给定一个序列，打印它的最长回文子序列。
例子 ：
Input : BBABCBCAB
Output : BABCBAB
The above output is the longest
palindromic subsequence of given
sequence. "BBBBB" and "BBCBB" are
also palindromic subsequences of
the given sequence, but not the
longest ones.
Input : GEEKSFORGEEKS
Output : Output can be either EEKEE
or EESEE or EEGEE, ..
我们在下面的文章中讨论了一种解决方案，以找到最长回文子序列的长度。
动态编程|第12组(最长回文序列)
在这篇文章中，讨论了打印最长回文子序列的解决方案。
此问题接近最长公共子序列(LCS)问题。实际上，我们可以使用LCS作为子例程来解决此问题。以下是使用LCS的两步解决方案。
1)反转给定序列并将反转存储在另一个数组中，例如rev [0..n-1]
2)给定序列和rev []的LCS将是最长回文序列。
3)一旦找到LCS，就可以打印LCS。
下面是上述方法的实现：
C++
/* CPP program to print longest palindromic
subsequence */
#include
using namespace std;
/* Returns LCS X and Y */
string lcs(string &X, string &Y)
{
int m = X.length();
int n = Y.length();
int L[m+1][n+1];
/* Following steps build L[m+1][n+1] in bottom
up fashion. Note that L[i][j] contains
length of LCS of X[0..i-1] and Y[0..j-1] */
for (int i=0; i<=m; i++)
{
for (int j=0; j<=n; j++)
{
if (i == 0 || j == 0)
L[i][j] = 0;
else if (X[i-1] == Y[j-1])
L[i][j] = L[i-1][j-1] + 1;
else
L[i][j] = max(L[i-1][j], L[i][j-1]);
}
}
// Following code is used to print LCS
int index = L[m][n];
// Create a string length index+1 and
// fill it with \0
string lcs(index+1, '\0');
// Start from the right-most-bottom-most
// corner and one by one store characters
// in lcs[]
int i = m, j = n;
while (i > 0 && j > 0)
{
// If current character in X[] and Y
// are same, then current character
// is part of LCS
if (X[i-1] == Y[j-1])
{
// Put current character in result
lcs[index-1] = X[i-1];
i--;
j--;
// reduce values of i, j and index
index--;
}
// If not same, then find the larger of
// two and go in the direction of larger
// value
else if (L[i-1][j] > L[i][j-1])
i--;
else
j--;
}
return lcs;
}
// Returns longest palindromic subsequence
// of str
string longestPalSubseq(string &str)
{
// Find reverse of str
string rev = str;
reverse(rev.begin(), rev.end());
// Return LCS of str and its reverse
return lcs(str, rev);
}
/* Driver program to test above function */
int main()
{
string str = "GEEKSFORGEEKS";
cout << longestPalSubseq(str);
return 0;
} Java
// Java program to print longest palindromic
//subsequence
class GFG {
/* Returns LCS X and Y */
static String lcs(String a, String b) {
int m = a.length();
int n = b.length();
char X[] = a.toCharArray();
char Y[] = b.toCharArray();
int L[][] = new int[m + 1][n + 1];
/* Following steps build L[m+1][n+1] in bottom
up fashion. Note that L[i][j] contains
length of LCS of X[0..i-1] and Y[0..j-1] */
for (int i = 0; i <= m; i++) {
for (int j = 0; j <= n; j++) {
if (i == 0 || j == 0) {
L[i][j] = 0;
} else if (X[i - 1] == Y[j - 1]) {
L[i][j] = L[i - 1][j - 1] + 1;
} else {
L[i][j] = Math.max(L[i - 1][j], L[i][j - 1]);
}
}
}
// Following code is used to print LCS
int index = L[m][n];
// Create a String length index+1 and
// fill it with \0
char[] lcs = new char[index + 1];
// Start from the right-most-bottom-most
// corner and one by one store characters
// in lcs[]
int i = m, j = n;
while (i > 0 && j > 0) {
// If current character in X[] and Y
// are same, then current character
// is part of LCS
if (X[i - 1] == Y[j - 1]) {
// Put current character in result
lcs[index - 1] = X[i - 1];
i--;
j--;
// reduce values of i, j and index
index--;
} // If not same, then find the larger of
// two and go in the direction of larger
// value
else if (L[i - 1][j] > L[i][j - 1]) {
i--;
} else {
j--;
}
}
String ans = "";
for (int x = 0; x < lcs.length; x++) {
ans += lcs[x];
}
return ans;
}
// Returns longest palindromic subsequence
// of str
static String longestPalSubseq(String str) {
// Find reverse of str
String rev = str;
rev = reverse(rev);
// Return LCS of str and its reverse
return lcs(str, rev);
}
static String reverse(String str) {
String ans = "";
// convert String to character array
// by using toCharArray
