在Manacher的算法第1部分和第2部分中，我们介绍了一些基础知识，了解LPS长度数组以及如何基于四种情况有效地计算长度数组。在这里，我们将实现相同的功能。
我们已经看到，在情况1和情况2中不需要新的字符比较。在情况3和情况4中，需要进行新的比较。
在下图中，
如果根本需要比较，我们将只比较实际字符，它们位于“奇数”位置，例如1、3、5、7等。
即使位置不字符串代表一个字符，所以没有比较，将在预制甚至位置。
如果在不同奇数位置的两个字符匹配，则它们将使LPS长度增加2。
根据处理偶数和奇数位置的方式，有许多种实现方法。一种方法是创建一个新的字符串1日，我们插入的所有位置，甚至一些独特的字符(比如＃，$等)，然后运行算法上(避免的偶数和奇数位置的处理方式不同)。其他方法可能是处理给定的字符串本身，但此处应适当处理偶数和奇数位置。
在这里，我们将从给定的字符串本身开始。当需要扩展和字符比较时，我们将在左右位置逐一扩展。当找到奇数位置时，将进行比较，并且LPS长度将增加1。当找到偶数位置时，不进行比较，并且LPS长度将增加1(因此，总体而言，左侧和右侧的一个奇数和一个偶数位置将使LPS长度增加2)。
C
// A C program to implement Manacher’s Algorithm
#include
#include
char text[100];
void findLongestPalindromicString()
{
int N = strlen(text);
if(N == 0)
return;
N = 2*N + 1; //Position count
int L[N]; //LPS Length Array
L[0] = 0;
L[1] = 1;
int C = 1; //centerPosition
int R = 2; //centerRightPosition
int i = 0; //currentRightPosition
int iMirror; //currentLeftPosition
int expand = -1;
int diff = -1;
int maxLPSLength = 0;
int maxLPSCenterPosition = 0;
int start = -1;
int end = -1;
//Uncomment it to print LPS Length array
//printf("%d %d ", L[0], L[1]);
for (i = 2; i < N; i++)
{
//get currentLeftPosition iMirror for currentRightPosition i
iMirror = 2*C-i;
//Reset expand - means no expansion required
expand = 0;
diff = R - i;
//If currentRightPosition i is within centerRightPosition R
if(diff >= 0)
{
if(L[iMirror] < diff) // Case 1
L[i] = L[iMirror];
else if(L[iMirror] == diff && R == N-1) // Case 2
L[i] = L[iMirror];
else if(L[iMirror] == diff && R < N-1) // Case 3
{
L[i] = L[iMirror];
expand = 1; // expansion required
}
else if(L[iMirror] > diff) // Case 4
{
L[i] = diff;
expand = 1; // expansion required
}
}
else
{
L[i] = 0;
expand = 1; // expansion required
}
if (expand == 1)
{
//Attempt to expand palindrome centered at currentRightPosition i
//Here for odd positions, we compare characters and
//if match then increment LPS Length by ONE
//If even position, we just increment LPS by ONE without
//any character comparison
while (((i + L[i]) < N && (i - L[i]) > 0) &&
( ((i + L[i] + 1) % 2 == 0) ||
(text[(i + L[i] + 1)/2] == text[(i-L[i]-1)/2] )))
{
L[i]++;
}
}
if(L[i] > maxLPSLength) // Track maxLPSLength
{
maxLPSLength = L[i];
maxLPSCenterPosition = i;
}
// If palindrome centered at currentRightPosition i
// expand beyond centerRightPosition R,
// adjust centerPosition C based on expanded palindrome.
