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希望以上方法能够帮助您解决问题。

相关问题

1. Complexity [20 marks] (A)Prove that is both and . [4 marks] (B)Consider the following functions of . Put them in order from smallest to largest asymptotic growth rate. [8 marks] (C)Let be the processing time of an algorithm for the input of size . Which is the asymptotic time complexity of this algorithm, or ? Please show your working to justify your answer. [8 marks]

A：证明 既是 又是 。[4 分]
B：考虑 的以下函数。将它们按从最小到最大的渐近增长率排序。[8 分]
C：让 是算法对输入大小 的处理时间。该算法的渐近时间复杂度是 还是 ？请出示您的计算步骤以证明您的答案。[8 分]

A string consisting of lowercase English letters, (, and ) is said to be a good string if you can make it an empty string by the following procedure: First, remove all lowercase English letters. Then, repeatedly remove consecutive () while possible. For example, ((a)ba) is a good string, because removing all lowercase English letters yields (()), from which we can remove consecutive () at the 2-nd and 3-rd characters to obtain (), which in turn ends up in an empty string. You are given a good string S. We denote by S i ​ the i-th character of S. For each lowercase English letter a, b, …, and z, we have a ball with the letter written on it. Additionally, we have an empty box. For each i=1,2, … ,∣S∣ in this order, Takahashi performs the following operation unless he faints. If S i ​ is a lowercase English letter, put the ball with the letter written on it into the box. If the ball is already in the box, he faints. If S i ​ is (, do nothing. If S i ​ is ), take the maximum integer j less than i such that the j-th through i-th characters of S form a good string. (We can prove that such an integer j always exists.) Take out from the box all the balls that he has put in the j-th through i-th operations. Determine if Takahashi can complete the sequence of operations without fainting.用cpp解决

这道题的意思是，给定一个字符串S，S是一个好的字符串，如果您可以通过以下过程将其转换为空字符串：首先，删除所有小写英文字母。然后，反复删除连续的()，直到不可能为止。例如，((a)ba)是一个好的字符串，因为删除所有小写英文字母后得到(())，从中我们可以在第2和第3个字符处删除连续的()以获得()，而后者最终变为空字符串。您将得到一个好的字符串S。我们用S i 表示S的第i个字符。对于小写英文字母a，b，…和z，我们都有一个写有该字母的小球。另外，我们有一个空盒子。对于按此顺序的i=1,2,…,|S|，高桥除非他昏倒，否则执行以下操作。如果S i 是小写英文字母，将写有该字母的球放入盒子中。如果球已经在盒子中，他就会昏倒。如果S i 是(，则什么也不做。如果S i 是)，则取出最大的整数j，使得S的第j到第i个字符形成一个好的字符串。 （我们可以证明这样的整数j总是存在的。）从第j次到第i次