【LeetCode】115.Distinct Subsequences

Description：

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

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).

example:
S = "rabbbit", T = "rabbit"

Return 3.

题目思考：

题目给定两个字符串，只可以用删除字符的方法从第一个字符串变换到第二个字符串，求出一共有多少种变换方法；

这是动态规划思想常见应用的典型题目。

Solution：

class Solution {
public:
    int numDistinct(string s, string t) {
        int len = t.length();
        int *memo = new int[len + 1];
        for (int i = 0; i < len + 1; i++) {
            memo[i] = 0;
        }
        memo[0] = 1;
        for (int i = 1; i < s.length() + 1; i++) {
            for (int j = len - 1; j >= 0; j--) {
                memo[j + 1] += s[i - 1] == t[j] ? memo[j] : 0;
            }
        }
        return memo[len];
    }
};
int main(int argc, const char * argv[]) {
    Solution s;
    cout << s.numDistinct("rabbbit", "rabbit") << endl;
    return 0;
}