Leetcode:distinct subsequences

Distinct subsequences


Total Accepted: 51556 Total Submissions: 177996 Difficulty: Hard

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 was formed from the original string by deleting some (can be none) of the C Haracters

without disturbing the relative positions of the remaining characters. (Ie, " ACE "  is a subsequence of " ABCDE "  while " AEC "  is not).

Here are an example:
S = "rabbbit" , T ="rabbit"

Return 3 .

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Test instructions: The possible transformation of s to T.

Idea: Dynamic regulation

Set: S = "Rabbbit", t= "Rabbit"

Dp[t.length () +1][s.length () +1];

Manual calculation can be done by:

J 0 1 2 3 4 5 6 7    

I S R a b b b i t

0 T 1 1 1 1 1 1 1 1

1 r 0 1 1 1 1 1 1 1

2 a 0 0 1 1 1 1 1 1

3 b 0 0 0 1 2 3 3 3

4 b 0 0 00 1 3 3 3

5 I 0 0 0 0 0 03 3

6 t 0 0 0 0 0 0 03

The result is: 3 (==dp[t.length ()][s.length ()]);

Observe the above DP the number of dashes in the table, the generation process can be obtained:

if (t[i] = = S[j]) dp[i][j] = Dp[i-1][j-1] + dp[i][j-1];

else dp[i][j] = dp[i][j-1];

That

When t[i] = = S[j], the current character can be preserved or discarded;

When t[i]! = S[j], the current character can only be discarded.

When I==0, the T is empty, when there is only one transformation possible, that is, remove all the characters in S.

Java code:

public class Solution {public    int numdistinct (string s, String t) {                int m = T.length ();        int n = s.length ();                Int[][] dp = new INT[M+1][N+1];                for (int i=0;i<=m;i++) dp[i][0] = 0;        for (int j=0;j<=n;j++) dp[0][j] = 1;                for (int i=1;i<=m;i++) {for            (int j=1;j<=n;j++) {                if (S.charat (j-1) ==t.charat (i-1))                    dp[i][j] = dp[i-1 ][J-1] + dp[i][j-1];                else                    dp[i][j] = dp[i][j-1];            }        }                return dp[m][n];}    }

Leetcode:distinct subsequences