(N)$\u3060\u304c\u3001\u5358\u8abf\u6027\u304c\u3042\u308b\u306e\u3067\u4e8c\u5206\u63a2\u7d22\u3067\u6700\u5c0f\u306ek\u3092\u63a2\u7d22\u3067\u304d\u308b\u3002\u5168\u4f53$O(N\\log N)$\u3002<\/p>\n\n\n\n

C: A\u306b\u64cd\u4f5c\u3092\u884c\u3046\u3068\u5fc5\u305a\u305d\u306e\u64cd\u4f5c\u3092\u3057\u305f\u4f4d\u7f6e\u306b2\u3064\u540c\u3058\u5024\u304c\u4e26\u3093\u3060\u72b6\u614b\u306b\u306a\u308b\u3002\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u6700\u521d\u304b\u3089\u4e00\u81f4\u3057\u3066\u3044\u308b(A=B)\u5834\u5408\u3067\u306a\u3044\u9650\u308aB\u306b\u306f\u6700\u4f4e\u3067\u3082\u4e00\u304b\u62402\u3064\u540c\u3058\u5024\u304c\u4e26\u3093\u3067\u3044\u308b\u7b87\u6240\u304c\u5fc5\u8981\u306b\u306a\u308b\u3002\u306a\u306e\u3067\u3053\u308c\u3092\u307e\u305a\u5224\u5b9a\u3059\u308b\u3002$A_{N+1}=A_1$\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3002<\/p>\n\n\n\n

A\u306b\u64cd\u4f5c\u3092\u884c\u3063\u3066\u3069\u3046\u3044\u3046\u3053\u3068\u304c\u51fa\u6765\u308b\u304b\u3092\u8003\u3048\u308b\u3002\u307e\u305a\u3001\u3050\u308b\u3050\u308b\u56de\u3059\u3053\u3068\u304c\u51fa\u6765\u308b\u3002\u305f\u3060\u30572\u3064\u540c\u3058\u5024\u304c\u4e26\u3076\u7b87\u6240\u3092\u6700\u4f4e1\u304b\u6240\u4f5c\u308b\u3068\u3044\u3046\u6761\u4ef6\u4ed8\u304d\u30022\u3064\u540c\u3058\u5024\u304c\u4e26\u3076\u7b87\u6240\u306f\u4efb\u610f\u306b\u79fb\u52d5\u3067\u304d\u308b\u306e\u3067\u6700\u4f4e1\u304b\u6240\u3042\u308a\u3055\u3048\u3059\u308c\u3070\u3088\u3044\u3002\u305d\u308c\u304b\u3089\u540c\u3058\u5024\u3092\u5e83\u3052\u308b\u3053\u3068\u304c\u51fa\u6765\u308b\u30021,2,3,4,5…\u3068\u3044\u3046\u90e8\u5206\u304c\u3042\u3063\u305f\u30891,3,3,3,1…\u306b\u3067\u304d\u308b\u3002\u524d\u306b\u3082\u5f8c\u308d\u306b\u3082\u5e83\u3052\u308b\u3053\u3068\u304c\u51fa\u6765\u308b\u306e\u306f\u56de\u8ee2\u3067\u304d\u308b\u3053\u3068\u304b\u3089\u5c0e\u304b\u308c\u308b\u3002\u305d\u3057\u3066\u91cd\u8981\u306a\u70b9\u3068\u3057\u3066\u3001\u5883\u76ee\u3092\u5897\u3084\u3059\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u30021,1,2,2\u304b\u30891,2,1,2\u3092\u932c\u6210\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n

\u4ee5\u4e0a\u3092\u8e0f\u307e\u3048\u308b\u3068\u3001B\u3092\u30e9\u30f3\u30ec\u30f3\u30b0\u30b9\u5727\u7e2e\u3057\u3066\u6587\u5b57\u3060\u3051\u3092\u53d6\u308a\u51fa\u3057\u305f\u6587\u5b57\u5217($B’$\u3068\u3059\u308b)\u304cA\u306e\u90e8\u5206\u5217\u3067\u3042\u308c\u3070\u826f\u3055\u305d\u3046\u3060\u3068\u3044\u3046\u3053\u3068\u304c\u5206\u304b\u308b\u3002\u305f\u3060\u3057\u3001\u4efb\u610f\u306b\u56de\u8ee2\u3067\u304d\u308b\u306e\u3067A\u3092\u56de\u8ee2\u3055\u305b\u305f\u3044\u305a\u308c\u304b\u306e\u6587\u5b57\u5217\u306e\u90e8\u5206\u5217\u3067\u3042\u308c\u3070\u826f\u3044\u3002\u3053\u3053\u304c\u96e3\u3057\u304f\u3001\u53b3\u5bc6\u306a\u8a3c\u660e\u304c\u51fa\u6765\u306a\u304b\u3063\u305f\u3002<\/p>\n\n\n\n

