设S是一个长度为n的非空字符串，其中的字符各不相同，则其互异的非平凡子串（非空且不同于S本身）个数为（ ）。
- A.2n-1
- B.n2
- C.n（n+1）/2
- D.（n+2）（n-1）/2
正确答案及解析
正确答案
解析
比如S字串为“abcdefg”，长度为7，则S中的包含的互不相同的字串有如下一些：
1.长度为6的个数为2：“abcdef”和“bcdefg”
2.长度为5的个数为3：“abcde”,“bcdef”,“cdefg”
.
3.长度为1的个数为7：“a”,“b”,“c”,“d”,“e”,“f”,“g”
个数总和就是2+3+4+5+6+7=（2+7）×（7-2+1）/2
同理，字符串长度为n，一个字符的字符串个数为n，除原字符串外最长的字符串为n-1个字符，个数有2个，按照推理，共有：2+3+……+n=（2+n）（n-1）/2个。
其中：
等差数列{an}的通项公式为：an=a1+（n-1）d。
前n项和公式为：Sn=n×a1+n（n-1）d/2或Sn=n（a1+an）/2。
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