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.
给定字符串S和T，通过删除S中的若干个字符可以得到T，则T称为S的子序列，问有多少种删法可以得到T
class Solution {
public:
int numDistinct(string S, string T) {
if(S.length()==0 || S.length()==0)return 0;
if(S.length()<T.length())return 0; //如果S==T,返回1， 认为有1种转换方式
vector<vector<int> >matrix(S.length()+1, vector<int>(T.length()+1, 0));
//初始化matrix[0][0]
matrix[0][0]=1;
//初始化对角线
for(int j=1; j<=T.length(); j++)
matrix[0][j]=0;
//初始化第一列
for(int i=1; i<=S.length(); i++)
matrix[i][0]=1;
//考虑其他i>j的情况
for(int i=1; i<=S.length(); i++){
for(int j=1; j<=T.length(); j++){
if(S[i-1]==T[j-1])matrix[i][j]=matrix[i-1][j-1]+matrix[i-1][j];
else matrix[i][j]=matrix[i-1][j];
}
}
return matrix[S.length()][T.length()];
}
};LeetCode: Distinct Subsequences [115],布布扣,bubuko.com
LeetCode: Distinct Subsequences [115]
原文地址：http://blog.csdn.net/harryhuang1990/article/details/28588043
