# Smallest Palindromic Subsequence of Even Length in Range [L, R]

• Difficulty Level : Medium
• Last Updated : 25 May, 2021

Given a string of size N and some queries, the task is to find the lexicographically smallest palindromic subsequence of even length in range [L, R] for each query. If no such palindromic subsequence exists then the print -1.
Examples:

Input: str = “dbdeke”, query[][] = {{0, 5}, {1, 5}, {1, 3}}
Output: dd
ee
-1
Explanation: dd
In the first query, possible palindromic subsequences are “dd”, “ee”, “ddee” and “dd” which are lexicographically smallest.
In the second query, only possible palindromic subsequence is “ee”.
In the third query, no such palindromic subsequence is possible.
Input: str = “abcd”, query[][] = {{0, 3}}
Output: -1

Approach: The main observation of this problem is if there exists a palindromic subsequence, then it must be of length > 2. Therefore the resultant subsequence will be a string of length > 2 with the same characters. Choose the smallest character among those characters which have a frequency greater than 1 in the range [L, R] and print that character twice. If there is no such character exists then print -1.
Below is the implementation of above approach:

## C++

 `// C++ program to find lexicographically smallest``// palindromic subsequence of even length` `#include ``using` `namespace` `std;``const` `int` `N = 100001;` `// Frequency array for each character``int` `f[N];` `// Preprocess the frequency array calculation``void` `precompute(string s, ``int` `n)``{``    ``// Frequency array to track each character``    ``// in position 'i'``    ``for` `(``int` `i = 0; i < n; i++) {``        ``f[s[i] - ``'a'``][i]++;``    ``}` `    ``// Calculating prefix sum``    ``// over this frequency array``    ``// to get frequency of a character``    ``// in a range [L, R].``    ``for` `(``int` `i = 0; i < 26; i++) {``        ``for` `(``int` `j = 1; j < n; j++) {``            ``f[i][j] += f[i][j - 1];``        ``}``    ``}``}` `// Util function for palindromic subsequences``int` `palindromicSubsequencesUtil(``int` `L, ``int` `R)``{` `    ``int` `c, ok = 0;` `    ``// Find frequency of all characters``    ``for` `(``int` `i = 0; i < 26; i++) {` `        ``// For each character``        ``// find it's frequency``        ``// in range [L, R]``        ``int` `cnt = f[i][R];``        ``if` `(L > 0)``            ``cnt -= f[i][L - 1];` `        ``if` `(cnt > 1) {` `            ``// If frequency in this range is > 1,``            ``// then we must take this character,``            ``// as it will give``            ``// lexicographically smallest one``            ``ok = 1;``            ``c = i;``            ``break``;``        ``}``    ``}` `    ``// There is no character``    ``// in range [L, R] such``    ``// that it's frequency is > 1.``    ``if` `(ok == 0) {` `        ``return` `-1;``    ``}` `    ``// Return the character's value``    ``return` `c;``}` `// Function to find lexicographically smallest``// palindromic subsequence of even length``void` `palindromicSubsequences(``int` `Q[], ``int` `l)``{``    ``for` `(``int` `i = 0; i < l; i++) {` `        ``// Find in the palindromic subsequences``        ``int` `x``            ``= palindromicSubsequencesUtil(``                ``Q[i], Q[i]);` `        ``// No such subsequence exists``        ``if` `(x == -1) {``            ``cout << -1 << ``"\n"``;``        ``}``        ``else` `{``            ``char` `c = ``'a'` `+ x;``            ``cout << c << c << ``"\n"``;``        ``}``    ``}``}` `// Driver Code``int` `main()``{``    ``string str = ``"dbdeke"``;``    ``int` `Q[] = { { 0, 5 },``                   ``{ 1, 5 },``                   ``{ 1, 3 } };``    ``int` `n = str.size();``    ``int` `l = ``sizeof``(Q) / ``sizeof``(Q);` `    ``// Function calls``    ``precompute(str, n);` `    ``palindromicSubsequences(Q, l);` `    ``return` `0;``}`

