LeetCode-Distinct Subsequences

最新推荐文章于 2020-06-06 05:36:44 发布

原创最新推荐文章于 2020-06-06 05:36:44 发布 · 361 阅读

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#leetcode #Distinct Subsequence

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本文介绍了一种解决特定字符串匹配问题的算法：计算一个字符串作为另一个字符串子序列出现的不同方式的数量。通过动态规划方法实现了高效的解决方案，并给出了具体的C++实现代码。

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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.

Solution:

Code:

<span style="font-size:14px;">class Solution {
public:
    int numDistinct(string S, string T) {
        const int lengthS = S.size(), lengthT = T.size();
        int **dp = new int *[lengthS+1];
        for (int i = 0; i < lengthS+1; ++i) {
            dp[i] = new int[lengthT+1];
            memset(dp[i], 0, sizeof(int)*(lengthT+1));
        }
        for (int i = 0; i < lengthS+1; ++i)
            dp[i][0] = 1;
        for (int i = 1; i < lengthS+1; ++i)
            for (int j = 1; j < lengthT+1; ++j)
                dp[i][j] = dp[i-1][j]+(S[i-1]==T[j-1]?dp[i-1][j-1]:0);
        int result = dp[lengthS][lengthT];
        for (int i = 0; i < lengthS+1; ++i)
            delete [] dp[i];
        delete [] dp;
        return result;
    }
};</span>