char[] try1 = str.toCharArray();
for (int i = try1.length - 1; i >= 0; i--) {
ans += try1[i];
}
return ans;
}
/* Driver program to test above function */
public static void main(String[] args) {
String str = "GEEKSFORGEEKS";
System.out.println(longestPalSubseq(str));
}
}Python3
# Python3 program to print longest
# palindromic subsequence
# Returns LCS X and Y
def lcs_(X, Y) :
m = len(X)
n = len(Y)
L = [[0] * (n + 1)] * (m + 1)
# Following steps build L[m+1][n+1]
# in bottom up fashion. Note that
# L[i][j] contains length of LCS of
# X[0..i-1] and Y[0..j-1]
for i in range(n + 1) :
for j in range(n + 1) :
if (i == 0 or j == 0) :
L[i][j] = 0;
elif (X[i - 1] == Y[j - 1]) :
L[i][j] = L[i - 1][j - 1] + 1;
else :
L[i][j] = max(L[i - 1][j],
L[i][j - 1]);
# Following code is used to print LCS
index = L[m][n];
# Create a string length index+1 and
# fill it with \0
lcs = ["\n "] * (index + 1)
# Start from the right-most-bottom-most
# corner and one by one store characters
# in lcs[]
i, j= m, n
while (i > 0 and j > 0) :
# If current character in X[] and Y
# are same, then current character
# is part of LCS
if (X[i - 1] == Y[j - 1]) :
# Put current character in result
lcs[index - 1] = X[i - 1]
i -= 1
j -= 1
# reduce values of i, j and index
index -= 1
# If not same, then find the larger of
# two and go in the direction of larger
# value
elif(L[i - 1][j] > L[i][j - 1]) :
i -= 1
else :
j -= 1
ans = ""
for x in range(len(lcs)) :
ans += lcs[x]
return ans
# Returns longest palindromic
# subsequence of str
def longestPalSubseq(string) :
# Find reverse of str
rev = string[: : -1]
# Return LCS of str and its reverse
return lcs_(string, rev)
# Driver Code
if __name__ == "__main__" :
string = "GEEKSFORGEEKS";
print(longestPalSubseq(string))
# This code is contributed by RyugaC#
// C# program to print longest palindromic
//subsequence
using System;
public class GFG {
/* Returns LCS X and Y */
static String lcs(String a, String b) {
int m = a.Length;
int n = b.Length;
char []X = a.ToCharArray();
char []Y = b.ToCharArray();
int [,]L = new int[m + 1,n + 1];
int i, j;
/* Following steps build L[m+1,n+1] in bottom
up fashion. Note that L[i,j] contains
length of LCS of X[0..i-1] and Y[0..j-1] */
for (i = 0; i <= m; i++) {
for (j = 0; j <= n; j++) {
if (i == 0 || j == 0) {
L[i,j] = 0;
} else if (X[i - 1] == Y[j - 1]) {
L[i,j] = L[i - 1,j - 1] + 1;
} else {
L[i,j] = Math.Max(L[i - 1,j], L[i,j - 1]);
}
}
}
// Following code is used to print LCS
int index = L[m,n];
// Create a String length index+1 and
// fill it with \0
char[] lcs = new char[index + 1];
// Start from the right-most-bottom-most
// corner and one by one store characters
// in lcs[]
i = m; j = n;
while (i > 0 && j > 0) {
// If current character in X[] and Y
// are same, then current character
// is part of LCS
if (X[i - 1] == Y[j - 1]) {
// Put current character in result
lcs[index - 1] = X[i - 1];
i--;
j--;
// reduce values of i, j and index
index--;
} // If not same, then find the larger of
// two and go in the direction of larger
// value
else if (L[i - 1,j] > L[i,j - 1]) {
i--;
} else {
j--;
}
}
String ans = "";
for (int x = 0; x < lcs.Length; x++) {
ans += lcs[x];
}
return ans;
}
// Returns longest palindromic subsequence
// of str
static String longestPalSubseq(String str) {
// Find reverse of str
String rev = str;
rev = reverse(rev);
// Return LCS of str and its reverse
return lcs(str, rev);
}
static String reverse(String str) {
String ans = "";
// convert String to character array
// by using toCharArray
char[] try1 = str.ToCharArray();
for (int i = try1.Length - 1; i >= 0; i--) {
ans += try1[i];
}
return ans;
}
/* Driver program to test above function */
public static void Main() {
String str = "GEEKSFORGEEKS";
Console.Write(longestPalSubseq(str));
}
}
// This code is contributed by 29AjayKumar输出：
EEGEE