Largest number that is not a perfect square
Given n integers, find the largest number is not a perfect square. Print -1 if there is no number that is perfect square.
Examples:
Input : arr[] = {16, 20, 25, 2, 3, 10|
Output : 20
Explanation: 20 is the largest number
that is not a perfect square
Input : arr[] = {36, 64, 10, 16, 29, 25|
Output : 29
A normal solution is to sort the elements and sort the n numbers and start checking from back for a non perfect square number using sqrt() function. The first number from the end which is not a perfect square number is our answer. The complexity of sorting is O(n log n) and of sqrt() function is log n, so at the worst case the complexity is O(n log n log n).
The efficient solution is to iterate for all the elements using traversal in O(n) and compare every time with the maximum element, and store the maximum of all non perfect squares. The number stored in maximum will be our answer.
Below is the illustration of the above approach:
CPP
// CPP program to find the largest non perfect// square number among n numbers#include <bits/stdc++.h>using namespace std;bool check(int n){ // takes the sqrt of the number int d = sqrt(n); // checks if it is a perfect square number if (d * d == n) return true; return false;}// function to find the largest non perfect square numberint largestNonPerfectSquareNumber(int a[], int n){ // stores the maximum of all non perfect square numbers int maxi = -1; // traverse for all elements in the array for (int i = 0; i < n; i++) { // store the maximum if not a perfect square if (!check(a[i])) maxi = max(a[i], maxi); } return maxi;}// driver code to check the above functionsint main(){ int a[] = { 16, 20, 25, 2, 3, 10 }; int n = sizeof(a) / sizeof(a[0]); // function call cout << largestNonPerfectSquareNumber(a, n); return 0;} |
Java
// Java program to find the// largest non perfect// square number among n numbersimport java.io.*; class GfG{ static Boolean check(int n){ // takes the sqrt of the number int d = (int)Math.sqrt(n); // checks if it is a perfect square number if (d * d == n) return true; return false;} // function to find the largest// non perfect square numberstatic int largestNonPerfectSquareNumber(int a[], int n){ // stores the maximum of all // non perfect square numbers int maxi = -1; // traverse for all elements in the array for (int i = 0; i < n; i++) { // store the maximum if // not a perfect square if (!check(a[i])) maxi = Math.max(a[i], maxi); } return maxi;} public static void main (String[] args) { int a[] = { 16, 20, 25, 2, 3, 10 }; int n = a.length; // function call System.out.println(largestNonPerfectSquareNumber(a, n)); }}// This code is contributed by Gitanjali. |
Python3
# python program to find# the largest non perfect# square number among n numbersimport mathdef check( n): # takes the sqrt of the number d = int(math.sqrt(n)) # checks if it is a # perfect square number if (d * d == n): return True return False # function to find the largest# non perfect square numberdef largestNonPerfectSquareNumber(a, n): # stores the maximum of all # non perfect square numbers maxi = -1 # traverse for all elements # in the array for i in range(0,n): # store the maximum if # not a perfect square if (check(a[i])==False): maxi = max(a[i], maxi) return maxi# driver codea = [ 16, 20, 25, 2, 3, 10 ]n= len(a)# function callprint (largestNonPerfectSquareNumber(a, n))# This code is contributed by Gitanjali. |
C#
// C# program to find the largest non perfect// square number among n numbersusing System;class GfG { static bool check(int n) { // takes the sqrt of the number int d = (int)Math.Sqrt(n); // checks if it is a perfect // square number if (d * d == n) return true; return false; } // function to find the largest // non perfect square number static int largestNonPerfectSquareNumber( int []a, int n) { // stores the maximum of all // non perfect square numbers int maxi = -1; // traverse for all elements in // the array for (int i = 0; i < n; i++) { // store the maximum if // not a perfect square if (!check(a[i])) maxi = Math.Max(a[i], maxi); } return maxi; } // driver code to check the above functions public static void Main () { int []a = { 16, 20, 25, 2, 3, 10 }; int n = a.Length; // function call Console.WriteLine( largestNonPerfectSquareNumber(a, n)); }}// This code is contributed by vt_m. |
PHP
<?php// PHP program to find// the largest non perfect// square number among n// numbersfunction check($n){ // takes the sqrt // of the number $d = sqrt($n); // checks if it is a // perfect square number if ($d * $d == $n) return true; return false;}// function to find the largest// non perfect square numberfunction largestNonPerfectSquareNumber($a, $n){ // stores the maximum of // all non perfect square // numbers $maxi = -1; // traverse for all // elements in the array for ($i = 0; $i < $n; $i++) { // store the maximum if // not a perfect square if (!check($a[$i])) $maxi = max($a[$i], $maxi); } return $maxi;} // Driver Code $a = array(16, 20, 25, 2, 3, 10); $n = count($a); // function call echo largestNonPerfectSquareNumber($a, $n);// This code is contributed by anuj_67.?> |
Javascript
<script>// JavaScript program to find the// largest non perfect// square number among n numbersfunction check(n){ // takes the sqrt of the number let d = Math.sqrt(n); // checks if it is a perfect square number if (d * d == n) return true; return false;} // function to find the largest// non perfect square numberfunction largestNonPerfectSquareNumber(a, n){ // stores the maximum of all // non perfect square numbers let maxi = -1; // traverse for all elements in the array for (let i = 0; i < n; i++) { // store the maximum if // not a perfect square if (!check(a[i])) maxi = Math.max(a[i], maxi); } return maxi;} // Driver Code let a = [ 16, 20, 25, 2, 3, 10 ]; let n = a.length; // function call document.write(largestNonPerfectSquareNumber(a, n)); </script> |
Output:
20
Time complexity can be considered as O(n) as sqrt() function can be implemented in O(1) time for fixed size (32 bit or 64 bit) integers [Refer Wiki for details]
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