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.

題意&解題思路：

找出S串中含有多少個T串，求子序列。典型的動態規劃。

dp[i][j]表示在 S[0 ~ i-1] 中含有 dp[i][j] 個 T[0 ~ j-1]序列。假設已知 dp[i-1][j-1] 及 dp[i-1][j]，則當 S[i-1] == T[j-1] 時dp[i][j] = dp[i-1][j-1] + dp[i-1][j] ，當 S[i-1] ！= T[j-1] 時dp[i][j] =  dp[i-1][j] ， 又當 j = 1 時，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];
    }
};