題目

Given a string s, return the number of palindromic substrings in it. 
 A string is a palindrome when it reads the same backward as forward. 
 A substring is a contiguous sequence of characters within the string. 

 Example 1: 
Input: s = "abc"
Output: 3
Explanation: Three palindromic strings: "a", "b", "c".

 Example 2: 
Input: s = "aaa"
Output: 6
Explanation: Six palindromic strings: "a", "a", "a", "aa", "aa", "aaa".

 Constraints: 
 1 <= s.length <= 1000 
 s consists of lowercase English letters. 
 

方法

Manacher法

• 時間複雜度：O(n)
• 空間複雜度：O(n)

class Solution {
    public int countSubstrings(String s) {
        String s1 = preProcess(s);
        int length = s1.length();
        int c=0,maxR=0,ans=0;
        int[] p = new int[length];
        for(int i=1;i<length-1;i++){
            if(i<maxR){
                p[i] = Math.min(maxR-i,p[2*c-i]);
            }
            int left = i-p[i];
            int right = i+p[i];
            while(left>=0&&right<length&&s1.charAt(left)==s1.charAt(right)){
                left--;
                right++;
                p[i]++;
            }
            if(maxR<p[i]+i){
                maxR = p[i]+i;
                c = i;
            }
            ans += p[i]/2;
        }

        return ans;
    }
    private String preProcess(String s){
        StringBuffer stringBuffer = new StringBuffer("^#");
        for (int i=0;i<s.length();i++){
            stringBuffer.append(s.charAt(i)+"#");
        }
        stringBuffer.append("$");
        return stringBuffer.toString();
    }
}