LeetCode刷题笔录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

.

看到这种string的subsequences的问题基本上第一反应就是DP。这道题的递推关系稍微难想一点。

设A[i,j]是S[0,i]和T[0,j]的子序列数，则有两种情况：

S[i] != T[j]，那么S[i]并没有做出什么贡献，T[0,j]在S[0,i]中的子序列数就等于S[0,i-1]中的子序列数。因此A[i,j]=A[i-1,j]

S[i] = T[j]，那么A[i,j]=A[i-1,j]+A[i-1,j-1]，即要再加除去S[i]和T[j]的结果。

public class Solution {
public int numDistinct(String S, String T) {
int sLen = S.length();
int tLen = T.length();
int[][] res = new int[sLen + 1][tLen + 1];

//base case. if t is empty then the number of sub sequences is always 1
for(int i = 0; i <= sLen; i++){
res[i][0] = 1;
}

for(int i = 1; i <= sLen; i++){
for(int j = 1; j <= tLen; j++){
if(S.charAt(i - 1) == T.charAt(j - 1))
res[i][j] = res[i - 1][j] + res[i - 1][j - 1];
else
res[i][j] = res[i - 1][j];
}
}

return res[sLen][tLen];

}
}