原文:https://www . geesforgeks . org/find-number-distinct-回文-子字符串-给定-string/
给定一串小写 ASCII 字符，找到它的所有不同的连续回文子串。
示例:
Input: str = "abaaa"
Output: Below are 5 palindrome sub-strings
a
aa
aaa
aba
b
Input: str = "geek"
Output: Below are 4 palindrome sub-strings
e
ee
g
k
第一步:使用改进的 Manacher 算法查找所有回文:
将每个字符视为一个轴心，在两侧展开，以所考虑的轴心字符为中心查找偶数和奇数长度回文的长度，并将长度存储在 2 个数组中(奇数&偶数)。
这一步的时间复杂度是 O(n^2)
第二步:将所有找到的回文插入 HashMap:
将上一步找到的回文全部插入 HashMap。还将字符串中的所有单个字符插入到 HashMap 中(以生成不同的单字母回文子字符串)。
这个步骤的时间复杂度是 O(n^3)假设散列插入搜索花费 O(1)个时间。请注意，一个字符串最多只能有 O(n^2)回文子字符串。在下面的 C++代码中，有序 hashmap 用于插入和搜索时间复杂度为 O(Logn)的地方。在 C++中，使用红黑树实现有序 hashmap。
第三步:打印不同的回文以及这种不同回文的数量:
最后一步是打印 HashMap 中存储的所有值(由于 HashMap 的属性，只有不同的元素会被散列)。地图的大小给出了不同回文连续子串的数量。
以下是上述想法的实现。
// C++ program to find all distinct palindrome sub-strings
// of a given string
#include
#include
using namespace std;
// Function to print all distinct palindrome sub-strings of s
void palindromeSubStrs(string s)
{
map<string, int> m;
int n = s.size();
// table for storing results (2 rows for odd-
// and even-length palindromes
int R[2][n+1];
// Find all sub-string palindromes from the given input
// string insert 'guards' to iterate easily over s
s = "@" + s + "#";
for (int j = 0; j <= 1; j++)
{
int rp = 0; // length of 'palindrome radius'
R[j][0] = 0;
int i = 1;
while (i <= n)
{
// Attempt to expand palindrome centered at i
while (s[i - rp - 1] == s[i + j + rp])
rp++; // Incrementing the length of palindromic
// radius as and when we find vaid palindrome
// Assigning the found palindromic length to odd/even
// length array
R[j][i] = rp;
int k = 1;
while ((R[j][i - k] != rp - k) && (k < rp))
{
R[j][i + k] = min(R[j][i - k],rp - k);
k++;
}
rp = max(rp - k,0);
i += k;
}
}
// remove 'guards'
s = s.substr(1, n);
// Put all obtained palindromes in a hash map to
// find only distinct palindromess
m[string(1, s[0])]=1;
for (int i = 1; i <= n; i++)
{
for (int j = 0; j <= 1; j++)
for (int rp = R[j][i]; rp > 0; rp--)
m[s.substr(i - rp - 1, 2 * rp + j)]=1;
m[string(1, s[i])]=1;
}
//printing all distinct palindromes from hash map
cout << "Below are " << m.size()-1
<< " palindrome sub-strings";
map<string, int>::iterator ii;
for (ii = m.begin(); ii!=m.end(); ++ii)
cout << (*ii).first << endl;
}
// Driver program
int main()
{
palindromeSubStrs("abaaa");
return 0;
}
// Java program to find all distinct palindrome
// sub-strings of a given string
import java.util.Map;
import java.util.TreeMap;
public class GFG
{
// Function to print all distinct palindrome
// sub-strings of s
static void palindromeSubStrs(String s)
{
//map<string, int> m;
TreeMap<String , Integer> m = new TreeMap<>();
int n = s.length();
// table for storing results (2 rows for odd-
// and even-length palindromes
int[][] R = new int[2][n+1];
// Find all sub-string palindromes from the
// given input string insert 'guards' to
// iterate easily over s
s = "@" + s + "#";
for (int j = 0; j <= 1; j++)
{
int rp = 0; // length of 'palindrome radius'
R[j][0] = 0;
int i = 1;
while (i <= n)
{
// Attempt to expand palindrome centered
// at i
while (s.charAt(i - rp - 1) == s.charAt(i +
j + rp))
rp++; // Incrementing the length of
// palindromic radius as and
// when we find valid palindrome
// Assigning the found palindromic length
// to odd/even length array
R[j][i] = rp;
int k = 1;
while ((R[j][i - k] != rp - k) && (k < rp))
{
R[j][i + k] = Math.min(R[j][i - k],
rp - k);
k++;
}
rp = Math.max(rp - k,0);
i += k;
}
}
// remove 'guards'
s = s.substring(1, s.length()-1);
// Put all obtained palindromes in a hash map to
// find only distinct palindromess
m.put(s.substring(0,1), 1);
for (int i = 1; i < n; i++)
{
for (int j = 0; j <= 1; j++)
for (int rp = R[j][i]; rp > 0; rp--)
m.put(s.substring(i - rp - 1, i - rp - 1
+ 2 * rp + j), 1);
m.put(s.substring(i, i + 1), 1);
}
// printing all distinct palindromes from
// hash map
System.out.println("Below are " + (m.size())
