Distinct Subsequences

题目原型：

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.

基本思路：

根据递推式 t[i][j] = t[i][j-1] + (S[i]==T[j])?t[i-1][j-1]:0（i字符串T的下标，j是字符串S的下标）得出。

	public int numDistinct(String S, String T)
	{
		int[][] num = new int[T.length()+1][S.length()+1];
		//初始化边缘条件
		for(int i = 0;i<S.length();i++)
			num[0][i] = 0;
		for(int i = 0;i<T.length();i++)
			num[i][0] = 0;
		
		for(int indexS = 1;indexS<=S.length();indexS++)
		{
			for(int indexT = 1;indexT<=indexS&&indexT<=T.length();indexT++)
			{
				if(S.charAt(indexS-1)==T.charAt(indexT-1))
				{
					//当T的长度为1时
					if(indexT==1)
						num[indexT][indexS] = num[indexT][indexS-1]+1;
					else
						num[indexT][indexS] = num[indexT][indexS-1]+num[indexT-1][indexS-1];
				}
				else
					num[indexT][indexS] = num[indexT][indexS-1];
			}
		}
		return num[T.length()][S.length()];
	}

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Distinct Subsequences

原文：http://blog.csdn.net/cow__sky/article/details/21879905