以下方法的费用是多少.您如何计算?
What is the cost of the following method. How do you calculate it?
public String joinWords(String[] words) { String sentence = ""; for (String w : words) { sentence = sentence + word; } return sentence; }推荐答案
假定两个长度为r和s的字符串的字符串连接成本为O(r + s)-历史上在Java中就是这种情况但可能会更改-运行时间为O(mn),其中n是字符总数在输入字符串中,m是输入字符串的数量.
Assuming that the cost of string concatenation is O(r + s) for two strings of lengths r and s - which historically was the case in Java but may change going forward - the runtime would be O(mn), where n is the total number of characters in the input strings and m is the number of input strings.
要看到这一点,请注意,如果字符串长度为n1,n2,...,n_m,则运行时将为
To see this, note that if the string lengths are n1, n2, ..., n_m, then the runtime will be
n1 +(n1 + n2)+(n1 + n2 + n3)+ ... +(n1 + n2 + ... + n_m)
n1 + (n1 + n2) + (n1 + n2 + n3) + ... + (n1 + n2 + ... + n_m)
= m(n_1)+(m-1)(n_2)+(m -2)(n-3)+ ... + n_m
= m(n_1) + (m - 1)(n_2) + (m - 2)(n-3) + ... + n_m
= m(n_1 + n_2 + ... + n_m)-n_2-2n_3-3n_4-...-(m-1)n_m
= m(n_1 + n_2 + ... + n_m) - n_2 - 2n_3 - 3n_4 - ... - (m - 1)n_m
受n_1 + ... + n_m = n的约束,当n_1 = n且所有其他值均为0时,此值最大化.在这种情况下,运行时间变为mn,因此运行时间为O(mn)
Subject to the constraint that n_1 + ... + n_m = n, this is maximized when n_1 = n and all the other values are 0. In that case, the runtime becomes mn, so the runtime is O(mn).
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简单字符串连接的时间复杂度
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