[LeetCode]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.

方法：dp

a[i][j]表示T中前j个在S的前i个出现的个数。

则

if S[i] != T[j]

a[i][j] = a[i-1][j]，相当于如果S中前i-1个可以表示T中前j个的话，那么多一个S[i]也不会影响。

if S[i] == T[j]

a[i][j] = a[i-1][j] + a[i-1][j-1]

class Solution {
public:
    int numDistinct(string S, string T) {
        int* a = new int[T.size()];
        memset(a, 0, sizeof(int) * T.size());
        
        for (int i = 0; i < S.size(); i++) {
            for (int j = T.size()-1; j >= 0; j--) {
                if (S[i] == T[j]) { 
                    if (j==0) a[j] += 1;
                    else a[j] += a[j-1];
                }
            }
        }
        return a[T.size()-1];
    }
};