Closest perfect square and its distance

Given a positive integer N. The task is to find the perfect square number closest to N and steps required to reach this number from N.

Note: The closest perfect square to N can be either less than, equal to or greater than N and steps is referred to the difference between N and the closest perfect square.

Examples:

Input: N = 1500
Output: Perfect square = 1521, Steps = 21
For N = 1500
Closest perfect square greater than N is 1521.
So steps required is 21.
Closest perfect square less than N is 1444.
So steps required is 56.
The minimum of these two is 1521 with steps 21.

Input: N = 2
Output: Perfect Square = 1, Steps = 1
For N = 2
Closest perfect square greater than N is 4.
So steps required is 2.
Closest perfect square less than N is 1.
So steps required is 1.
The minimum of these two is 1.



Approach:

  • If N is a perefct square then print N and steps as 0.
  • Else, find the first perfect square number > N and note its difference with N.
  • Then, find the first perfect square number < N and note its difference with N.
  • And print the perfect square resulting in the minimum of these two differences obtained and also the difference as the minimum steps.

Below is the implementation of the above approach:

C++

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// CPP program to find the closest perfect square
// taking minimum steps to reach from a number
  
#include<bits/stdc++.h>
using namespace std;
  
  
    // Function to check if a number is
    // perfect square or not
    bool isPerfect(int N)
    {
        if ((sqrt(N) - floor(sqrt(N))) != 0)
            return false;
        return true;
    }
  
    // Function to find the closest perfect square
    // taking minimum steps to reach from a number
    void getClosestPerfectSquare(int N)
    {
        if (isPerfect(N))
        {
            cout<<N<<" "<<"0"<<endl;
            return;
        }
  
        // Variables to store first perfect
        // square number
        // above and below N
        int aboveN = -1, belowN = -1;
        int n1;
  
        // Finding first perfect square
        // number greater than N
        n1 = N + 1;
        while (true) {
            if (isPerfect(n1)) {
                aboveN = n1;
                break;
            }
            else
                n1++;
        }
  
        // Finding first perfect square
        // number less than N
        n1 = N - 1;
        while (true) {
            if (isPerfect(n1)) {
                belowN = n1;
                break;
            }
            else
                n1--;
        }
  
        // Variables to store the differences
        int diff1 = aboveN - N;
        int diff2 = N - belowN;
  
        if (diff1 > diff2)
            cout<<belowN<<" "<<diff2;
        else
            cout<<aboveN<<" "<<diff1;
    }
  
    // Driver code
    int main()
    {
        int N = 1500;
  
        getClosestPerfectSquare(N);
    }
//This code is contributed by
// Surendra_Gangwar

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Java














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// Java program to find the closest perfect square 


// taking minimum steps to reach from a number 


  


class GFG { 


  


    // Function to check if a number is 


    // perfect square or not 


    static boolean isPerfect(int N) 


    { 


        if ((Math.sqrt(N) - Math.floor(Math.sqrt(N))) != 0) 


            return false; 


        return true; 


    } 


  


    // Function to find the closest perfect square 


    // taking minimum steps to reach from a number 


    static void getClosestPerfectSquare(int N) 


    { 


        if (isPerfect(N)) { 


            System.out.println(N + " "


                               + "0"); 


            return; 


        } 


  


        // Variables to store first perfect 


        // square number 


        // above and below N 


        int aboveN = -1, belowN = -1; 


        int n1; 


  


        // Finding first perfect square 


        // number greater than N 


        n1 = N + 1; 


        while (true) { 


            if (isPerfect(n1)) { 


                aboveN = n1; 


                break; 


            } 


            else


                n1++; 


        } 


  


        // Finding first perfect square 


        // number less than N 


        n1 = N - 1; 


        while (true) { 


            if (isPerfect(n1)) { 


                belowN = n1; 


                break; 


            } 


            else


                n1--; 


        } 


  


        // Variables to store the differences 


        int diff1 = aboveN - N; 


        int diff2 = N - belowN; 


  


        if (diff1 > diff2) 


            System.out.println(belowN + " " + diff2); 


        else


            System.out.println(aboveN + " " + diff1); 


    } 


  


    // Driver code 


    public static void main(String args[]) 


    { 


        int N = 1500; 


  


        getClosestPerfectSquare(N); 


