一、回文字符串（Palindromic String）
回文字符串（Palindromic String）是指前、后向读起来完全相同的字符串。
回文字符串除了答题似乎没有什么用处 :P
二、求解思路
求解字符串的回文子串的基本思路：
1、遍历每个位置；
2、先看有没有以位置i为中心的回文串（举例ABCBA）。所以我们要比较i+1和i-1是否相等，i+2和i-2是否相等，一直比较到字符串某一端点结束，或者中途发现不等的字符；
3、再看有没有以位置i为对称中心的回文串（举例ABBA）。所以我们要先看i和i+1等不等，如果等，那再看i-1和i+2是否相等，i-2和i+3是否相等，一直比较到字符串某一端点结束，或者中途发现不等的字符。
Manacher算法是一位名叫Manacher的人在1975年提出的一种算法，解决的问题是求最长回文子串。Manacher算法的核心思路就是利用之前求得的臂长( 即之前求出的Len值) 来减少时间复杂度，也就是说通过前面求出的Len值来加速求出当前下标i的 Len[i]，快速求出所有的Len 值就是该算法的目的。
速度！
三、源代码
3.1 文本格式
using System;
using System.Text;
using System.Collections;
using System.Collections.Generic;
namespace Legalsoft.Truffer.Algorithm
{
// C# program to implement Manacher's Algorithm
// This code is contributed by PrinciRaj1992
public static class Palindromic_String
{
public static string Manacher(string text)
{
int N = text.Length;
if (N == 0)
{
return "";
}
N = 2 * N + 1;
int[] lengthArray = new int[N + 1];
lengthArray[0] = 0;
lengthArray[1] = 1;
int centerPosition = 1;
int centerRightPosition = 2;
int currentRightPosition = 0;
int currentLeftPosition;
int maxLPSLength = 0;
int maxLPSCenterPosition = 0;
int start = -1;
int end = -1;
int diff = -1;
// Uncomment it to print LPS Length array
for (currentRightPosition = 2; currentRightPosition < N; currentRightPosition++)
{
// get currentLeftPosition iMirror for currentRightPosition i
currentLeftPosition = 2 * centerPosition - currentRightPosition;
lengthArray[currentRightPosition] = 0;
diff = centerRightPosition - currentRightPosition;
// 如果 currentRightPosition 范围内
if (diff > 0)
{
lengthArray[currentRightPosition] = Math.Min(lengthArray[currentLeftPosition], diff);
}
// 尝试扩展以 currentRightPosition i为中心的回文。
// 对于奇数位置，我们比较字符，如果匹配，则将LPS长度增加1。
// 即使是位置，我们只是将LPS增加1，而不进行任何字符比较。
while (((currentRightPosition + lengthArray[currentRightPosition]) + 1 < N && (currentRightPosition - lengthArray[currentRightPosition]) > 0) &&
(((currentRightPosition + lengthArray[currentRightPosition] + 1) % 2 == 0) ||
(text[(currentRightPosition + lengthArray[currentRightPosition] + 1) / 2] == text[(currentRightPosition - lengthArray[currentRightPosition] - 1) / 2])))
{
lengthArray[currentRightPosition]++;
}
// 重新计算maxLPSLength
if (lengthArray[currentRightPosition] > maxLPSLength)
{
maxLPSLength = lengthArray[currentRightPosition];
maxLPSCenterPosition = currentRightPosition;
}
// 如果以currentRightPosition为中心的回文扩展到centerRightPosition之外，
// 根据扩展的回文调整centerPosition
if (currentRightPosition + lengthArray[currentRightPosition] > centerRightPosition)
{
centerPosition = currentRightPosition;
centerRightPosition = currentRightPosition + lengthArray[currentRightPosition];
}
}
start = (maxLPSCenterPosition - maxLPSLength) / 2;
end = start + maxLPSLength - 1;
if (end > start)
{
StringBuilder sb = new StringBuilder();
for (int i = start; i <= end; i++)
{
sb.Append(text.Substring(i, 1));
}
return sb.ToString();
}
return "";
}
}
}
-------------------------------------------------------
POWER BY TRUFFER.CN
3.2 代码格式
using System;
using System.Text;
using System.Collections;
using System.Collections.Generic;
namespace Legalsoft.Truffer.Algorithm
{
// C# program to implement Manacher's Algorithm
// This code is contributed by PrinciRaj1992
public static class Palindromic_String
{
public static string Manacher(string text)
{
int N = text.Length;
if (N == 0)
{
return "";
}
N = 2 * N + 1;
int[] lengthArray = new int[N + 1];
lengthArray[0] = 0;
lengthArray[1] = 1;
int centerPosition = 1;
int centerRightPosition = 2;
int currentRightPosition = 0;
int currentLeftPosition;
int maxLPSLength = 0;
int maxLPSCenterPosition = 0;
int start = -1;
int end = -1;
int diff = -1;
// Uncomment it to print LPS Length array
for (currentRightPosition = 2; currentRightPosition < N; currentRightPosition++)
{
// get currentLeftPosition iMirror for currentRightPosition i
currentLeftPosition = 2 * centerPosition - currentRightPosition;
lengthArray[currentRightPosition] = 0;
diff = centerRightPosition - currentRightPosition;
// 如果 currentRightPosition 范围内
if (diff > 0)
{
lengthArray[currentRightPosition] = Math.Min(lengthArray[currentLeftPosition], diff);
}
// 尝试扩展以 currentRightPosition i为中心的回文。
// 对于奇数位置，我们比较字符，如果匹配，则将LPS长度增加1。
// 即使是位置，我们只是将LPS增加1，而不进行任何字符比较。
while (((currentRightPosition + lengthArray[currentRightPosition]) + 1 < N && (currentRightPosition - lengthArray[currentRightPosition]) > 0) &&
(((currentRightPosition + lengthArray[currentRightPosition] + 1) % 2 == 0) ||
(text[(currentRightPosition + lengthArray[currentRightPosition] + 1) / 2] == text[(currentRightPosition - lengthArray[currentRightPosition] - 1) / 2])))
{
lengthArray[currentRightPosition]++;
}
// 重新计算maxLPSLength
if (lengthArray[currentRightPosition] > maxLPSLength)
{
maxLPSLength = lengthArray[currentRightPosition];
maxLPSCenterPosition = currentRightPosition;
}
// 如果以currentRightPosition为中心的回文扩展到centerRightPosition之外，
// 根据扩展的回文调整centerPosition
if (currentRightPosition + lengthArray[currentRightPosition] > centerRightPosition)
{
centerPosition = currentRightPosition;
centerRightPosition = currentRightPosition + lengthArray[currentRightPosition];
}
}
start = (maxLPSCenterPosition - maxLPSLength) / 2;
end = start + maxLPSLength - 1;
if (end > start)
{
StringBuilder sb = new StringBuilder();
for (int i = start; i <= end; i++)
{
sb.Append(text.Substring(i, 1));
}
return sb.ToString();
}
return "";
}
}
}
