# Check if a Lexicographical Pythagorean Triplets exists in range [0, K) of lexicographically largest string

Given a string str and a positive integer K. The task is to find if there exist a Pythagorean Triples in the first window of size K of a string which have the same characters as str but is largest in lexicographical order

Note: Every character is in lower case and consider the following values for each alphabet to check if there exist Pythagorean triples: a = 1, b = 2,  . . ., y = 25, z = 26.

A triplet(ch1, ch2, ch3) is called Pythagorean triples if (ch1)2 + (ch2)2 = (ch3)2.

Examples:

Input: str = “abxczde”, K = 4
Output: NO
Explanation: The lexicographically largest string having the same characters is zxedcba.
The first window of size 4 is “zxed”, which does not contain any such triplet.

Input: str = “abcdef”, K = 4
Output: YES
Explanation: The lexicographically largest string possible is “fedcba”.
The first window of size 4 has “fedc” which have a triplet (c, d, e) that is Pythagorean.

Input: str = “dce”, K = 2
Output: NO
Explanation: As window size is less than 3, choosing a triple is not possible.

Approach: This problem can be solved using Greedy algorithm. Follow the steps below for approach:

Below is the implementation of the approach:

## C++

 `// C++ code to implement the above approach`   `#include ` `using` `namespace` `std;`   `// Function to check for` `// Lexicographical Pythagorean triplet` `bool` `Pythagorean(string s, ``int` `k)` `{` `    ``// If k is less than 3 no triple possible` `    ``if` `(k < 3) {` `        ``return` `false``;` `    ``}`   `    ``// Sort the string in descending order` `    ``sort(s.begin(), s.end(), greater<``char``>());`   `    ``// Loop to check Pythagorean triples` `    ``for` `(``int` `i = 0; i < k - 2; ++i) {`   `        ``// Variables to define boundary of window` `        ``int` `r = k - 1;` `        ``int` `l = i + 1;`   `        ``// Loop for using two pointer approach` `        ``// to find the other two elements` `        ``while` `(r > l) {` `            ``int` `a = ``pow``(s[i] - ``'a'` `+ 1, 2);` `            ``int` `b = ``pow``(s[l] - ``'a'` `+ 1, 2);` `            ``int` `c = ``pow``(s[r] - ``'a'` `+ 1, 2);`   `            ``// If triple is found` `            ``if` `(a == b + c) {` `                ``return` `true``;` `            ``}`   `            ``// If 'a' is greater` `            ``else` `if` `(a > b + c) {` `                ``r--;` `            ``}`   `            ``// If 'a' is less` `            ``else` `                ``l++;` `        ``}` `    ``}`   `    ``// No such triple found` `    ``return` `false``;` `}`   `// Driver code` `int` `main()` `{` `    ``string str = ``"abcdef"``;` `    ``int` `K = 4;` `    ``bool` `ans = Pythagorean(str, K);` `    ``if` `(ans)` `        ``cout << ``"YES"``;` `    ``else` `        ``cout << ``"NO"``;` `    ``return` `0;` `}`

## Java

 `// Java code to implement the above approach` `import` `java.util.*;`   `public` `class` `GFG` `{` `// Utility function to reverse an array` `static` `void` `reverse(``char``[] a)` `{` `    ``int` `i, n = a.length;` `    ``char` `t;` `    ``for` `(i = ``0``; i < n / ``2``; i++)` `    ``{` `        ``t = a[i];` `        ``a[i] = a[n - i - ``1``];` `        ``a[n - i - ``1``] = t;` `    ``}` `}    `   `// Function to check for` `// Lexicographical Pythagorean triplet` `static` `boolean` `Pythagorean(String str, ``int` `k)` `{` `    ``// If k is less than 3 no triple possible` `    ``if` `(k < ``3``) {` `        ``return` `false``;` `    ``}`   `    ``// Sort the string in descending order` `    ``char``[] s = str.toCharArray();` `    ``Arrays.sort(s);` `    ``reverse(s);`   `    ``// Loop to check Pythagorean triples` `    ``for` `(``int` `i = ``0``; i < k - ``2``; ++i) {`   `        ``// Variables to define boundary of window` `        ``int` `r = k - ``1``;` `        ``int` `l = i + ``1``;`   `        ``// Loop for using two pointer approach` `        ``// to find the other two elements` `        ``while` `(r > l) {` `            ``int` `a = (``int``)Math.pow(s[i] - ``'a'` `+ ``1``, ``2``);` `            ``int` `b = (``int``)Math.pow(s[l] - ``'a'` `+ ``1``, ``2``);` `            ``int` `c = (``int``)Math.pow(s[r] - ``'a'` `+ ``1``, ``2``);`   `            ``// If triple is found` `            ``if` `(a == b + c) {` `                ``return` `true``;` `            ``}`   `            ``// If 'a' is greater` `            ``else` `if` `(a > b + c) {` `                ``r--;` `            ``}`   `            ``// If 'a' is less` `            ``else` `                ``l++;` `        ``}` `    ``}`   `    ``// No such triple found` `    ``return` `false``;` `}`   `// Driver code` `public` `static` `void` `main(String args[])` `{` `    ``String str = ``"abcdef"``;` `    ``int` `K = ``4``;` `    ``boolean` `ans = Pythagorean(str, K);` `    ``if` `(ans)` `        ``System.out.println(``"YES"``);` `    ``else` `        ``System.out.println(``"NO"``);` `}` `}` `// This code is contributed by Samim Hossain Mondal.`

