[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.

找到T在S中有几种子序列表示，如： S = “rabbbit”, T = “rabbit”

[ rabb b it rab b bit ra b bbit ] 三种

动规解决，找到转移方程： if (s[i] == t[j]) {   dp[i][j] = dp[i-1][j-1] + dp[i-1][j]; } else {   dp[i][j] = dp[i-1][j]; }

dp[i-1][j-1] 表示s[0:i-1]已经有这么多个t[0:j-1]的子序列。 dp[i-1][j] 表示s[0:i-1]已经有这么多个t[0:j]的子序列。 如果s[i] == t[j]， 可以在dp[i-1][j]数量的基础上新增dp[i-1][j-1]个子序列。