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Posts tagged as “Palindrome”

花花酱 LeetCode 730. Count Different Palindromic Subsequences

Problem:

Given a string S, find the number of different non-empty palindromic subsequences in S, and return that number modulo 10^9 + 7.

A subsequence of a string S is obtained by deleting 0 or more characters from S.

A sequence is palindromic if it is equal to the sequence reversed.

Two sequences A_1, A_2, ... and B_1, B_2, ... are different if there is some i for which A_i != B_i.

Example 1:

Input: 
S = 'bccb'
Output: 6
Explanation: 
The 6 different non-empty palindromic subsequences are 'b', 'c', 'bb', 'cc', 'bcb', 'bccb'.
Note that 'bcb' is counted only once, even though it occurs twice.

Example 2:

Input: 
S = 'abcdabcdabcdabcdabcdabcdabcdabcddcbadcbadcbadcbadcbadcbadcbadcba'
Output: 104860361
Explanation: 
There are 3104860382 different non-empty palindromic subsequences, which is 104860361 modulo 10^9 + 7.

Note:

 

  • The length of S will be in the range [1, 1000].
  • Each character S[i] will be in the set {'a', 'b', 'c', 'd'}.



Idea:

DP

 

Solution 1: Recursion with memoization

Time complexity: O(n^2)
Space complexity: O(n^2)

C++

Python

Java

Solution 2: DP

C++

Pyhton

Related Problems:

花花酱 LeetCode 680. Valid Palindrome II

Problem:

Given a non-empty string s, you may delete at most one character. Judge whether you can make it a palindrome.

Example 1:

Example 2:

Note:

  1. The string will only contain lowercase characters a-z. The maximum length of the string is 50000.

Idea:

Greedy, delete the first unmatched char



Time complexity

O(n)

Solution: