Closest perfect square and its distance

Difficulty Level : Easy
Last Updated : 10 May, 2021

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++

// 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

Java

// 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);
    }
}

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#

// 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..

PHP

<?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.
?>

Javascript

<script>
 
    // Javascript 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 ((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
    function getClosestPerfectSquare(N)
    {
        if (isPerfect(N)) {
            document.write(N + " " + "0" + "</br>");
            return;
        }
   
        // Variables to store first perfect
        // square number
        // above and below N
        let aboveN = -1, belowN = -1;
        let 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
        let diff1 = aboveN - N;
        let diff2 = N - belowN;
   
        if (diff1 > diff2)
            document.write(belowN + " " + diff2);
        else
            document.write(aboveN + " " + diff1);
    }
     
    let N = 1500;
   
      getClosestPerfectSquare(N);
     
</script>

Output:

1521 21

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.

My Personal Notes

Related Articles

C++

Java

Python3

C#

PHP

Javascript