## Python3

 `# Python Program to implement` `# the above approach`   `# Function to check for` `# Lexicographical Pythagorean triplet` `def` `Pythagorean(st, k):`   `    ``# If k is less than 3 no triple possible` `    ``if` `(k < ``3``):` `        ``return` `False`   `    ``# Sort the string in descending order` `    ``s ``=` `[]` `    ``for` `i ``in` `range``(``len``(st)):` `         ``s.append(st[i])` `    ``s.sort()` `    ``s.reverse()`   `    ``# Loop to check Pythagorean triples` `    ``for` `i ``in` `range``(k ``-` `2``):` `        ``# Variables to define boundary of window` `        ``r ``=` `k ``-` `1` `        ``l ``=` `i ``+` `1`   `        ``# Loop for using two pointer approach` `        ``# to find the other two elements` `        ``while` `(r > l):` `            ``a ``=` `pow``(``ord``(s[i]) ``-` `ord``(``'a'``) ``+` `1``, ``2``)` `            ``b ``=` `pow``(``ord``(s[l]) ``-` `ord``(``'a'``) ``+` `1``, ``2``)` `            ``c ``=` `pow``(``ord``(s[r]) ``-` `ord``(``'a'``) ``+` `1``, ``2``)` `            `  `            ``# If triple is found` `            ``if` `(a ``=``=` `b ``+` `c):` `                ``return` `True` `            `    `            ``# If 'a' is greater` `            ``elif` `(a > b ``+` `c) :` `                ``r ``-``=` `1`   `            ``# If 'a' is less` `            ``else``:` `                ``l ``+``=` `1` `        `  `    `  `    ``# No such triple found` `    ``return` `False`   `# Driver code` `str` `=` `"abcdef"` `K ``=` `4` `ans ``=` `Pythagorean(``str``, K)` `if` `(ans):` `    ``print``(``"YES"``)` `else``:` `    ``print``(``"NO"``)`   `# This code is contributed by gfgking`

## C#

 `// C# code to implement the above approach` `using` `System;`   `public` `class` `GFG` `{` `// Utility function to reverse an array` `static` `void` `reverse(``char``[] a)` `{` `    ``int` `i, n = a.Length;` `    ``char` `t;` `    ``for` `(i = 0; i < n / 2; i++)` `    ``{` `        ``t = a[i];` `        ``a[i] = a[n - i - 1];` `        ``a[n - i - 1] = t;` `    ``}` `}    `   `// Function to check for` `// Lexicographical Pythagorean triplet` `static` `bool` `Pythagorean(``string` `str, ``int` `k)` `{` `    ``// If k is less than 3 no triple possible` `    ``if` `(k < 3) {` `        ``return` `false``;` `    ``}`   `    ``// Sort the string in descending order` `    ``char``[] s = str.ToCharArray();` `    ``Array.Sort(s);` `    ``reverse(s);`   `    ``// Loop to check Pythagorean triples` `    ``for` `(``int` `i = 0; i < k - 2; ++i) {`   `        ``// Variables to define boundary of window` `        ``int` `r = k - 1;` `        ``int` `l = i + 1;`   `        ``// Loop for using two pointer approach` `        ``// to find the other two elements` `        ``while` `(r > l) {` `            ``int` `a = (``int``)Math.Pow(s[i] - ``'a'` `+ 1, 2);` `            ``int` `b = (``int``)Math.Pow(s[l] - ``'a'` `+ 1, 2);` `            ``int` `c = (``int``)Math.Pow(s[r] - ``'a'` `+ 1, 2);`   `            ``// If triple is found` `            ``if` `(a == b + c) {` `                ``return` `true``;` `            ``}`   `            ``// If 'a' is greater` `            ``else` `if` `(a > b + c) {` `                ``r--;` `            ``}`   `            ``// If 'a' is less` `            ``else` `                ``l++;` `        ``}` `    ``}`   `    ``// No such triple found` `    ``return` `false``;` `}`   `// Driver code` `public` `static` `void` `Main()` `{` `    ``string` `str = ``"abcdef"``;` `    ``int` `K = 4;` `    ``bool` `ans = Pythagorean(str, K);` `    ``if` `(ans)` `        ``Console.Write(``"YES"``);` `    ``else` `        ``Console.Write(``"NO"``);` `}` `}` `// This code is contributed by Samim Hossain Mondal.`

## Javascript

 ``

Output

`YES`

Time Complexity: O(K2)
Auxiliary Space: O(1)

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