## Java

 `// Java program to find lexicographically smallest``// palindromic subsequence of even length``import` `java.util.*;` `class` `GFG{``static` `int` `N = ``100001``;` `// Frequency array for each character``static` `int` `[][]f = ``new` `int``[``26``][N];` `// Preprocess the frequency array calculation``static` `void` `precompute(String s, ``int` `n)``{``    ``// Frequency array to track each character``    ``// in position 'i'``    ``for` `(``int` `i = ``0``; i < n; i++)``    ``{``        ``f[s.charAt(i) - ``'a'``][i]++;``    ``}` `    ``// Calculating prefix sum``    ``// over this frequency array``    ``// to get frequency of a character``    ``// in a range [L, R].``    ``for` `(``int` `i = ``0``; i < ``26``; i++)``    ``{``        ``for` `(``int` `j = ``1``; j < n; j++)``        ``{``            ``f[i][j] += f[i][j - ``1``];``        ``}``    ``}``}` `// Util function for palindromic subsequences``static` `int` `palindromicSubsequencesUtil(``int` `L, ``int` `R)``{``    ``int` `c = ``0``, ok = ``0``;` `    ``// Find frequency of all characters``    ``for` `(``int` `i = ``0``; i < ``26``; i++)``    ``{` `        ``// For each character``        ``// find it's frequency``        ``// in range [L, R]``        ``int` `cnt = f[i][R];``        ``if` `(L > ``0``)``            ``cnt -= f[i][L - ``1``];` `        ``if` `(cnt > ``1``)``        ``{` `            ``// If frequency in this range is > 1,``            ``// then we must take this character,``            ``// as it will give``            ``// lexicographically smallest one``            ``ok = ``1``;``            ``c = i;``            ``break``;``        ``}``    ``}` `    ``// There is no character``    ``// in range [L, R] such``    ``// that it's frequency is > 1.``    ``if` `(ok == ``0``)``    ``{``        ``return` `-``1``;``    ``}` `    ``// Return the character's value``    ``return` `c;``}` `// Function to find lexicographically smallest``// palindromic subsequence of even length``static` `void` `palindromicSubsequences(``int` `Q[][], ``int` `l)``{``    ``for` `(``int` `i = ``0``; i < l; i++)``    ``{` `        ``// Find in the palindromic subsequences``        ``int` `x = palindromicSubsequencesUtil(``                           ``Q[i][``0``], Q[i][``1``]);` `        ``// No such subsequence exists``        ``if` `(x == -``1``)``        ``{``            ``System.out.print(-``1` `+ ``"\n"``);``        ``}``        ``else``        ``{``            ``char` `c = (``char``) (``'a'` `+ x);``            ``System.out.print((``char``) c + ``""` `+``                             ``(``char``) c + ``"\n"``);``        ``}``    ``}``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``String str = ``"dbdeke"``;``    ``int` `Q[][] = { { ``0``, ``5` `},``                  ``{ ``1``, ``5` `},``                  ``{ ``1``, ``3` `} };``    ``int` `n = str.length();``    ``int` `l = Q.length;` `    ``// Function calls``    ``precompute(str, n);` `    ``palindromicSubsequences(Q, l);``}``}` `// This code is contributed by PrinciRaj1992`

## Python3

 `# Python3 program to find lexicographically``# smallest palindromic subsequence of even length``N ``=` `100001` `# Frequency array for each character``f ``=` `[[ ``0` `for` `x ``in` `range` `(N)]``         ``for` `y ``in` `range` `(``26``)]` `# Preprocess the frequency array calculation``def` `precompute(s, n):` `    ``# Frequency array to track each character``    ``# in position 'i'``    ``for` `i ``in` `range``(n):``        ``f[``ord``(s[i]) ``-` `ord``(``'a'``)][i] ``+``=` `1` `    ``# Calculating prefix sum``    ``# over this frequency array``    ``# to get frequency of a character``    ``# in a range [L, R].``    ``for` `i ``in` `range``(``26``):``        ``for` `j ``in` `range``(``1``, n):``            ``f[i][j] ``+``=` `f[i][j ``-` `1``]` `# Util function for palindromic subsequences``def` `palindromicSubsequencesUtil(L, R):` `    ``ok ``=` `0` `    ``# Find frequency of all characters``    ``for` `i ``in` `range``(``26``):` `        ``# For each character``        ``# find it's frequency``        ``# in range [L, R]``        ``cnt ``=` `f[i][R]``        ``if` `(L > ``0``):``            ``cnt ``-``=` `f[i][L ``-` `1``]` `        ``if` `(cnt > ``1``):` `            ``# If frequency in this range is > 1,``            ``# then we must take this character,``            ``# as it will give``            ``# lexicographically smallest one``            ``ok ``=` `1``            ``c ``=` `i``            ``break``        ` `    ``# There is no character``    ``# in range [L, R] such``    ``# that it's frequency is > 1.``    ``if` `(ok ``=``=` `0``):``        ``return` `-``1` `    ``# Return the character's value``    ``return` `c` `# Function to find lexicographically smallest``# palindromic subsequence of even length``def` `palindromicSubsequences(Q, l):` `    ``for` `i ``in` `range``(l):` `        ``# Find in the palindromic subsequences``        ``x ``=` `palindromicSubsequencesUtil(Q[i][``0``],``                                        ``Q[i][``1``])` `        ``# No such subsequence exists``        ``if` `(x ``=``=` `-``1``):``            ``print``(``-``1``)``        ` `        ``else` `:``            ``c ``=` `ord``(``'a'``) ``+` `x``            ``print``(``2` `*` `chr``(c))` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:` `    ``st ``=` `"dbdeke"``    ``Q ``=` `[ [ ``0``, ``5` `],``          ``[ ``1``, ``5` `],``          ``[ ``1``, ``3` `] ]``          ` `    ``n ``=` `len``(st)``    ``l ``=` `len``(Q)` `    ``# Function calls``    ``precompute(st, n)` `    ``palindromicSubsequences(Q, l)` `# This code is contributed by chitranayal   `