\u3068\u308a\u3042\u3048\u305a\u56de\u8ee2\u3092\u8a31\u3059\u5834\u5408\u306e\u51e6\u7406\u306e\u30bb\u30aa\u30ea\u30fc\u3068\u3057\u3066A\u306e\u9577\u3055\u30922\u500d\u306b\u3057\u3066\u304a\u304f($A’$\u3068\u3059\u308b)\u3002$B’$\u304c\u3053\u308c\u306e\u90e8\u5206\u5217\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u307e\u305a\u5224\u5b9a\u3059\u308b\u3002\u3053\u3053\u3067\u90e8\u5206\u5217\u3067\u306a\u3051\u308c\u3070\u5373\u30a2\u30a6\u30c8\u3060\u304c\u3001\u90e8\u5206\u5217\u3067\u3042\u3063\u3066\u3082OK\u3068\u306f\u65ad\u5b9a\u3067\u304d\u306a\u3044\u3002$A=(1,1,2,2), B’=(1,2,1,2)$\u3068\u3044\u3063\u305f\u30b1\u30fc\u30b9\u3092\u8003\u3048\u308b\u3068\u3001$B’$\u306f$A$\u3092\u3069\u3046\u56de\u8ee2\u3055\u305b\u3066\u3082\u305d\u306e\u90e8\u5206\u5217\u306b\u306f\u306a\u3089\u306a\u3044\u304c\u3001$A’=(1,1,2,2,1,1,2,2)$\u306e\u90e8\u5206\u5217\u306b\u306f\u306a\u3063\u3066\u3057\u307e\u3046\u3002\u3053\u308c\u3092\u306f\u3058\u304f\u305f\u3081\u306b\u3001$A’$\u306e\u90e8\u5206\u5217\u3068\u3057\u3066$B’$\u3092\u53d6\u308a\u51fa\u3057\u305f\u3068\u304d\u306b$A’$\u4e0a\u3067\u9577\u3055\u304c$N$\u3092\u8d85\u3048\u306a\u3044\u3053\u3068\u3092\u30c1\u30a7\u30c3\u30af\u3059\u308b\u3002<\/p>\n\n\n\n

\u524d\u304b\u3089\u30de\u30c3\u30c1\u3057\u3066$A’_k$\u3067\u7d42\u308f\u3063\u305f\u5834\u5408\u3001$B’$\u304c$A’: [k-N+1, k]$\u306e\u90e8\u5206\u5217\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3059\u308b\u3002\u3053\u308c\u3067\u90e8\u5206\u5217\u3060\u3063\u305f\u3089\u30bb\u30fc\u30d5\u3001\u90e8\u5206\u5217\u3067\u306a\u304b\u3063\u305f\u3089\u30a2\u30a6\u30c8\u3002N\u306e\u7bc4\u56f2\u5185\u306b\u53ce\u307e\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u304b\u3081\u3066\u3084\u308b\u3068\u3044\u3046\u6c17\u6301\u3061\u3067\u3053\u3046\u3044\u3046\u611f\u3058\u306e\u5b9f\u88c5\u3092\u3057\u305f\u304c\u3001\u6b63\u5f53\u6027\u306e\u8a3c\u660e\u306f\u51fa\u6765\u306a\u304b\u3063\u305f\u3002\u3068\u306b\u304b\u304fAC\u3057\u305f\u306e\u3067\u30e8\u30b7\uff01(\u3088\u304f\u306a\u3044)<\/p>\n\n\n\n

D: 1\u306e\u4f4d\u7f6e\u3055\u3048\u7279\u5b9a\u3067\u304d\u308c\u307020000\u56de\u7a0b\u5ea6\u3067\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u51fa\u6765\u305d\u3046\u3068\u3044\u3046\u3053\u3068\u306f\u5206\u304b\u3063\u305f\u304c\u30011\u3092\u7279\u5b9a\u3059\u308b\u65b9\u6cd5\u304c\u601d\u3044\u3064\u304b\u306a\u304b\u3063\u305f\u3002\u5f8c\u3067upsolve\u3057\u305f\u3044\u3002<\/p>\n\n\n\n

\n\n\n\n

\u7b4b\u30c8\u30ec\u3092\u3057\u305f\u3002\u4eca\u65e5\u306f\u80cc\u7b4b\u3002<\/p>\n\n\n\n

\n\n\n\n

\u4e00\u65e5\u4e2d\u30ed\u30c3\u30af\u30de\u30f3X\u3092\u30d7\u30ec\u30a4\u3057\u307e\u304f\u3063\u3066\u3044\u305f\u3002\u4e00\u6c17\u306b\u30e9\u30b9\u30dc\u30b9\u30b7\u30b0\u30de\u307e\u3067\u7a81\u304d\u9032\u3093\u3060\u3002<\/p>\n\n\n\n

