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Largest number that is not a perfect square
  • Difficulty Level : Basic
  • Last Updated : 30 Oct, 2020

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 number
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 = max(a[i], maxi);
    }
    return maxi;
}
  
// driver code to check the above functions
int 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 numbers
  
import 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 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;
}
  
    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 numbers
  
import math
def 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 number
def 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 code
a = [ 16, 20, 25, 2, 3, 10 ]
n= len(a)
  
# function call
print (largestNonPerfectSquareNumber(a, n))
  
# This code is contributed by Gitanjali.


C#




// C# program to find the largest non perfect 
// square number among n numbers
using 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 
// numbers
  
function 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 number
function 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.
?>



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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