Palindromic Substrings

update Aug 13,2017 23:40

Given a string, your task is to count how many palindromic substrings in this string.

The substrings with different start indexes or end indexes are counted as different substrings even they consist of same characters.

Example 1:

Input: "abc"
Output: 3
Explanation: Three palindromic strings: "a", "b", "c".

Example 2:

Input: "aaa"
Output: 6
Explanation: Six palindromic strings: "a", "a", "a", "aa", "aa", "aaa".

Note: The input string length won't exceed 1000.

Basic Idea:

题目要求所有的回文子序列个数（连续的，不可以有间隔），最直观的方法就是以每个字符为中心，向两边扩张。扩张的同时要考虑单数和双数的情况。对于单数，则 expand(i, i)，对于双数，则是 expand(i, i+1)。

对于求最长回文子序列长度（不需要连续）的问题，在dp章节中，这里.

Python Code:

    class Solution(object):
        def countSubstrings(self, s):
            """
            :type s: str
            :rtype: int
            """
            # 以left和right为初始位置，向两边扩张，每次得到新回文序列，则count++
            def expand(left, right):
                while left <= right and left >= 0 and right < len(s) and s[left] == s[right]:
                    self.count += 1
                    left -= 1
                    right += 1

            self.count = 0
            for i in range(len(s)):
                expand(i, i)
                expand(i, i + 1)
            return self.count

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