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2020-2021:teams:farmer_john:2020.7.27 [2020/08/02 15:25] jjleo [题解] |
2020-2021:teams:farmer_john:2020.7.27 [2020/08/02 15:46] (当前版本) jjleo [题解] |
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=====CF Marmots (easy)===== | =====CF Marmots (easy)===== | ||
====题意==== | ====题意==== | ||
+ | 给出$250$个点,问符合随即均匀分布还是泊松分布。 | ||
====题解==== | ====题解==== | ||
+ | ??? | ||
=====CF Marmots (medium)===== | =====CF Marmots (medium)===== | ||
====题意==== | ====题意==== | ||
+ | 求出简单版本中两种分布对应的参数。 | ||
====题解==== | ====题解==== | ||
+ | ??? | ||
=====CF Fake News (medium)===== | =====CF Fake News (medium)===== | ||
====题意==== | ====题意==== | ||
+ | 构造两个字符串$s,p$,满足$s$有恰好$n$个子序列等于$p$,要求两者长度均不超过$200$。$(n \le 10^6)$ | ||
====题解==== | ====题解==== | ||
+ | 当$n=1$时,$s=a,p=a$满足条件,当$n=2$时,$s=abb,p=ab$满足条件。\\ | ||
+ | 我们设$t$为形如$abcd \cdots$的字符串,并保证任何时刻两字符串均满足$s=tu,p=t$,其中$u$可为空。显然$n=1,2$的解满足该条件。\\ | ||
+ | 设$t$尾部字符的下一个字母为$x$。\\ | ||
+ | 考虑$n->2n+1$的变换,,$s=txuxx,p=tx$即满足条件,其中$tx$贡献一个子序列,而$tu$中有$n$个$t$的子序列,因此$tuxx$贡献$2n$个子序列。\\ | ||
+ | 同理有$n->2n+2$的变换,,$s=txxuxx,p=tx$,证明同上。\\ | ||
+ | 根据这个变换即可以$n=1$或$n=2$为起点,构造出符合条件的长度为$O(\log n)$的字符串。 | ||
=====CF Fake News (hard)===== | =====CF Fake News (hard)===== | ||
====题意==== | ====题意==== | ||
+ | 给定一个字符串,问所有本质不同子串出现次数的平方和。 | ||
====题解==== | ====题解==== | ||
+ | 后缀自动机模板题。 | ||
=====CF Send the Fool Further! (medium)===== | =====CF Send the Fool Further! (medium)===== | ||
====题意==== | ====题意==== |