+ " palindrome sub-strings");
for (Map.Entry<String, Integer> ii:m.entrySet())
System.out.println(ii.getKey());
}
// Driver program
public static void main(String args[])
{
palindromeSubStrs("abaaa");
}
}
// This code is contributed by Sumit Ghosh
# Python program Find all distinct palindromic sub-strings
# of a given string
# Function to print all distinct palindrome sub-strings of s
def palindromeSubStrs(s):
m = dict()
n = len(s)
# table for storing results (2 rows for odd-
# and even-length palindromes
R = [[0 for x in xrange(n+1)] for x in xrange(2)]
# Find all sub-string palindromes from the given input
# string insert 'guards' to iterate easily over s
s = "@" + s + "#"
for j in xrange(2):
rp = 0 # length of 'palindrome radius'
R[j][0] = 0
i = 1
while i <= n:
# Attempt to expand palindrome centered at i
while s[i - rp - 1] == s[i + j + rp]:
rp += 1 # Incrementing the length of palindromic
# radius as and when we find valid palindrome
# Assigning the found palindromic length to odd/even
# length array
R[j][i] = rp
k = 1
while (R[j][i - k] != rp - k) and (k < rp):
R[j][i+k] = min(R[j][i-k], rp - k)
k += 1
rp = max(rp - k, 0)
i += k
# remove guards
s = s[1:len(s)-1]
# Put all obtained palindromes in a hash map to
# find only distinct palindrome
m[s[0]] = 1
for i in xrange(1,n):
for j in xrange(2):
for rp in xrange(R[j][i],0,-1):
m[s[i - rp - 1 : i - rp - 1 + 2 * rp + j]] = 1
m[s[i]] = 1
# printing all distinct palindromes from hash map
print "Below are " + str(len(m)) + " pali sub-strings"
for i in m:
print i
# Driver program
palindromeSubStrs("abaaa")
# This code is contributed by BHAVYA JAIN and ROHIT SIKKA
// C# program to find all distinct palindrome
// sub-strings of a given string
using System;
using System.Collections.Generic;
class GFG
{
// Function to print all distinct palindrome
// sub-strings of s
public static void palindromeSubStrs(string s)
{
//map
Dictionary < string,
int > m = new Dictionary < string,
int > ();
int n = s.Length;
// table for storing results (2 rows for odd-
// and even-length palindromes
int[, ] R = new int[2, n + 1];
// Find all sub-string palindromes from the
// given input string insert 'guards' to
// iterate easily over s
s = "@" + s + "#";
for (int j = 0; j <= 1; j++)
{
int rp = 0; // length of 'palindrome radius'
R[j, 0] = 0;
int i = 1;
while (i <= n)
{
// Attempt to expand palindrome centered
// at i
while (s[i - rp - 1] == s[i + j + rp])
// Incrementing the length of
// palindromic radius as and
// when we find valid palindrome
rp++;
// Assigning the found palindromic length
// to odd/even length array
R[j, i] = rp;
int k = 1;
while ((R[j, i - k] != rp - k) && k < rp)
{
R[j, i + k] = Math.Min(R[j, i - k], rp - k);
k++;
}
rp = Math.Max(rp - k, 0);
i += k;
}
}
// remove 'guards'
s = s.Substring(1);
// Put all obtained palindromes in a hash map to
// find only distinct palindromess
if (!m.ContainsKey(s.Substring(0, 1)))
m.Add(s.Substring(0, 1), 1);
else
m[s.Substring(0, 1)]++;
for (int i = 1; i < n; i++)
{
for (int j = 0; j <= 1; j++)
for (int rp = R[j, i]; rp > 0; rp--)
{
if (!m.ContainsKey(s.Substring(i - rp - 1, 2 * rp + j)))
m.Add(s.Substring(i - rp - 1, 2 * rp + j), 1);
else
m[s.Substring(i - rp - 1, 2 * rp + j)]++;
}
if (!m.ContainsKey(s.Substring(i, 1)))
m.Add(s.Substring(i, 1), 1);
else
m[s.Substring(i, 1)]++;
}
// printing all distinct palindromes from
// hash map
Console.WriteLine("Below are " + (m.Count));
foreach(KeyValuePair < string, int > ii in m)
Console.WriteLine(ii.Key);
}
// Driver Code
public static void Main(string[] args)
{
palindromeSubStrs("abaaa");
}
}
// This code is contributed by
// sanjeev2552
输出:
Below are 5 palindrome sub-strings
a
aa
aaa
aba
b
类似问题:
统计一串中所有回文子串
本文由 Vignesh Narayanan 和 Sowmya Sampath 供稿。如果你发现任何不正确的地方，或者你想分享更多关于上面讨论的话题的信息，请写评论。
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