if (i + L[i] > R)
{
C = i;
R = i + L[i];
}
//Uncomment it to print LPS Length array
//printf("%d ", L[i]);
}
//printf("\n");
start = (maxLPSCenterPosition - maxLPSLength)/2;
end = start + maxLPSLength - 1;
//printf("start: %d end: %d\n", start, end);
printf("LPS of string is %s : ", text);
for(i=start; i<=end; i++)
printf("%c", text[i]);
printf("\n");
}
int main(int argc, char *argv[])
{
strcpy(text, "babcbabcbaccba");
findLongestPalindromicString();
strcpy(text, "abaaba");
findLongestPalindromicString();
strcpy(text, "abababa");
findLongestPalindromicString();
strcpy(text, "abcbabcbabcba");
findLongestPalindromicString();
strcpy(text, "forgeeksskeegfor");
findLongestPalindromicString();
strcpy(text, "caba");
findLongestPalindromicString();
strcpy(text, "abacdfgdcaba");
findLongestPalindromicString();
strcpy(text, "abacdfgdcabba");
findLongestPalindromicString();
strcpy(text, "abacdedcaba");
findLongestPalindromicString();
return 0;
} Java
// A Java program to implement Manacher’s Algorithm
import java.lang.*;
class GFG{
public static void findLongestPalindromicString(
String text)
{
int N = text.length();
if(N == 0)
return;
// Position count
N = 2 * N + 1;
// LPS Length Array
int []L = new int [N];
L[0] = 0;
L[1] = 1;
// centerPosition
int C = 1;
// centerRightPosition
int R = 2;
// currentRightPosition
int i = 0;
// currentLeftPosition
int iMirror;
int expand = -1;
int diff = -1;
int maxLPSLength = 0;
int maxLPSCenterPosition = 0;
int start = -1;
int end = -1;
// Uncomment it to print LPS Length array
// printf("%d %d ", L[0], L[1]);
for (i = 2; i < N; i++)
{
// Get currentLeftPosition iMirror
// for currentRightPosition i
iMirror = 2 * C - i;
// Reset expand - means no
// expansion required
expand = 0;
diff = R - i;
// If currentRightPosition i is
// within centerRightPosition R
if(diff >= 0)
{
// Case 1
if(L[iMirror] < diff)
L[i] = L[iMirror];
// Case 2
else if(L[iMirror] == diff && R == N - 1)
L[i] = L[iMirror];
// Case 3
else if(L[iMirror] == diff && R < N - 1)
{
L[i] = L[iMirror];
// Expansion required
expand = 1;
}
// Case 4
else if(L[iMirror] > diff)
{
L[i] = diff;
// Expansion required
expand = 1;
}
}
else
{
L[i] = 0;
// Expansion required
expand = 1;
}
if (expand == 1)
{
// Attempt to expand palindrome centered
// at currentRightPosition i. Here for odd
// positions, we compare characters and
// if match then increment LPS Length by ONE
// If even position, we just increment LPS
// by ONE without any character comparison
try
{
while (((i + L[i]) < N &&
(i - L[i]) > 0) &&
(((i + L[i] + 1) % 2 == 0) ||
(text.charAt((i + L[i] + 1) / 2) ==
text.charAt((i - L[i] - 1) / 2))))
{
L[i]++;
}
}
catch (Exception e)
{
assert true;
}
}
// Track maxLPSLength
if(L[i] > maxLPSLength)
{
maxLPSLength = L[i];
maxLPSCenterPosition = i;
}
// If palindrome centered at
// currentRightPosition i expand
// beyond centerRightPosition R,
// adjust centerPosition C based
// on expanded palindrome.
if (i + L[i] > R)
{
C = i;
R = i + L[i];
}
//Uncomment it to print LPS Length array
//System.out.print("%d ", L[i]);
}
start = (maxLPSCenterPosition -
maxLPSLength) / 2;
end = start + maxLPSLength - 1;
//System.out.print("start: %d end: %d\n",
// start, end);
System.out.print("LPS of string is " +
text + " : ");
for(i = start; i <= end; i++)
System.out.print(text.charAt(i));
System.out.println();
}
// Driver code
public static void main(String []args)
{
String text1="babcbabcbaccba";
findLongestPalindromicString(text1);
String text2="abaaba";
findLongestPalindromicString(text2);
String text3= "abababa";
findLongestPalindromicString(text3);
String text4="abcbabcbabcba";
findLongestPalindromicString(text4);
String text5="forgeeksskeegfor";
findLongestPalindromicString(text5);
String text6="caba";
findLongestPalindromicString(text6);
String text7="abacdfgdcaba";
findLongestPalindromicString(text7);
String text8="abacdfgdcabba";
findLongestPalindromicString(text8);
String text9="abacdedcaba";
findLongestPalindromicString(text9);
}
}
// This code is contributed by SoumikMondalPython
# Python program to implement Manacher's Algorithm
def findLongestPalindromicString(text):
N = len(text)
if N == 0:
return
N = 2*N+1 # Position count
L = [0] * N
L[0] = 0
L[1] = 1
C = 1 # centerPosition
R = 2 # centerRightPosition
i = 0 # currentRightPosition
iMirror = 0 # currentLeftPosition
maxLPSLength = 0
maxLPSCenterPosition = 0
start = -1
end = -1
diff = -1
# Uncomment it to print LPS Length array
# printf("%d %d ", L[0], L[1]);
for i in xrange(2,N):
# get currentLeftPosition iMirror for currentRightPosition i
iMirror = 2*C-i
L[i] = 0
diff = R - i
# If currentRightPosition i is within centerRightPosition R
if diff > 0:
L[i] = min(L[iMirror], diff)
# Attempt to expand palindrome centered at currentRightPosition i
# Here for odd positions, we compare characters and
# if match then increment LPS Length by ONE
# If even position, we just increment LPS by ONE without
# any character comparison
try:
while ((i+L[i]) < N and (i-L[i]) > 0) and \
(((i+L[i]+1) % 2 == 0) or \
(text[(i+L[i]+1)/2] == text[(i-L[i]-1)/2])):
L[i]+=1
except Exception as e:
pass
if L[i] > maxLPSLength: # Track maxLPSLength
maxLPSLength = L[i]
maxLPSCenterPosition = i
# If palindrome centered at currentRightPosition i
# expand beyond centerRightPosition R,
# adjust centerPosition C based on expanded palindrome.
if i + L[i] > R:
C = i
R = i + L[i]
# Uncomment it to print LPS Length array
# printf("%d ", L[i]);
start = (maxLPSCenterPosition - maxLPSLength) / 2
end = start + maxLPSLength - 1
print "LPS of string is " + text + " : ",
print text[start:end+1],
print "\n",
# Driver program
text1 = "babcbabcbaccba"
findLongestPalindromicString(text1)
text2 = "abaaba"
findLongestPalindromicString(text2)
text3 = "abababa"
findLongestPalindromicString(text3)
text4 = "abcbabcbabcba"
findLongestPalindromicString(text4)
text5 = "forgeeksskeegfor"
findLongestPalindromicString(text5)
text6 = "caba"
findLongestPalindromicString(text6)
text7 = "abacdfgdcaba"
findLongestPalindromicString(text7)
text8 = "abacdfgdcabba"
findLongestPalindromicString(text8)
text9 = "abacdedcaba"
findLongestPalindromicString(text9)
# This code is contributed by BHAVYA JAINC#
// A C# program to implement Manacher’s Algorithm
using System;
using System.Diagnostics;
public class GFG
{
public static void findLongestPalindromicString(
String text)
{
int N = text.Length;
if(N == 0)
return;
// Position count
N = 2 * N + 1;
// LPS Length Array
int []L = new int [N];
L[0] = 0;
L[1] = 1;
// centerPosition
int C = 1;
// centerRightPosition
int R = 2;
// currentRightPosition
int i = 0;
// currentLeftPosition
int iMirror;
int expand = -1;
int diff = -1;
int maxLPSLength = 0;
int maxLPSCenterPosition = 0;
int start = -1;
int end = -1;
// Uncomment it to print LPS Length array
// printf("%d %d ", L[0], L[1]);
for (i = 2; i < N; i++)
{
// Get currentLeftPosition iMirror
// for currentRightPosition i
iMirror = 2 * C - i;
// Reset expand - means no
// expansion required
expand = 0;
diff = R - i;
// If currentRightPosition i is
// within centerRightPosition R
if(diff >= 0)
{
// Case 1
if(L[iMirror] < diff)
L[i] = L[iMirror];
// Case 2
else if(L[iMirror] == diff && R == N - 1)
L[i] = L[iMirror];
// Case 3
else if(L[iMirror] == diff && R < N - 1)
{
L[i] = L[iMirror];
// Expansion required
expand = 1;
}
// Case 4
else if(L[iMirror] > diff)
{
L[i] = diff;
// Expansion required
expand = 1;
}
}
else
{
L[i] = 0;
// Expansion required
expand = 1;
}
if (expand == 1)
{
// Attempt to expand palindrome centered
// at currentRightPosition i. Here for odd
// positions, we compare characters and
// if match then increment LPS Length by ONE
// If even position, we just increment LPS
// by ONE without any character comparison
try
{
while (((i + L[i]) < N &&
(i - L[i]) > 0) &&
(((i + L[i] + 1) % 2 == 0) ||
(text[(i + L[i] + 1) / 2] ==
text[(i - L[i] - 1) / 2])))
{
L[i]++;
}
}
catch (Exception)
{
Debug.Assert(true);
}
}
// Track maxLPSLength
if(L[i] > maxLPSLength)
{
maxLPSLength = L[i];
maxLPSCenterPosition = i;
}
// If palindrome centered at
// currentRightPosition i expand
// beyond centerRightPosition R,
// adjust centerPosition C based
// on expanded palindrome.
if (i + L[i] > R)
{
C = i;
R = i + L[i];
}
//Uncomment it to print LPS Length array
//System.out.print("%d ", L[i]);
}
start = (maxLPSCenterPosition -
maxLPSLength) / 2;
end = start + maxLPSLength - 1;
//System.out.print("start: %d end: %d\n",
// start, end);
Console.Write("LPS of string is " +
text + " : ");
for(i = start; i <= end; i++)
Console.Write(text[i]);
Console.WriteLine();
}
// Driver code
static public void Main ()
{
String text1 = "babcbabcbaccba";
findLongestPalindromicString(text1);
String text2 = "abaaba";
findLongestPalindromicString(text2);
String text3 = "abababa";
findLongestPalindromicString(text3);
String text4 = "abcbabcbabcba";
findLongestPalindromicString(text4);
String text5 = "forgeeksskeegfor";
findLongestPalindromicString(text5);
String text6 = "caba";
findLongestPalindromicString(text6);
String text7 = "abacdfgdcaba";
findLongestPalindromicString(text7);
String text8 = "abacdfgdcabba";
findLongestPalindromicString(text8);
String text9 = "abacdedcaba";
findLongestPalindromicString(text9);
}
}
// This code is contributed by Dharanendra L V.输出：
LPS of string is babcbabcbaccba : abcbabcba
LPS of string is abaaba : abaaba
LPS of string is abababa : abababa
LPS of string is abcbabcbabcba : abcbabcbabcba
LPS of string is forgeeksskeegfor : geeksskeeg
LPS of string is caba : aba
LPS of string is abacdfgdcaba : aba
LPS of string is abacdfgdcabba : abba
LPS of string is abacdedcaba : abacdedcaba