Distinct Subsequences

最新推荐文章于 2024-03-21 01:52:03 发布

Nereus_Li

最新推荐文章于 2024-03-21 01:52:03 发布

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分类专栏： LeetCode 文章标签： DP

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本文介绍了如何使用动态规划计算给定字符串中另一个字符串的唯一子序列数量，并提供了实现示例。

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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.

#include<iostream>
#include<vector>
#include<string>
using namespace std;

int numDistinct(string S, string T) {
	int lengthS = S.size();
	int lengthT = T.size();

	vector<vector<int>>M(lengthS+1,vector<int>(lengthT+1,0));
	for (int i =0;i!=M.size();++i)
		M[i][0] =1;
	for (int i =1;i!=M.size();++i)
	{
		for (int j =1;j!=lengthT+1;++j)
		{
			if (S[i-1]==T[j-1])
				M[i][j] = M[i-1][j-1]+M[i-1][j];
			else
				M[i][j] = M[i-1][j];
		}
	}
	return M[lengthS][lengthT];
}