首页 > 代码库 > 30. Distinct Subsequences
30. Distinct Subsequences
Distinct Subsequences
OJ: https://oj.leetcode.com/problems/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
.
思想:动态规划。 D[i][j] = D[i][j-1] + (T[i-1] == S[j-1] ? D[i-1][j-1] : 0);
// DP: D[i][j] = D[i][j-1] + (T[i-1] == S[j-1] ? D[i-1][j-1] : 0);class Solution {public: int numDistinct(string S, string T) { int m = T.length(); int n = S.length(); if(!m) return 1; if(m > n) return 0; vector<vector<int> > D(m+1, vector<int>(n+1)); for(int i = 1; i <= m; ++i) D[i][0] = 0; for(int i = 0; i <= n; ++i) D[0][i] = 1; for(int i = 0; i < m; ++i) for(int j = 0; j < n; ++j) D[i+1][j+1] = D[i+1][j] + (T[i] == S[j] ? D[i][j] : 0); return D[m][n]; }};
改进后:空间复杂度 O(T.size()).
class Solution {public: int numDistinct(string S, string T) { int m = T.length(); vector<int> num(m+1, 0); // num[i] is distinct numbers of T[1,...,i] in string S num[0] = 1; for(int i = 1; i <= S.length(); ++i) for(int j = min(i, m); j >= 1; --j) // key to notice. if(T[j-1] == S[i-1]) num[j] += num[j-1]; // num[j-1] 为上次字符串时,T[1,...,j-1] 的 distinct numbers。 return num[m]; }};
30. Distinct Subsequences
声明:以上内容来自用户投稿及互联网公开渠道收集整理发布,本网站不拥有所有权,未作人工编辑处理,也不承担相关法律责任,若内容有误或涉及侵权可进行投诉: 投诉/举报 工作人员会在5个工作日内联系你,一经查实,本站将立刻删除涉嫌侵权内容。