Distinct Subsequences

Description

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).

Example
Given S = "rabbbit", T = "rabbit", return 3.

Challenge:
Do it in O(n2) time and O(n) memory.
O(n2) memory is also acceptable if you do not know how to optimize memory.

Link

Lintcode_ladder

Method

1. x
2. x

Example

1. 1

class Solution {
public:    
    /**
     * @param S, T: Two string.
     * @return: Count the number of distinct subsequences
     */
    int numDistinct(string& s1, string& s2) {
        // write your code here
        if (s1.empty()) {
            return 0;
        }
        int n1 = s1.size();
        int n2 = s2.size();
        vector<vector<int>> dp(n1+1, vector<int>(n2+1, 0));
        for (int i = 0; i <= n1; ++i) {
            dp[i][0] = 1;
        }
        for (int i = 1; i <= n1; ++i) {
            for (int j = 1; j <= n2; ++j) {
                dp[i][j] = dp[i-1][j];
                if (s1[i-1] == s2[j-1]) {
                    dp[i][j] += dp[i-1][j-1];
                }
                // if the last letter is the same
                // dp[abcc][abc] = dp[abc][ab] + dp[abc][abc] 
                // if (s1[i-1] == s2[j-1]) {
                //     dp[i][j] = dp[i-1][j-1] + dp[i-1][j];
                // } else {
                // // when s1[abcd] s2[abc]
                // // d != c => dp[abcd][abc] = dp[abc][abc]
                //     dp[i][j] = dp[i-1][j];
                // }
            }
        }
        return dp[n1][n2];
    }
};

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