Count of pairs of strings whose concatenation forms a palindromic string
Given an array A[ ] consisting of N strings, the task is to count the number of pairs of possible strings that on merging forms a Palindromic String or can be rearranged to form a Palindromic String.
Example :
Input: N = 6, A[ ] = {aab, abcac, dffe, ed, aa, aade}
Output: 6
Explanation:
All possible pairs of strings which generates a palindromic string:
{aab, abcac} = aabccbaa
{aab, aa} = aabaa
{abcac, aa} = aacbcaa
{dffe, ed} = fdeedf
{dffe, aade} = edfaafde
{ed, aade} = edaade or aeddea
Hence, total possible pairs = 6Input: N = 3, A[ ] = {aa, bb, cd}
Output: 1
Explanation:
The only possible pair of strings which generates palindromic string:
{aa, bb} = abba
Hence, total possible pairs = 1
Naive Approach:
The simplest approach to solve this problem is to generate all possible pairs from the given array and merge these pairs to generate new strings. For each of those merged strings, generate all possible permutations of the string and for each permutation, check whether it is a palindromic string or not and increment the count accordingly.
Time Complexity: O(N2 * L! * L), where L is the maximum length of a string.
Auxiliary Space: O(M)
Efficient Approach:
A palindromic string can always be formed when at most one character has an odd occurrence and remaining every character has even occurrence. Since rearrangement of the characters in the merged string is allowed, so we only need to count the frequency of characters in the merged string and check if it satisfies to be a palindromic string or not.
Illustration:
1. Every character has even occurrence
Strings “aab” and “abcac” can be merged and rearranged to form a palindromic string “aababcac” with each character having even frequency2. One character has odd occurrence
Strings “aab” and “aa” can be merged to form a palindromic string “aabaa” with a character(‘b’) having odd frequency and the rest having even frequency.
Hence, it can be observed that two pairs of strings of the following types can be merged to form a palindromic string:
- The frequency of each character in both strings are same.
- At most one character in both the strings has a different frequency.
Follow the steps below to solve the problem:
- Traverse the given array and for every string, store the frequency of each character.
- Assign parity (0 or 1) to each frequency. Assign 0 for even frequency and 1 for odd frequency.
- Initialize a map to store the frequencies of each frequency array generated.
- Since, rearrangement is allowed, reverse the parity of each character and include the frequency array in map.
- Finally, return the total count of similar frequency arrays, which will give the required count of pairs.
Below is the implementation of the above approach:
C++
// C++ Program to find // palindromic string #include <bits/stdc++.h> using namespace std; int getCount( int N, vector<string>& s) { // Stores frequency array // and its count map<vector< int >, int > mp; // Total number of pairs int ans = 0; for ( int i = 0; i < N; i++) { // Initializing array of size 26 // to store count of character vector< int > a(26, 0); // Counting occurrence of each // character of current string for ( int j = 0; j < s[i].size(); j++) { a[s[i][j] - 'a' ]++; } // Convert each count to parity(0 or 1) // on the basis of its frequency for ( int j = 0; j < 26; j++) { a[j] = a[j] % 2; } // Adding to answer ans += mp[a]; // Frequency of single character // can be possibly changed, // so change its parity for ( int j = 0; j < 26; j++) { vector< int > changedCount = a; if (a[j] == 0) changedCount[j] = 1; else changedCount[j] = 0; ans += mp[changedCount]; } mp[a]++; } return ans; } int main() { int N = 6; vector<string> A = { "aab" , "abcac" , "dffe" , "ed" , "aa" , "aade" }; cout << getCount(N, A); return 0; } |
Java
// Java program to find // palindromic string import java.util.*; class GFG{ static int getCount( int N, List<String> s) { // Stores frequency array // and its count Map<List<Integer>, Integer> mp = new HashMap<>(); // Total number of pairs int ans = 0 ; for ( int i = 0 ; i < N; i++) { // Initializing array of size 26 // to store count of character List<Integer> a = new ArrayList<>( 26 ); for ( int k = 0 ; k < 26 ; k++) a.add( 0 ); // Counting occurrence of each // character of current string for ( int j = 0 ; j < s.get(i).length(); j++) { a.set((s.get(i).charAt(j) - 'a' ), a.get(s.get(i).charAt(j) - 'a' ) + 1 ); } // Convert each count to parity(0 or 1) // on the basis of its frequency for ( int j = 0 ; j < 26 ; j++) { a.set(j, a.get(j) % 2 ); } // Adding to answer ans += mp.getOrDefault(a, 0 ); // Frequency of single character // can be possibly changed, // so change its parity for ( int j = 0 ; j < 26 ; j++) { List<Integer> changedCount = new ArrayList<>(); changedCount.addAll(a); if (a.get(j) == 0 ) changedCount.set(j, 1 ); else changedCount.set(j, 0 ); ans += mp.getOrDefault(changedCount, 0 ); } mp.put(a, mp.getOrDefault(a, 0 ) + 1 ); } return ans; } // Driver code public static void main (String[] args) { int N = 6 ; List<String> A = Arrays.asList( "aab" , "abcac" , "dffe" , "ed" , "aa" , "aade" ); System.out.print(getCount(N, A)); } } // This code is contributed by offbeat |
