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Distinct Subsequences.cpp
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Distinct Subsequences.cpp
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/*
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).
Link: http://www.lintcode.com/en/problem/distinct-subsequences/
Example:
Given S = "rabbbit", T = "rabbit", return 3.
Solution: We use a range to represent to available area.
Source: None
*/
class Solution {
public:
/**
* @param S, T: Two string.
* @return: Count the number of distinct subsequences
*/
int numDistinct(string &S, string &T) {
// write your code here
if (S.empty()) {
return 0;
}
if (S.length() < T.length()) {
return 0;
}
if (T.empty()) {
return 1;
}
vector<vector<int>> dp(S.length() + 1, vector<int>(T.length() + 1, 0));
for (int i = 0; i < S.length(); i++) {
dp[i][0] = 1;
for (int j = 0; j < T.length(); j++) {
if (S[i] == T[j]) {
dp[i + 1][j + 1] = dp[i][j + 1] + dp[i][j];
} else {
dp[i + 1][j + 1] = dp[i][j + 1];
}
}
}
return dp[S.length()][T.length()];
}
};