\u30e9\u30a4\u30d5\u6700\u5927\u5024\u30a2\u30c3\u30d7\u3092\u56de\u53ce\u3057\u305f\u307b\u304b\u3001\u30c0\u30e1\u30fc\u30b8\u8efd\u6e1b\u3068\u982d\u7a81\u304d\u306e\u30d1\u30ef\u30fc\u30a2\u30c3\u30d7\u3092\u56de\u53ce\u3057\u305f\u7d50\u679c\u3001\u3042\u3093\u306a\u306b\u30e0\u30ea\u30e0\u30ea\u8a00\u3063\u3066\u305f\u30dc\u30b9\u305f\u3061\u304c\u304a\u3088\u305d\u96d1\u5175\u3068\u5316\u3057\u305f\u3002\u30b5\u30d6\u30bf\u30f3\u30af\u30823\u3064\u307e\u3067\u306b\u5897\u3048\u305f\u3002<\/p>\n\n\n\n

\u3042\u3068\u8aac\u660e\u66f8\u3092\u3061\u3083\u3093\u3068\u8aad\u3093\u3060\u7d50\u679c\u3001\u30c0\u30c3\u30b7\u30e5\u58c1\u30b8\u30e3\u30f3\u30d7\u3092\u4f1a\u5f97\u3057\u305f\u3002\u6614\u306e\u30b2\u30fc\u30e0\u3068\u3044\u3046\u306e\u306f\u8aac\u660e\u66f8\u3092\u8aad\u3080\u3082\u306e\u3060\u306d\u3002<\/p>\n\n\n\n

\u6700\u521d\u306f\u7121\u7406\u30b2\u30fc\u306b\u3057\u304b\u601d\u3048\u306a\u304b\u3063\u305f\u304c\u3001\u306a\u3093\u3060\u304b\u3093\u3060\u8aac\u660e\u66f8\u4ee5\u5916\u4f55\u3082\u898b\u305a\u306b\u3061\u3083\u3093\u3068\u9032\u3081\u308b\u3053\u3068\u304c\u51fa\u6765\u3066\u3057\u3063\u304b\u308a\u4f5c\u3089\u308c\u305f\u30b2\u30fc\u30e0\u306b\u611f\u3058\u3066\u3044\u308b\u3002\u3084\u308a\u5fdc\u3048\u3082\u3057\u3063\u304b\u308a\u611f\u3058\u305f\u3002\u30d1\u30ef\u30fc\u30a2\u30c3\u30d7\u304c\u521d\u4ee3\u30b7\u30ea\u30fc\u30ba\u306b\u8f2a\u3092\u304b\u3051\u3066\u91cd\u8981\u306a\u30d5\u30a1\u30af\u30bf\u30fc\u306b\u306a\u3063\u3066\u3044\u308b\u306e\u3067\u6700\u521d\u306e\u3068\u3063\u304b\u304b\u308a\u304c\u96e3\u3057\u3044\u611f\u3058\u306b\u306a\u3063\u3066\u3044\u308b\u304b\u3082\u3002\u305d\u3053\u306f\u3082\u3046\u3061\u3087\u3063\u3068\u8abf\u6574\u3067\u304d\u305f\u3093\u3058\u3083\u306a\u3044\u304b\u3068\u3044\u3046\u98a8\u306b\u601d\u3046\u304c\u3001\u30ed\u30c3\u30af\u30de\u30f3\u30b7\u30ea\u30fc\u30ba\u3068\u3044\u3048\u3070\u30b9\u30c6\u30fc\u30b8\u9078\u629e\u753b\u9762\u306a\u306e\u3067\u305d\u3053\u3092\u5909\u3048\u308b\u306e\u3082\u306a\u3042\u3068\u3044\u3046\u611f\u3058\u304c\u3059\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

ARC154\u306b\u51fa\u305f\u3002 A: \u9811\u5f35\u3063\u3066\u8003\u5bdf\u3059\u308b\u3068\u3001\u3068\u306b\u304b\u304f\u7247\u4e00\u65b9\u3092\u3067\u304b\u304f\u3057\u3066\u7247\u4e00\u65b9\u3092\u5c0f\u3055\u304f\u3059\u308b\u3068\u6700\u5c0f\u306b\u306a\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u3002\u3042\u3068\u306fA\u3068B\u306emod 998244353\u3092\u8a08\u7b97\u3057\u3066\u639b\u3051\u5408\u308f\u305b\u308b\u3060\u3051\u3002 B: \u9006\u306e\u64cd\u4f5c\u3092\u8003\u3048\u308b\u3068\u300c\u4efb\u610f\u306e … <\/p>\n

Read more » “2023\/1\/22(\u65e5)”<\/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-4034","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/posts\/4034","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=4034"}],"version-history":[{"count":4,"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/posts\/4034\/revisions"}],"predecessor-version":[{"id":4038,"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/posts\/4034\/revisions\/4038"}],"wp:attachment":[{"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/media?parent=4034"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/categories?post=4034"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/k.foolslab.net\/dailyreport\/wp-json\/wp\/v2\/tags?post=4034"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}