CF79-D<\/a><\/p>\n<\/p>\n
\n <\/p>\n
<\/p>\n
<\/p>\n
\u9996\u5148\u8003\u8651\u8fde\u7eed\u7ffb\u8f6c \\(a\\) \u4e2a\u786c\u5e01\u7684\u64cd\u4f5c\u8981\u600e\u4e48\u5b9e\u73b0\u3002<\/p>\n
\u8bbe \\(s_i \\kern 4pt (1 \\leq i \\leq n)\\) \u4e3a\u7b2c \\(i\\) \u4e2a\u786c\u5e01\u7684\u72b6\u6001\uff0c\\(0\\) \u8868\u793a\u6b63\u9762\u671d\u4e0a\uff0c\\(1\\) \u8868\u793a\u53cd\u9762\u671d\u4e0a\u3002<\/p>\n
\u5f53\u7136\u6700\u6734\u7d20\u7684\u505a\u6cd5\u5c31\u662f for<\/span>\u00a0 \u4e00\u904d\u533a\u95f4\uff0c\u628a\u91cc\u9762\u7684\u6bcf\u4e2a\u6570 \\(s_i \\kern 4pt \\scriptsize\\wedge=\\normalsize \\kern 1pt 1\\) \u3002\u4f46\u662f\u8fd9\u6837\u505a\u663e\u7136<\/strong>\u662f\u4e0d\u4f18\u7684\u3002<\/p>\n\u53d1\u73b0\u56e0\u4e3a\u6bcf\u4e2a\u786c\u5e01\u662f\u6b63\u9762\u671d\u4e0a\u8fd8\u662f\u53cd\u9762\u671d\u4e0a\u53ea\u4e0e\u7ffb\u8f6c\u5b83\u6b21\u6570\u7684\u5947\u5076\u6027<\/strong>\u6709\u5173\uff0c\u6240\u4ee5\u53ef\u4ee5\u8bb0\u4e00\u4e2a\u5dee\u5206\u6570\u7ec4<\/strong>\uff08\u5176\u5b9e\u662f\u5f02\u6216\u6570\u7ec4\uff09<\/del>\u8868\u793a\u76f8\u90bb\u4e24\u4e2a \\(s\\) \u7684\u5f02\u6216\u503c\u3002\u5373\u8bb0 \\(b_i = s_i \\oplus s_{i+1} \\kern 4pt (1 \\leq i \\leq n-1)\\)\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u5b83\u7684\u6b63\u786e\u6027\uff0c\u518d\u4ee4 \\(b_0=s_1,\\kern 4pt b_n=s_n\\) \u3002\u7b2c \\(i\\) \u4e2a\u786c\u5e01\u7684\u72b6\u6001\u5c31\u53ef\u4ee5\u901a\u8fc7 \\(b_0 \\oplus b_1 \\oplus \\cdots \\oplus b_{i-1}\\) \u6765\u8868\u793a\u3002<\/p>\n\u8fd9\u6837\u5c31\u53ef\u4ee5\u65b9\u4fbf\u7684\u8868\u793a\u51fa\u7ffb\u8f6c\u4e00\u4e2a\u533a\u95f4\u5185\u7684\u6240\u6709\u786c\u5e01\u7684\u64cd\u4f5c\u3002\u8981\u7ffb\u8f6c \\(l\\) ~ \\(r\\) \u5185\u7684\u6240\u6709\u786c\u5e01\uff0c\u53ea\u8981\u628a \\(b_{l-1}\\) \u548c \\(b_r\\)<\/strong> \u90fd \\(\\scriptsize\\wedge=\\normalsize \\kern 1pt 1\\) \u5c31\u53ef\u4ee5\u4e86\u3002\u56e0\u4e3a\u5728\u524d\u7f00\u548c\uff08\u5176\u5b9e\u662f\u524d\u7f00\u5f02\u6216\uff09<\/del>\u7684\u65f6\u5019\uff0c\u66f4\u6539\u4e86\u533a\u95f4\u5934\u524d\u4e00\u4f4d\u5947\u5076\u6027\uff0c\u533a\u95f4\u5185\u7684\u6240\u6709\u6570\u7684\u5947\u5076\u6027\u4e5f\u4f1a\u5bf9\u5e94\u6539\u53d8\uff1b\u66f4\u6539\u533a\u95f4\u5c3e\u7684\u5947\u5076\u6027\uff0c\u533a\u95f4\u5916\u7684\u6570\u7684\u5947\u5076\u6027\u4e0d\u53d7\u5f71\u54cd\u3002<\/p>\n\u53ef\u4ee5\u5feb\u901f\u8fdb\u884c\u533a\u95f4\u5185\u7684\u64cd\u4f5c\u4e4b\u540e\uff0c\u518d\u8003\u8651\u8fd9\u4e2a\u95ee\u9898\u7684\u672c\u8d28<\/strong>\u662f\u4ec0\u4e48\u3002<\/p>\n\u521d\u59cb\u72b6\u6001\u7684 \\(s\\) \u4e3a \\(\\underbrace {0,0, \\cdots ,0}_n\\) \uff0c\u5dee\u5206\u540e\u5f97\u5230\u521d\u59cb\u72b6\u6001\u7684 \\(b\\) \u4e3a \\(\\underbrace {0,0, \\cdots ,0}_{n + 1}\\) \u3002<\/p>\n
