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Distinct Subsequences

2024-07-10 02:17:24   222人阅读

题目

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.

方法

典型的动态规划的思想。递推公式：如果 S[i]=T[j]，dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j]， 否则dp[i][j] =  dp[i - 1][j]
	public int numDistinct(String S, String T) {
        if (S == null || T == null) {
        	return 0;
        }
        if (S.length() < T.length()) {
        	return 0;
        }
        int lenS = S.length();
        int lenT = T.length();
        int[][] dp = new int[lenS + 1][lenT + 1];
        for (int i = 0; i < lenS; i++) {
        	dp[i][0] = 1;
        }
        for (int i = 1; i <= lenS; i++) {
        	for (int j = 1; j <= lenT; j++) {
        		dp[i][j] = dp[i - 1][j];
                if(S.charAt(i-1) ==T.charAt(j-1)) {  
                    dp[i][j] += dp[i-1][j-1];  
                } 
        	}
        }
        return dp[lenS][lenT];
    }


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