【leetcode】940. Distinct Subsequences II

题目如下：

Given a string S, count the number of distinct, non-empty subsequences of S .

Since the result may be large, return the answer modulo 10^9 + 7.

Example 1:
Input: "abc"
Output: 7
Explanation: The 7 distinct subsequences are "a", "b", "c", "ab", "ac", "bc", and "abc".
Example 2:
Input: "aba"
Output: 6
Explanation: The 6 distinct subsequences are "a", "b", "ab", "ba", "aa" and "aba".
Example 3:
Input: "aaa"
Output: 3
Explanation: The 3 distinct subsequences are "a", "aa" and "aaa".

解题思路：记dp[i]为以S[i]元素结尾可以组成的子串的个数，很显然dp[0] = 1。显然dp[i]的前一个元素可以是dp[0] ~ dp[i-1]中的任何一个，那么应该有dp[i] = dp[0] + dp[1] +...dp[i-1]。这是对于元素没有重复的情况。假设S[j]是S[0-i]中与S[i]下标最接近的元素并且有S[i] = S[j]，那么在以S[i]结尾的子串中，前一个元素是在S[0]~S[j-1]中的任何一个，都会和以S[j]结尾的子串中并且前一个元素是在S[0]~S[j-1]中的任何一个重复，因此这种情况下dp[i] = dp[j]+dp[j+1] + ... dp[i-1]。最后，返回的结果应该为sum(dp）。

代码如下：

class Solution(object):def distinctSubseqII(self, S):""":type S: str:rtype: int"""dp = [1] * len(S)for i in range(1,len(S)):for j in range(i-1,-1,-1):if S[i] != S[j]:dp[i] += dp[j]else:dp[i] += dp[j]dp[i] -= 1break#print dpreturn sum(dp) % (pow(10,9) + 7)

转载于:https://www.cnblogs.com/seyjs/p/10412749.html

【leetcode】940. Distinct Subsequences II相关推荐

【Leetcode】115. Distinct Subsequences
又是一道DP的题目,个人感觉DP的题目比较难,主要因为:(1)DP的难点是寻找子问题,如果找到很好的子问题,那么就可以瞬间搞定.(2)通常也会带有一点backtracking的思想,有时候总是优先想到 ...
【leetcode】132. Palindrome Partitioning II
题目如下: 解题思路:本题是[leetcode]131. Palindrome Partitioning的升级版,要求的是求出最小cuts,如果用[leetcode]131. Palindrome P ...
【LeetCode】House Robber I II 解题报告
[题目] I You are a professional robber planning to rob houses along a street. Each house has a certain ...
【leetcode】Jump Game I, II 跳跃游戏一和二
题目: Jump Game I: Given an array of non-negative integers, you are initially positioned at the first ...
【leetcode】667. Beautiful Arrangement II
题目如下: Given two integers n and k, you need to construct a list which contains ndifferent positive in ...
【leetcode】324.摆动排序 II （四种解法，快速排序+3way-partition等，java实现）
324. 摆动排序 II 难度中等给定一个无序的数组 nums,将它重新排列成 nums[0] < nums[1] > nums[2] < nums[3]... 的顺序. 示例 1 ...
【LeetCode】1140-石子游戏II
爱丽丝和鲍勃继续他们的石子游戏.许多堆石子排成一行,每堆都有正整数颗石子 piles[i].游戏以谁手中的石子最多来决出胜负. 爱丽丝和鲍勃轮流进行,爱丽丝先开始.最初,M = 1. 在每个玩家的回 ...
【leetcode】45. Jump Game II 非负数组的最少跳跃步数
1. 题目 Given an array of non-negative integers, you are initially positioned at the first index of th ...
【leetcode】910. Smallest Range II
题目如下: 解题思路:我的思路是先找出最大值.对于数组中任意一个元素A[i]来说,如果A[i] + K 是B中的最大值,那么意味着从A[i+1]开始的元素都要减去K,即如果有A[i] + K > ...

【leetcode】940. Distinct Subsequences II

【leetcode】940. Distinct Subsequences II相关推荐

最新文章

热门文章