Python3
# Python3 program to find # palindromic string from collections import defaultdict def getCount(N, s): # Stores frequency array # and its count mp = defaultdict( lambda : 0 ) # Total number of pairs ans = 0 for i in range (N): # Initializing array of size 26 # to store count of character a = [ 0 ] * 26 # Counting occurrence of each # character of current string for j in range ( len (s[i])): a[ ord (s[i][j]) - ord ( 'a' )] + = 1 # Convert each count to parity(0 or 1) # on the basis of its frequency for j in range ( 26 ): a[j] = a[j] % 2 # Adding to answer ans + = mp[ tuple (a)] # Frequency of single character # can be possibly changed, # so change its parity for j in range ( 26 ): changedCount = a[:] if (a[j] = = 0 ): changedCount[j] = 1 else : changedCount[j] = 0 ans + = mp[ tuple (changedCount)] mp[ tuple (a)] + = 1 return ans # Driver code if __name__ = = '__main__' : N = 6 A = [ "aab" , "abcac" , "dffe" , "ed" , "aa" , "aade" ] print (getCount(N, A)) # This code is contributed by Shivam Singh |
C#
// C# program to find // palindromic string using System; using System.Collections.Generic; class GFG { static int CompareLists(List< int > a, List< int > b) { // Check the length of both lists first if (a.Count != b.Count) { return a.Count - b.Count; } // Compare each element of the lists for ( int i = 0; i < a.Count; i++) { if (a[i] != b[i]) { return a[i] - b[i]; } } return 0; } static int getCount( int N, List< string > s) { // Stores frequency array // and its count Dictionary<List< int >, int > mp = new Dictionary<List< int >, int >( new ListComparer()); // Total number of pairs int ans = 0; for ( int i = 0; i < N; i++) { // Initializing array of size 26 // to store count of character List< int > a = new List< int >( new int [26]); // Counting occurrence of each // character of current string for ( int j = 0; j < s[i].Length; j++) { a[s[i][j] - 'a' ]++; } // Convert each count to parity(0 or 1) // on the basis of its frequency for ( int j = 0; j < 26; j++) { a[j] %= 2; } // Adding to answer ans += mp.GetValueOrDefault(a, 0); // Frequency of single character // can be possibly changed, // so change its parity for ( int j = 0; j < 26; j++) { List< int > changedCount = new List< int >(a); if (a[j] == 0) changedCount[j] = 1; else changedCount[j] = 0; ans += mp.GetValueOrDefault(changedCount, 0); } mp[a] = mp.GetValueOrDefault(a, 0) + 1; } return ans; } // Driver code static void Main( string [] args) { int N = 6; List< string > A = new List< string >{ "aab" , "abcac" , "dffe" , "ed" , "aa" , "aade" }; Console.Write(getCount(N, A)); } } class ListComparer : IEqualityComparer<List< int > > { public bool Equals(List< int > a, List< int > b) { // Compare the elements of both lists if (a.Count != b.Count) { return false ; } for ( int i = 0; i < a.Count; i++) { if (a[i] != b[i]) { return false ; } } return true ; } public int GetHashCode(List< int > list) { // Generate a hash code based on the elements of the // list int hash = 17; foreach ( int element in list) { hash = hash * 31 + element; } return hash; } } // This code is contributed by phasing17 |
Javascript
// JS Program to find // palindromic string function getCount(N, s) { // Stores frequency array // and its count let mp = new Map(); // Total number of pairs let ans = 0; for (let i = 0; i < N; i++) { // Initializing array of size 26 // to store count of character let a = []; for (let i = 0; i < 26; i++) { a.push(0); } // Counting occurrence of each // character of current string for (let j = 0; j < s[i].length; j++) { // console.log("p : ",); a[s[i][j].charCodeAt(0) - 'a' .charCodeAt(0)]++; } // Convert each count to parity(0 or 1) // on the basis of its frequency for (let j = 0; j < 26; j++) { a[j] = a[j] % 2; } // Adding to answer let str = "" ; for (let m = 0; m < a.length; m++) { str += a[m]; } if (!mp.has(str)) { mp.set(str, 0); ans += mp.get(str); } else ans += mp.get(str); // Frequency of single character // can be possibly changed, // so change its parity for (let j = 0; j < 2; j++) { let changedCount = a; if (a[j] == 0) changedCount[j] = 1; else changedCount[j] = 0; let str2 = "" ; for (let p = 0; p < changedCount.length; p++) { str2 += changedCount[p]; } if (!mp.has(str2)) { mp.set(str2, 0); ans += mp.get(str2); } else ans += mp.get(str2); } mp.set(str, mp.get(str)+1.5); } return ans; } let N = 6; let A = [ "aab" , "abcac" , "dffe" , "ed" , "aa" , "aade" ]; console.log(getCount(N, A)); // This code is contributed by ksam24000. |
6
Time Complexity: O(N*(L+log(N))), where L is the maximum length of a string
Auxiliary Space: O(N)
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