    } 


} 



















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Python3





# Python3 program to find the closest

# perfect square taking minimum steps

# to reach from a number 


# Function to check if a number is

# perfect square or not

from math import sqrt, floor

def isPerfect(N):

	if (sqrt(N) – floor(sqrt(N)) != 0):

		return False

	return True


# Function to find the closest perfect square

# taking minimum steps to reach from a number

def getClosestPerfectSquare(N):

	if (isPerfect(N)):

		print(N, “0”)

		return


	# Variables to store first perfect

	# square number above and below N

	aboveN = -1

	belowN = -1

	n1 = 0


	# Finding first perfect square

	# number greater than N

	n1 = N + 1

	while (True):

		if (isPerfect(n1)):

			aboveN = n1

			break

		else:

			n1 += 1


	# Finding first perfect square

	# number less than N

	n1 = N – 1

	while (True):

		if (isPerfect(n1)):

			belowN = n1

			break

		else:

			n1 -= 1


	# Variables to store the differences

	diff1 = aboveN – N

	diff2 = N – belowN 


	if (diff1 > diff2):

		print(belowN, diff2)

	else:

		print(aboveN, diff1)


# Driver code

N = 1500

getClosestPerfectSquare(N)


# This code is contributed

# by sahishelangia



C#














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// C# program to find the closest perfect square 


// taking minimum steps to reach from a number 


using System; 


  


class GFG { 


  


    // Function to check if a number is 


    // perfect square or not 


    static bool isPerfect(int N) 


    { 


        if ((Math.Sqrt(N) - Math.Floor(Math.Sqrt(N))) != 0) 


            return false; 


        return true; 


    } 


  


    // Function to find the closest perfect square 


    // taking minimum steps to reach from a number 


    static void getClosestPerfectSquare(int N) 


    { 


        if (isPerfect(N)) { 


            Console.WriteLine(N + " "


                            + "0"); 


            return; 


        } 


  


        // Variables to store first perfect 


        // square number 


        // above and below N 


        int aboveN = -1, belowN = -1; 


        int n1; 


  


        // Finding first perfect square 


        // number greater than N 


        n1 = N + 1; 


        while (true) { 


            if (isPerfect(n1)) { 


                aboveN = n1; 


                break; 


            } 


            else


                n1++; 


        } 


  


        // Finding first perfect square 


        // number less than N 


        n1 = N - 1; 


        while (true) { 


            if (isPerfect(n1)) { 


                belowN = n1; 


                break; 


            } 


            else


                n1--; 


        } 


  


        // Variables to store the differences 


        int diff1 = aboveN - N; 


        int diff2 = N - belowN; 


  


        if (diff1 > diff2) 


            Console.WriteLine(belowN + " " + diff2); 


        else


            Console.WriteLine(aboveN + " " + diff1); 


    } 


  


    // Driver code 


    public static void Main() 


    { 


        int N = 1500; 


  


        getClosestPerfectSquare(N); 


    } 


} 


// This code is contributed by anuj_67.. 



















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PHP














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<?php 


// PHP program to find the closest perfect  


// square taking minimum steps to reach  


// from a number 


  


// Function to check if a number is 


// perfect square or not 


function isPerfect($N) 


{ 


    if ((sqrt($N) - floor(sqrt($N))) != 0) 


        return false; 


    return true; 


} 


  


// Function to find the closest perfect square 


// taking minimum steps to reach from a number 


function getClosestPerfectSquare($N) 


{ 


    if (isPerfect($N)) 


    { 


        echo $N, " ", "0", "\n"; 


        return; 


    } 


  


    // Variables to store first perfect 


    // square number 


    // above and below N 


    $aboveN = -1; 


    $belowN = -1; 


    $n1; 


  


    // Finding first perfect square 


    // number greater than N 


    $n1 = $N + 1; 


    while (true) 


    { 


        if (isPerfect($n1)) 


        { 


            $aboveN = $n1; 


            break; 


        } 


        else


            $n1++; 


    } 


  


    // Finding first perfect square 


    // number less than N 


    $n1 = $N - 1; 


    while (true) 


    { 


        if (isPerfect($n1)) 


        { 


            $belowN = $n1; 


            break; 


        } 


        else


            $n1--; 


    } 


  


    // Variables to store the differences 


    $diff1 = $aboveN - $N; 


    $diff2 = $N - $belowN; 


  


    if ($diff1 > $diff2) 


        echo $belowN, " " , $diff2; 


    else


        echo $aboveN, " ", $diff1; 


} 


  


// Driver code 


$N = 1500; 


getClosestPerfectSquare($N); 


  


// This code is contributed by ajit. 


?> 



















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Output:


1521 21






          
          
          
          

            

    

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