\u4e3e\u4e2a\u6817\u5b50\uff0c\u6709\u4e00\u4e2a \\(s\\) \u4e3a \\(0,0,0,1,1\\) \uff0c\u5dee\u5206\u540e\u5f97\u5230\u5b83\u7684 \\(b\\) \u4e3a \\(0,0,0,1,0,1\\) \u3002<\/p>\n
\u56e0\u4e3a\u64cd\u4f5c\u7684\u65e0\u5e8f\u6027\uff0c\u6240\u4ee5\u8981\u6c42\u7684\u7b54\u6848\u5c31\u662f\u628a \\(b\\) \u4e2d\u6240\u6709\u7684 \\(1\\) \u7ecf\u8fc7\u4e00\u7cfb\u5217\u64cd\u4f5c\u540e\u5168\u90e8\u53d8\u6210 \\(0\\)<\/strong> \u7684\u6700\u5c0f\u4ee3\u4ef7\u3002\u8fd9\u91cc\u7684\u64cd\u4f5c\u6307\u7684\u662f\u628a \\(b\\) \u4e2d\u7b2c \\(i\\) \u4f4d\u548c\u7b2c \\(i \\pm a\\) \u4f4d\u540c\u65f6\u7ffb\u8f6c<\/strong>\uff0c\u8fdb\u884c\u8fd9\u6837\u4e00\u6b21\u64cd\u4f5c\u7684\u4ee3\u4ef7\u4e3a \\(1\\) \u3002<\/p>\n\\(\\begin{array}{l} 0,{\\kern 4pt}0,{\\kern 4pt}0,{\\kern 4pt}1,{\\kern 4pt}0,{\\kern 4pt}1\\\\
\n\u00a0\\downarrow {\\kern 1pt} {\\kern 10pt} \\leftarrow 5 \\to {\\kern 9pt}\u00a0 \\downarrow \\\\ 1,{\\kern 4pt}0,{\\kern 4pt}0,{\\kern 4pt}1,{\\kern 4pt}0,{\\kern 4pt}0\\\\\u00a0 \\downarrow {\\kern 1pt} \\leftarrow 3 \\to \\downarrow \\\\ 0,{\\kern 4pt}0,{\\kern 4pt}0,{\\kern 4pt}0,{\\kern 4pt}0,{\\kern 4pt}0 \\end{array}\\)<\/p>\n
\u5982\u679c\u7b2c \\(i\\) \u4f4d\u548c\u7b2c \\(i \\pm a\\) \u4f4d\u90fd\u4e3a \\(1\\) \uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u901a\u8fc7\u4e00\u6b21\u64cd\u4f5c\u628a\u5b83\u4eec\u90fd\u53d8\u4e3a \\(0\\) \u3002<\/p>\n
\u6ce8\u610f\u5230\u53ef\u80fd\u4f1a\u51fa\u73b0\u6709\u7b2c \\(i\\) \u4f4d\u4e3a \\(1\\) \uff0c\u800c\u7b2c \\(i \\pm a\\) \u4f4d\u4e0d\u4e3a \\(1\\) \u7684\u60c5\u51b5\u3002\u5982\u679c\u6709\u89e3\u7684\u8bdd\uff0c\u90a3\u4e48\u7b2c \\(i \\pm a\\) \u4f4d\u4e00\u5b9a\u53ef\u4ee5\u901a\u8fc7\u5176\u4ed6\u4f4d\u7684\u64cd\u4f5c\u7ffb\u8f6c\u4e3a \\(1\\) \uff0c\u5426\u5219\u8fd9\u4e24\u4f4d\u5c06\u6c38\u8fdc\u65e0\u6cd5\u540c\u65f6\u6d88\u6389\u4e5f\u5c31\u65e0\u89e3\u4e86\u3002<\/p>\n
\uff08\u8fd9\u91cc\u672c\u6765\u597d\u50cf\u6709\u5f20\u56fe\uff0c\u4f46\u662f\u6211\u4e5f\u5fd8\u4e86\u662f\u4ec0\u4e48\u56fe\u4e86\u3002\u3002\u3002\u3002<\/p>\n
