Given an integer **K** such that there is a set of all possible perfect squares, each of length **K**. From this set of perfect squares, form a set of the longest possible length having those numbers which are anagram to each other. The task is to print the largest element present in the generated set of anagrams.

**Note:** If there is more than one set of maximum length, then print the largest number among them.

The

anagramof a string is another string that contains the same characters, only the order of characters are different.

**Examples:**

Input:K = 2

Output:81

Explanation:

All possible squares of length K = 2 are {16, 25, 36, 49, 64, 81}.

The possible anagram sets are [16], [25], [36], [49], [64], [81].

Therefore, each set is of the same size i.e., 1.

In this case, print the set containing the largest element, which is 81.

Input:K = 5

Output:96100

**Naive Approach:** The simplest approach is to store all possible** K** length perfect squares and form a valid anagram sets using recursion. Then, find the maximum element present in the set of longest length.

**Time Complexity:** O(N^{2})

**Auxiliary Space:** O(N)

**Efficient Approach:** The idea is based on the observation that on sorting the digits of the perfect squares, the sequence of anagram numbers becomes equal. Below are the steps:

- Initialise a Map to store all the anagram numbers corresponding to the numbers whose digit are arranged in sorted order.
- Generate all the perfect squares of length
**K**. - For each perfect square generated, insert the number in the
**Map**corresponding to the number whose digit is arranged in ascending order. - Traverse the
**Map**and print the largest number from the set of maximum length.

Below is the implementation of the above approach:

## CPP

`// C++ program for the above approach ` ` ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find the largest set of ` `// perfect squares which are anagram ` `// to each other ` `void` `printResult( ` ` ` `map<string, set<` `long` `long` `int` `> > m) ` `{ ` ` ` `auto` `max_itr = m.begin(); ` ` ` ` ` `long` `long` `maxi = -1; ` ` ` ` ` `for` `(` `auto` `itr = m.begin(); ` ` ` `itr != m.end(); ++itr) { ` ` ` ` ` `long` `long` `int` `siz1 ` ` ` `= (itr->second).size(); ` ` ` ` ` `// Check if size of maximum set ` ` ` `// is less than the current set ` ` ` `if` `(maxi < siz1) { ` ` ` ` ` `// Update maximum set ` ` ` `maxi = siz1; ` ` ` `max_itr = itr; ` ` ` `} ` ` ` ` ` `// If lengths are equal ` ` ` `else` `if` `(maxi == siz1) { ` ` ` ` ` `// Update maximum set to store ` ` ` `// the set with maximum element ` ` ` `if` `((*(max_itr->second).rbegin()) ` ` ` `< *(itr->second.rbegin())) { ` ` ` `maxi = siz1; ` ` ` `max_itr = itr; ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` ` ` `// Stores the max element from the set ` ` ` `long` `long` `int` `result ` ` ` `= *(max_itr->second).rbegin(); ` ` ` ` ` `// Print final Result ` ` ` `cout << result << endl; ` `} ` ` ` `// Function to find the ` `// perfect squares wich are anagrams ` `void` `anagramicSquares(` `long` `long` `int` `k) ` `{ ` ` ` `// Stores the sequence ` ` ` `map<string, set<` `long` `long` `int` `> > m; ` ` ` ` ` `// Initialize start and end ` ` ` `// of perfect squares ` ` ` `long` `long` `int` `end; ` ` ` `if` `(k % 2 == 0) ` ` ` `end = k / 2; ` ` ` `else` ` ` `end = ((k + 1) / 2); ` ` ` ` ` `long` `long` `int` `start = ` `pow` `(10, end - 1); ` ` ` `end = ` `pow` `(10, end); ` ` ` ` ` `// Iterate form start to end ` ` ` `for` `(` `long` `long` `int` `i = start; ` ` ` `i <= end; i++) { ` ` ` ` ` `long` `long` `int` `x = i * i; ` ` ` ` ` `// Converting int to string ` ` ` `ostringstream str1; ` ` ` `str1 << x; ` ` ` ` ` `string str = str1.str(); ` ` ` `if` `(str.length() == k) { ` ` ` ` ` `// Sort string for storing ` ` ` `// number at exact map position ` ` ` `sort(str.begin(), str.end()); ` ` ` ` ` `// Insert number at map ` ` ` `m[str].insert(x); ` ` ` `} ` ` ` `} ` ` ` ` ` `// Print result ` ` ` `printResult(m); ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `// Given K ` ` ` `long` `long` `int` `K = 2; ` ` ` ` ` `// Function Call ` ` ` `anagramicSquares(K); ` ` ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

**Output:**

81

**Time Complexity:** O(N)

**Auxiliary Space:** O(N)

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