{"id":193,"date":"2019-08-08T04:37:00","date_gmt":"2019-08-08T04:37:00","guid":{"rendered":"https:\/\/imwarming.com\/?p=193"},"modified":"2019-08-08T04:37:00","modified_gmt":"2019-08-08T04:37:00","slug":"sg%e5%87%bd%e6%95%b0%e5%85%a5%e9%97%a8%e7%90%86%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/imwarming.com\/?p=193","title":{"rendered":"sg\u51fd\u6570\u5165\u95e8\u7406\u89e3"},"content":{"rendered":"<p>\u9996\u5148\u7406\u89e3sg\u51fd\u6570\u5fc5\u987b\u5148\u7406\u89e3mex\u51fd\u6570<\/p>\n<p>mex\u662f\u6c42\u9664\u5b83\u96c6\u5408\u5185\u7684\u6700\u5c0f\u5927\u4e8e\u7b49\u4e8e0\u7684\u6574\u6570\uff0c\u4f8b\uff1amex{1\uff0c2}=0\uff1bmex{2}=0\uff1bmex{0\uff0c1\uff0c2}=3\uff1bmex{0\uff0c5}=1\u3002<\/p>\n<p>\u800csg\u51fd\u6570\u662f\u5565\u5462\uff1f<\/p>\n<p>\u5bf9\u4e8e\u4efb\u610f\u72b6\u6001 x \uff0c \u5b9a\u4e49 sg(x) = mex(f)\uff0c\u5176\u4e2df \u662f x 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\/><\/p>\n<p>\u770b\u4e0d\u61c2\uff0c\u54b1\u76f4\u63a5\u6765\u4e2a\u4f8b\u5b50\uff1a<\/p>\n<p>\u4f8b\u5982\uff1a\u53d6\u77f3\u5b50\u95ee\u9898\uff0c\u67091\u5806n\u4e2a\u7684\u77f3\u5b50\uff0c\u6bcf\u6b21\u53ea\u80fd\u53d6{1\uff0c3,4}\u4e2a\u77f3\u5b50\uff0c\u5148\u53d6\u5b8c\u77f3\u5b50\u8005\u80dc\u5229\uff0c\u90a3\u4e48\u5404\u4e2a\u6570\u7684sg\u503c\u4e3a\u591a\u5c11\uff1f<\/p>\n<p>sg[0]=0\uff0cf[]={1,3,4},<\/p>\n<p>&nbsp;<\/p>\n<p>x=1\u65f6\uff0c\u53ef\u4ee5\u53d6\u8d701-f{1}\u4e2a\u77f3\u5b50\uff0c\u5269\u4f59{0}\u4e2a\uff0cmex{sg[0]}={0}\uff0c\u6545sg[1]=1;<\/p>\n<p>x=2\u65f6\uff0c\u53ef\u4ee5\u53d6\u8d702-f{1}\u4e2a\u77f3\u5b50\uff0c\u5269\u4f59{1}\u4e2a\uff0cmex{sg[1]}={1}\uff0c\u6545sg[2]=0\uff1b<\/p>\n<p>x=3\u65f6\uff0c\u53ef\u4ee5\u53d6\u8d703-f{1,3}\u4e2a\u77f3\u5b50\uff0c\u5269\u4f59{2,0}\u4e2a\uff0cmex{sg[2],sg[0]}={0,0}\uff0c\u6545sg[3]=1;<\/p>\n<p>x=4\u65f6\uff0c\u53ef\u4ee5\u53d6\u8d704-f{1,3,4}\u4e2a\u77f3\u5b50\uff0c\u5269\u4f59{3,1,0}\u4e2a\uff0cmex{sg[3],sg[1],sg[0]}={1,1,0},\u6545sg[4]=2;<\/p>\n<p>x=5\u65f6\uff0c\u53ef\u4ee5\u53d6\u8d705-f{1,3,4}\u4e2a\u77f3\u5b50\uff0c\u5269\u4f59{4,2,1}\u4e2a\uff0cmex{sg[4],sg[2],sg[1]}={2,0,1},\u6545sg[5]=3\uff1b<\/p>\n<p>\u4ee5\u6b64\u7c7b\u63a8&#8230;..<\/p>\n<p>&nbsp; &nbsp;x &nbsp; &nbsp; &nbsp; &nbsp; 0 &nbsp;1 &nbsp;2 &nbsp;3 &nbsp;4 &nbsp;5 &nbsp;6 &nbsp;7 &nbsp;8&#8230;.<\/p>\n<p>sg[x] &nbsp; &nbsp; &nbsp;0 &nbsp;1 &nbsp;0 &nbsp;1 &nbsp;2 &nbsp;3 &nbsp;2 &nbsp;0 &nbsp;1&#8230;<\/p>\n<p>\u8ba1\u7b97\u4ece1-n\u8303\u56f4\u5185\u7684sg\u503c\u3002<\/p>\n<p>f(\u5b58\u50a8\u53ef\u4ee5\u8d70\u7684\u6b65\u6570\uff0cf[0]\u8868\u793a\u53ef\u4ee5\u6709\u591a\u5c11\u79cd\u8d70\u6cd5)<\/p>\n<p>\u8fd9\u4e0b\u5c31ojbk\u4e86\u5427<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/img2018.cnblogs.com\/blog\/1634852\/201908\/1634852-20190808123603064-901819851.jpg\" alt=\"\" width=\"190\" height=\"193\" \/><\/p>\n<p>f[]\u9700\u8981\u4ece\u5c0f\u5230\u5927\u6392\u5e8f<\/p>\n<p>1.\u53ef\u9009\u6b65\u6570\u4e3a1~m\u7684\u8fde\u7eed\u6574\u6570\uff0c\u76f4\u63a5\u53d6\u6a21\u5373\u53ef\uff0csg(x) = x % (m+1);<\/p>\n<p>2.\u53ef\u9009\u6b65\u6570\u4e3a\u4efb\u610f\u6b65\uff0csg(x)&nbsp;= x;<\/p>\n<p>3.