\u53d1\u73b0\u8fd9\u6837\u8fde\u9501\u64cd\u4f5c\u7684\u8fc7\u7a0b\u53ef\u4ee5\u8868\u793a\u5728\u4e00\u5f20\u65e0\u5411\u56fe<\/strong>\u4e2d\uff0c\u6bcf\u6b21\u6d88\u6389\u4e00\u5bf9 \\(1\\) \u5c31\u8868\u793a\u56fe\u4e2d\u7684\u4e00\u6761\u8def\u5f84\uff08\u6ce8\u610f<\/strong>\uff1a\u8def\u5f84\u4e2d\u53ef\u80fd\u4f1a\u5b58\u5728\u7ffb\u8f6c \\(0\\) \u7684\u4e2d\u95f4\u8282\u70b9\uff09\u3002\u6240\u4ee5\u628a \\(i\\) \u548c \\(i \\pm a\\) \u8fde\u4e00\u6761\u8fb9\u6743\u4e3a \\(1\\) \u7684\u65e0\u5411\u8fb9\uff0c\u5bf9\u6bcf\u4e00\u4e2a \\(b_i=1\\) \u7684 \\(i\\) \u90fd\u8dd1\u4e00\u904d\u5355\u6e90\u6700\u77ed\u8def\u5373\u53ef\u7b97\u51fa\u628a \\(i\\) \u548c \\(j\\) \u540c\u65f6\u7ffb\u8f6c<\/strong>\u6240\u9700\u8981\u7684\u6700\u5c0f\u4ee3\u4ef7\uff08\u8bb0\u5f55 \\(b_i=b_j=1\\) \u7684\u6700\u5c0f\u4ee3\u4ef7\u5373\u53ef\uff0c\u5176\u4ed6\u72b6\u6001\u90fd\u662f\u65e0\u7528\u7684\uff09\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u53ef\u4ee5\u4f7f\u7528 BFS<\/span>\u00a0 \u6765\u5b9e\u73b0\u3002<\/p>\n\u6700\u540e\u7684\u6700\u540e\uff0c\u77e5\u9053\u4e86\u540c\u65f6\u7ffb\u8f6c \\(b\\) \u4e2d\u4e24\u4e2a \\(1\\) \u7684\u6700\u5c0f\u4ee3\u4ef7\uff0c\u8981\u6c42\u7ffb\u8f6c \\(b\\) \u4e2d\u6240\u6709 \\(1\\) \u7684\u6700\u5c0f\u4ee3\u4ef7\u3002\u6ce8\u610f\u5230\u56e0\u4e3a \\(1 \\leq k \\leq 10\\)\uff0c\u6240\u4ee5 \\(b_i=1\\) \u7684 \\(i\\) \u7684\u4e2a\u6570\u4e0d\u4f1a\u8d85\u8fc7 \\(20\\) \u4e2a\uff0c\u53ef\u4ee5\u60f3\u5230 \u72b6\u538bDP<\/strong> \u3002\u628a \\(b_i=1\\) \u7684\u6570\u4f4d\u7684\u7ffb\u8f6c\u72b6\u6001<\/strong>\u538b\u6210\u4e00\u4e2a\u4e8c\u8fdb\u5236\u6570\uff0c\u67d0\u4e00\u4f4d\u4e0a\u4e3a \\(0\\) \u8868\u793a\u5bf9\u5e94 \\(b\\) \u4e2d\u7684\u8fd9\u4e00\u4f4d\u6ca1\u6709\u7ffb\u8f6c\uff0c\u4e3a \\(1\\) \u8868\u793a\u5bf9\u5e94 \\(b\\) \u4e2d\u7684\u8fd9\u4e00\u4f4d\u5df2\u7ecf\u88ab\u7ffb\u8f6c\u3002\u7b54\u6848\u7684\u72b6\u6001\u5c31\u4e3a \\(2^{num}-1\\) \uff0c\\(num\\) \u8868\u793a \\(b_i=1\\) \u7684 \\(i\\) \u7684\u4e2a\u6570\u3002<\/p>\n\u8f6c\u79fb\u4e5f\u5f88\u7b80\u5355\u3002\u5bf9\u4e8e\u5f53\u524d\u72b6\u6001 \\(bin\\) \uff0c\u5176\u4e2d\u7b2c \\(i\\) \u4f4d\u4e3a \\(1\\) \uff08\u5feb\u901f\u53d6\u4e2a lowbit()<\/code> \u5373\u53ef\uff09\uff0c\u679a\u4e3e\u5176\u4ed6\u4e3a \\(1\\) \u7684\u4f4d \\(j\\) \uff0c\\(f_{bin}=min\\{f_{bin-2^i-2^j}+dist_{i, j}\\}\\)<\/span> \uff08\\(dist_{i, j}\\) \u8868\u793a\u540c\u65f6\u7ffb\u8f6c \\(i\\) \u548c \\(j\\) \u5bf9\u5e94 \\(b\\) \u4e2d\u7684\u4e24\u4e2a\u6570\u4f4d\u7684\u6700\u5c0f\u4ee3\u4ef7\uff09\u3002<\/p>\n\u6700\u540e\u8f93\u51fa \\(f_{2^{num}-1}\\)<\/span> \u5373\u53ef\uff0c\u590d\u6742\u5ea6 \\(O(knl + k \\cdot 2^{2k})\\) \u3002<\/p>\n <\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
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