LeetCode-115.Distinct Subsequences

https://leetcode.com/problems/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.

动态规划题

转移式

dp[i][j] = dp[i - 1][j] + (s[i - 1] == t[j - 1] ? dp[i - 1][j - 1] : 0);

dp[i][j]表示源字符串s前i个字符转化为目的字符串前j个字符的转化方法个数

dp[i][j]由两部分构成，考虑s[0...i-1]转化为t[0...j]，直接删去s[i]。

如果s[i-1]==t[j-1]，则考虑s[0...i-1]转化为t[0...j-1]的方法个数即可

int numDistinct(string s, string t)    {        int sl = s.length(), tl = t.length();    if (sl < tl)    return 0;    vector<vector<int>> dp(sl + 1, vector<int>(tl + 1,0));    for (int i = 0; i <= sl; ++i)    dp[i][0] = 1;        for (int i = 1; i <= sl; ++i)    {    for (int j = 1; j <= tl; ++j)    {    if (i < j)    break;    dp[i][j] = dp[i - 1][j] + (s[i - 1] == t[j - 1] ? dp[i - 1][j - 1] : 0);    }    }    return dp[sl][tl];    }