\u53ef\u9009\u6b65\u6570\u4e3a\u4e00\u7cfb\u5217\u4e0d\u8fde\u7eed\u7684\u6570\uff0c\u7528getsg()\u8ba1\u7b97<\/p>\n<p>\u518d\u9644\u4e2a\u6a21\u677f\u5427<\/p>\n<div class=\"cnblogs_code\">\n<pre><span style=\"color: #008080;\"> 1<\/span> <span style=\"color: #008000;\">\/\/<\/span><span style=\"color: #008000;\">f[]\uff1a\u53ef\u4ee5\u53d6\u8d70\u7684\u77f3\u5b50\u4e2a\u6570\n<\/span><span style=\"color: #008080;\"> 2<\/span> <span style=\"color: #008000;\">\/\/<\/span><span style=\"color: #008000;\">sg[]:0~n\u7684sg\u51fd\u6570\u503c<\/span>\n<span style=\"color: #008080;\"> 3<\/span> <span style=\"color: #0000ff;\">int<\/span><span style=\"color: #000000;\"> f[maxn],sg[maxn],mex[maxn];\n<\/span><span style=\"color: #008080;\"> 4<\/span> <span style=\"color: #0000ff;\">void<\/span> getsg(<span style=\"color: #0000ff;\">int<\/span><span style=\"color: #000000;\"> n){\n<\/span><span style=\"color: #008080;\"> 5<\/span>     <span style=\"color: #0000ff;\">int<\/span><span style=\"color: #000000;\"> i,j;\n<\/span><span style=\"color: #008080;\"> 6<\/span>     memset(sg,<span style=\"color: #800080;\">0<\/span>,<span style=\"color: #0000ff;\">sizeof<\/span><span style=\"color: #000000;\">(sg));\n<\/span><span style=\"color: #008080;\"> 7<\/span>     <span style=\"color: #0000ff;\">for<\/span>(i=<span style=\"color: #800080;\">1<\/span>;i&lt;=n;i++<span style=\"color: #000000;\">){\n<\/span><span style=\"color: #008080;\"> 8<\/span>         memset(mex,<span style=\"color: #800080;\">0<\/span>,<span style=\"color: #0000ff;\">sizeof<\/span><span style=\"color: #000000;\">(mex));\n<\/span><span style=\"color: #008080;\"> 9<\/span>         <span style=\"color: #0000ff;\">for<\/span>(j=<span style=\"color: #800080;\">1<\/span>;f[j]&lt;=i&amp;&amp;f[j]&lt;=m;j++) <span style=\"color: #008000;\">\/\/<\/span><span style=\"color: #008000;\">\u6ce8\u610f\u52a0f[i]\u7684\u9650\u5b9a\u6761\u4ef6\uff0c\u6b64\u5904\u4e3af[j]&lt;=m<\/span>\n<span style=\"color: #008080;\">10<\/span>             mex[sg[i-f[j]]]=<span style=\"color: #800080;\">1<\/span><span style=\"color: #000000;\">;\n<\/span><span style=\"color: #008080;\">11<\/span>         <span style=\"color: #0000ff;\">for<\/span>(j=<span style=\"color: #800080;\">0<\/span>;j&lt;=n;j++){    <span style=\"color: #008000;\">\/\/<\/span><span style=\"color: #008000;\">\u6c42mex\u4e2d\u672a\u51fa\u73b0\u7684\u6700\u5c0f\u7684\u975e\u8d1f\u6574\u6570<\/span>\n<span style=\"color: #008080;\">12<\/span>             <span style=\"color: #0000ff;\">if<\/span>(mex[j]==<span style=\"color: #800080;\">0<\/span><span style=\"color: #000000;\">){\n<\/span><span style=\"color: #008080;\">13<\/span>                 sg[i]=<span style=\"color: #000000;\">j;\n<\/span><span style=\"color: #008080;\">14<\/span>                 <span style=\"color: #0000ff;\">break<\/span><span style=\"color: #000000;\">;\n<\/span><span style=\"color: #008080;\">15<\/span> <span style=\"color: #000000;\">            }\n<\/span><span style=\"color: #008080;\">16<\/span> <span style=\"color: #000000;\">        }\n<\/span><span style=\"color: #008080;\">17<\/span>         <span style=\"color: #008000;\">\/\/<\/span><span style=\"color: #008000;\">cout&lt;&lt;i&lt;&lt;\" \"&lt;&lt;sg[i]&lt;&lt;endl;<\/span>\n<span style=\"color: #008080;\">18<\/span> <span style=\"color: #000000;\">    }\n<\/span><span style=\"color: #008080;\">19<\/span> }<\/pre>\n<\/div>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u9996\u5148\u7406\u89e3sg\u51fd\u6570\u5fc5\u987b\u5148\u7406\u89e3mex\u51fd\u6570 mex\u662f\u6c42\u9664\u5b83\u96c6\u5408\u5185\u7684\u6700\u5c0f\u5927\u4e8e\u7b49\u4e8e0\u7684\u6574\u6570\uff0c\u4f8b\uff1amex{1\uff0c2 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