Distinct Subsequences

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.

解题思路：

不得不吐槽leetcode，连数据范围都不给，整的我只能根据错误的数据来决定开数组的大小。事实证明S串的长度可以很长，T串的长度很短。

dp[i][j] 表示S的前i个字符能够匹配T的前j个字符的方案数.

dp[i][j] = dp[i-1][j] + dp[i-1][j-1](S[i-1]=T[j-1])

class Solution {public:    int numDistinct(string s, string t) {        int len1 = s.length();        int len2 = t.length();        if(len2 > len1) return 0;        int dp[1010][110];        memset(dp, 0, sizeof(dp));        dp[0][0] = 1;        for(int i = 1; i <= len1; ++i) {            for(int j = 1; j <= min(i, len2); ++j) {                if(s[i-1] == t[j-1]) {                    dp[i][j] += dp[i-1][j-1];                }                dp[i][j] += dp[i-1][j];            }        }        return dp[len1][len2];    }};