{"id":1100,"date":"2024-02-14T11:07:06","date_gmt":"2024-02-14T03:07:06","guid":{"rendered":"http:\/\/ggapa.net:81\/?p=1100"},"modified":"2024-02-14T11:44:43","modified_gmt":"2024-02-14T03:44:43","slug":"codeforces-round-925-div-3cf1931","status":"publish","type":"post","link":"http:\/\/ggapa.net:81\/2024\/02\/14\/codeforces-round-925-div-3cf1931\/","title":{"rendered":"Codeforces Round 925 (Div. 3)(CF1931)"},"content":{"rendered":"<h1>A- D \u7b80\u5355<\/h1>\n<h1>F<\/h1>\n<p>\u5c06\u9898\u76ee\u6761\u4ef6\u8f6c\u5316\u4e00\u4e0b\uff0c\u76f8\u5f53\u4e8e\u5c31\u662f\u7ed9\u4e86\u4e00\u5806\u5148\u540e\u5173\u7cfb\uff0c\u8003\u8651\u5c06\u524d\u9762\u7684\u4e0e\u540e\u9762\u7684\u8fde\u8fb9\uff0c\u4e5f\u5c31\u662f $a_{ij} \\rightarrow a_{ij+1}$ \u8fde\u8fb9\uff0c\u7136\u540e\u7528\u62d3\u6251\u5224\u73af\uff0c\u5982\u679c\u65e0\u73af\u5219\u6709\u89e3\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002<\/p>\n<p>\u603b\u7ed3\uff1a<\/p>\n<ul>\n<li>\u5bf9\u4e8e\u9898\u76ee\u4e2d\u6709\u4e00\u5806\u5173\u7cfb\u65f6\uff0c\u53ef\u4ee5\u4e92\u76f8\u8fde\u8fb9\uff0c\u82e5\u6709\u73af\uff0c\u5219\u8bf4\u660e\u4e86\u5173\u7cfb\u4e0d\u6210\u7acb\u3002 <\/li>\n<li>\u2753\u8fde\u8fb9\u8fd8\u9002\u7528\u4e8e\u6392\u5e8f\u7c7b\u95ee\u9898\u3002<\/li>\n<\/ul>\n<h1>G<\/h1>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/espresso.codeforces.com\/d862915ed3dc627101b0e632c1c778b818648879.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/espresso.codeforces.com\/d862915ed3dc627101b0e632c1c778b818648879.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" \/><\/div><\/p>\n<p>\u56db\u4e2a\u62fc\u56fe\uff0c\u5176\u4e2a\u6570\u8bb0\u4e3a $c_1,c_2,c_3,c_4$ \uff0c\u5206\u6790\u62fc\u56fe\u7684\u51f9\u51f8\u6027\uff0c\u53ea\u6709\u62fc\u56fe 1\u30012 \u4f1a\u6539\u53d8\u6574\u4e2a\u5e8f\u5217\u7684\u51f9\u51f8\u6027\uff0c\u4e14 1\u30012 \u62fc\u56fe\u53ea\u80fd\u4ea4\u66ff\u62fc\u5728\u4e00\u8d77\u3002<\/p>\n<p>\u90a3\u4e48\u53ef\u4ee5\u5f97\u5230\uff0c\u82e5 $|c_1-c_2| &gt; 1$ \u5219\u95ee\u9898\u65e0\u89e3\uff0c\u5426\u5219\u4e00\u5b9a\u6709\u89e3\uff0c\u800c\u4e14\u62fc\u56fe 3\u30014 \u5e76\u4e0d\u4f1a\u76f8\u4e92\u5f71\u54cd\uff0c\u6211\u4eec\u53ef\u4ee5\u8fdb\u884c\u5206\u7c7b\u8ba8\u8bba\u3002<\/p>\n<ul>\n<li>\n<p>\u82e5 $c_1 = c_2 = 0$ \uff0c\u4e14 $c_3\\neq 0 \u4e14 c_4 \\neq 0$ \uff0c\u5219\u65e0\u89e3\uff0c\u5426\u5219\u65b9\u6848\u6570\u4e3a 1\u3002<\/p>\n<\/li>\n<li>\n<p>\u82e5 $c_1 = c_2$ \uff0c\u6709\u4e24\u79cd\u60c5\u51b5\uff1a<\/p>\n<ol>\n<li>\u82e5 1 \u5f00\u5934\uff0c\u90a3\u4e48 3 \u6709 $c_1$ \u4e2a\u5730\u65b9\u53ef\u4ee5\u63d2\u5165\uff0c4 \u6709 $c_1 + 1$ \u4e2a\u5730\u65b9\u53ef\u4ee5\u63d2\u5165\uff0c\u65b9\u6848\u6570\u4e3a $\\binom{c_1+c_3-1}{c_1-1} \\binom{c_2+c_4}{c_1}$ \u3002<\/li>\n<li>\u82e5 2 \u5f00\u5934\uff0c\u90a3\u4e48 3 \u6709 $c_1 + 1$ \u4e2a\u5730\u65b9\u53ef\u4ee5\u63d2\u5165\uff0c4 \u6709 $c_1$ \u4e2a\u5730\u65b9\u53ef\u4ee5\u63d2\u5165\uff0c\u65b9\u6848\u6570\u4e3a $\\binom{c_1+c_3}{c_1} \\binom{c_1+c_4-1}{c_1-1}$\u3002<\/li>\n<\/ol>\n<p>\u603b\u65b9\u6848\u6570\u4e3a\u4e8c\u8005\u7684\u548c $\\binom{c_1+c_3-1}{c_1-1} \\binom{c_2+c_4}{c_1} + \\binom{c_1+c_3}{c_1}\\binom{c_1+c_4-1}{c_1-1}$\u3002<\/p>\n<\/li>\n<li>\n<p>\u82e5 $c_1 = c_2 + 1$ \u62fc\u597d 1,2 \u53ea\u6709\u4e00\u79cd\u65b9\u6848\uff0c3,4 \u5747\u6709 $c_1$ \u4e2a\u5730\u65b9\u53ef\u4ee5\u63d2\u5165\uff0c\u65b9\u6848\u6570\u4e3a $\\binom{c_1+c_3 - 1}{c_1 - 1} \\binom{c_1+c_4-1}{c_1-1}$\u3002<\/p>\n<\/li>\n<li>\n<p>\u82e5 $c_1 = c_2 - 1$ \u62fc\u597d 1,2 \u4e5f\u53ea\u6709\u4e00\u79cd\u65b9\u6848\uff0c 3,4 \u5747\u6709 $c_1 + 1 $ \u4e2a\u5730\u65b9\u53ef\u4ee5\u63d2\u5165\uff0c\u65b9\u6848\u6570\u4e3a $\\binom{c_1+c_3}{c_1} \\binom{c_1+c_4}{c_1}$\u3002<\/p>\n<\/li>\n<\/ul>\n<p>\u9884\u5904\u7406\u7ec4\u5408\u6570\uff0c$O(1)$ \u8be2\u95ee\u5373\u53ef\u3002<\/p>\n<p>\u603b\u7ed3\uff1a <\/p>\n<ul>\n<li>\u82e5\u6709\u65e0\u89e3\u7684\u60c5\u51b5\uff0c\u53ef\u4ee5\u5148\u5206\u6790\u65e0\u89e3\u7684\u60c5\u51b5\u3002<\/li>\n<li>\u82e5\u67d0\u9879\u4e8b\u7269\u5bf9\u4e8e\u67d0\u4e9b\u6027\u8d28\u6ca1\u6709\u6539\u53d8\uff0c\u5219\u65e0\u9700\u5728\u610f\uff0c\u4f18\u5148\u5206\u6790\u60c5\u51b5\u6bd4\u8f83\u5c11\u4e14\u5bf9\u67d0\u4e9b\u6027\u8d28\uff08\u6bd4\u5982\u8bf4\u6709\u65e0\u89e3\uff09\u6709\u5f71\u54cd\u7684\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>A- D \u7b80\u5355 F \u5c06\u9898\u76ee\u6761\u4ef6\u8f6c\u5316\u4e00\u4e0b\uff0c\u76f8\u5f53\u4e8e\u5c31\u662f\u7ed9\u4e86\u4e00\u5806\u5148\u540e\u5173\u7cfb\uff0c\u8003\u8651\u5c06\u524d\u9762\u7684\u4e0e\u540e\u9762\u7684\u8fde\u8fb9\uff0c\u4e5f\u5c31\u662f $a_{ [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[34],"_links":{"self":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts\/1100"}],"collection":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/comments?post=1100"}],"version-history":[{"count":8,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts\/1100\/revisions"}],"predecessor-version":[{"id":1108,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts\/1100\/revisions\/1108"}],"wp:attachment":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/media?parent=1100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/categories?post=1100"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/tags?post=1100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}