## C#

 `// C# program to find lexicographically smallest``// palindromic subsequence of even length``using` `System;` `class` `GFG{``    ` `static` `int` `N = 100001;` `// Frequency array for each character``static` `int` `[,]f = ``new` `int``[26, N];` `// Preprocess the frequency array calculation``static` `void` `precompute(String s, ``int` `n)``{``    ` `    ``// Frequency array to track each character``    ``// in position 'i'``    ``for``(``int` `i = 0; i < n; i++)``    ``{``        ``f[s[i] - ``'a'``, i]++;``    ``}` `    ``// Calculating prefix sum``    ``// over this frequency array``    ``// to get frequency of a character``    ``// in a range [L, R].``    ``for``(``int` `i = 0; i < 26; i++)``    ``{``        ``for``(``int` `j = 1; j < n; j++)``        ``{``            ``f[i, j] += f[i, j - 1];``        ``}``    ``}``}` `// Util function for palindromic subsequences``static` `int` `palindromicSubsequencesUtil(``int` `L, ``int` `R)``{``    ``int` `c = 0, ok = 0;` `    ``// Find frequency of all characters``    ``for``(``int` `i = 0; i < 26; i++)``    ``{` `        ``// For each character``        ``// find it's frequency``        ``// in range [L, R]``        ``int` `cnt = f[i, R];``        ``if` `(L > 0)``            ``cnt -= f[i, L - 1];` `        ``if` `(cnt > 1)``        ``{` `            ``// If frequency in this range is > 1,``            ``// then we must take this character,``            ``// as it will give``            ``// lexicographically smallest one``            ``ok = 1;``            ``c = i;``            ``break``;``        ``}``    ``}` `    ``// There is no character``    ``// in range [L, R] such``    ``// that it's frequency is > 1.``    ``if` `(ok == 0)``    ``{``        ``return` `-1;``    ``}` `    ``// Return the character's value``    ``return` `c;``}` `// Function to find lexicographically smallest``// palindromic subsequence of even length``static` `void` `palindromicSubsequences(``int` `[,]Q, ``int` `l)``{``    ``for``(``int` `i = 0; i < l; i++)``    ``{``        ` `        ``// Find in the palindromic subsequences``        ``int` `x = palindromicSubsequencesUtil(Q[i, 0],``                                            ``Q[i, 1]);` `        ``// No such subsequence exists``        ``if` `(x == -1)``        ``{``            ``Console.Write(-1 + ``"\n"``);``        ``}``        ``else``        ``{``            ``char` `c = (``char``)(``'a'` `+ x);``            ``Console.Write((``char``) c + ``""` `+``                          ``(``char``) c + ``"\n"``);``        ``}``    ``}``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``String str = ``"dbdeke"``;``    ``int` `[,]Q = { { 0, 5 },``                 ``{ 1, 5 },``                 ``{ 1, 3 } };``    ``int` `n = str.Length;``    ``int` `l = Q.GetLength(0);` `    ``// Function calls``    ``precompute(str, n);` `    ``palindromicSubsequences(Q, l);``}``}` `// This code is contributed by amal kumar choubey`

## Javascript

 ``

Output:

```dd
ee
-1```

Time Complexity: O(26 * N + 26 * Q), where N is the length of string

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