Distinct Subsequences

时间：2014-03-05 18:08:33 收藏：0 阅读：437

Given a string S and a string T, count the number of distinct subsequences of T in S.

A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE" is a subsequence of "ABCDE" while "AEC" is not).

Here is an example:
S = "rabbbit", T = "rabbit"

Return 3.

--------------------
1. 如果T 比S长，直接返回0
2. 分两种情况
a. S[i - 1] == T[j - 1] , 这说明当前长度为j的T串应该等于长度为j的T串在长度为i - 1的S中出现的次数 + 长度为j - 1的T串在长度为i - 1的S串中出现的次数
b. S[i - 1] != T[j - 1]，这说明当前长度为j的T串在S总出现的次数等于它在长度为i - 1的S串中出现的额次数。

从上述状态转移方程，得到下边的代码。

class Solution {
public:
int numDistinct(string S, string T) {
int slen = S.length();
int tlen = T.length();
int ret[tlen + 1];
fill(ret, ret + tlen + 1, 0);
ret[0] = 1;
for (int i = 1; i <= slen; i++) {
for (int j = min(i, tlen); j > 0; j--) {
if (S[i - 1] == T[j - 1]) {
ret[j] += ret[j - 1];
}
}
}

return ret[tlen];
}
};

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原文：http://blog.csdn.net/icomputational/article/details/20490945