leetcode:115. 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.

题意&解题思路：

找出S串中含有多少个T串，求子序列。典型的动态规划。

dp[i][j]表示在 S[0 ~ i-1] 中含有 dp[i][j] 个 T[0 ~ j-1]序列。假设已知 dp[i-1][j-1] 及 dp[i-1][j]，则当 S[i-1] == T[j-1] 时dp[i][j] = dp[i-1][j-1] + dp[i-1][j] ，当 S[i-1] ！= T[j-1] 时dp[i][j] =  dp[i-1][j] ， 又当 j = 1 时，dp[i][j] = dp[i - 1][j] + （S[i-1] == T[j-1]）。

class Solution {public:    int numDistinct(string s, string t) {        int ls = s.length();        int lt = t.length();        int dp[ls+1][lt+1];        memset(dp, 0, sizeof(dp));        for(int j = 1; j <= lt; j++){            for(int i = j; i <= ls; i++){                dp[i][j] = dp[i-1][j];                if(j == 1)dp[i][j] += (s[i - 1] == t[j - 1]);                else {                    if(s[i - 1] == t[j - 1])dp[i][j] += dp[i - 1][j - 1];                }            }        }        return dp[ls][lt];    }};