[leedcode 115] 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.

public class Solution {
    public int numDistinct(String s, String t) {
        //这种题优先选择动态规划，推导公式非常重要，注意dp[i][j]的含义：
        //代表s中的i个字母，和t中的j个字母，s包含t的个数，
        //判断s中第i个字符是否等于t中第j个字符，如果相等，根据是否包含t[j-1]分两种情况：dp[i][j]=dp[i-1][j]+dp[i-1][j-1];
        int sl=s.length();
        int tl=t.length();
        int dp[][]=new int[sl+1][tl+1];
        for(int i=0;i<=sl;i++){
            dp[i][0]=1;
        }
        for(int j=1;j<=tl;j++){
            dp[0][j]=0;
        }

        for(int i=1;i<=sl;i++){
            for(int j=1;j<=tl;j++){
                if(i<j){
                    dp[i][j]=0;break;
                }
                if(s.charAt(i-1)!=t.charAt(j-1)){
                    dp[i][j]=dp[i-1][j];
                }else{
                    dp[i][j]=dp[i-1][j]+dp[i-1][j-1];
                }

            }
        }
        return dp[sl][tl];
    }
}