Find if it’s possible to rotate the page by an angle or not.

You are given three points a, b, c on a page. Find if it’s possible to rotate the page around the point by an angle, such that the new position of ‘a’ is same as the old position of ‘b’, and the new position of ‘b’ is same as the old position of ‘c’. If such angle exists print “Yes”, else “No”.
Examples:

Input : a1 = 0, a2 = 1, b1 = 1, b2 =  1,
        c1 = 1, c2 = 0
Output : Yes
Explanation : Rotate the page by 90 degree.

Input : a1 = 1, a2 = 1, b1 = 0, b2 = 0,
        c1 = 1000, c2 = 1000
Output : No

Rotation of page by some angle is only possible if the distance between points ‘a’ and ‘b’ is equal to distance between points ‘b’ and ‘c’. But if the points are on same line, there is no rotation at point ‘b’. The problem has no solution when ‘a’, ‘b’, ‘c’ are in the same line or dis(a, b) != dis(b, c)

C++

// C++ program to find if its possible
// to rotate page or not
#include<bits/stdc++.h>
using namespace std;

// function to find if it's possible
// to rotate page or not
void possibleOrNot(long long a1, long long a2,
                   long long b1, long long b2,
                   long long c1, long long c2){

    // Calculating distance b/w points
    long long dis1 = pow(b1 - a1, 2) +
                      pow(b2 - a2, 2);
    long long dis2 = pow(c1 - b1, 2) +
                      pow(c2 - b2, 2);

    // If distance is not equal
    if(dis1 != dis2)
        cout << "No";

    // If the points are in same line
    else if (b1 == ((a1 + c1) / 2.0) && b2 ==
                          ((a2 + c2) / 2.0))
        cout << "No";
    else
        cout << "Yes";
}

// Driver Code
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    // Points a, b, and c
    long long a1 = 1, a2 = 0, b1 = 2,
             b2 = 0, c1 = 3, c2 = 0;
    possibleOrNot(a1, a2, b1, b2, c1, c2);
    return 0;
}

Java

// java program to find if its possible
// to rotate page or not
import java.util.Arrays;

class GFG {

    // function to find if it's possible
    // to rotate page or not
    static void possibleOrNot(long a1,long a2,
                              long b1,long b2,
                              long c1,long c2)
    {

        // Calculating distance b/w points
        long dis1 = (long)Math.pow(b1 - a1, 2) +
                    (long) Math.pow(b2 - a2, 2);

        long dis2 = (long)Math.pow(c1 - b1, 2) +
                     (long)Math.pow(c2 - b2, 2);

        // If distance is not equal
        if(dis1 != dis2)
            System.out.print("No");

        // If the points are in same line
        else if (b1 == ((a1 + c1) / 2.0) &&
                       b2 == ((a2 + c2) / 2.0))
            System.out.print("No");
        else
            System.out.print("Yes");
    }

    // Driver method
    public static void main(String[] args)
    {

        // Points a, b, and c
        long a1 = 1, a2 = 0, b1 = 2,
                b2 = 0, c1 = 3, c2 = 0;

        possibleOrNot(a1, a2, b1, b2, c1, c2);
    }
}

// This code is contributed by Anant Agarwal.

Python3

# Python3 program to fill an
# array with frequencies.

# Function to find if it's possible
# to rotate page or not
def possibleOrNot(a1, a2, b1, b2, c1, c2):

    # Calculating distance b/w points
    dis1 = (pow(b1 - a1, 2) +
            pow(b2 - a2, 2))
    dis2 = (pow(c1 - b1, 2) +
            pow(c2 - b2, 2))

    # If distance is not equal
    if(dis1 != dis2):
        print("No")

    # If the points are in same line
    else if (b1 == ((a1 + c1) // 2.0) and
          b2 == ((a2 + c2) // 2.0)):
        print("No")
    else:
        print("Yes")

# Driver Code

# Points a, b, and c
a1, b1, c1 = 1, 2, 3
a2 = b2 = c2 = 0
possibleOrNot(a1, a2, b1, b2, c1, c2)

# This code is contributed by Anant Agarwal.

C#

// C# program to fill an array with frequencies.
using System;

class GFG
{
    // function to find if it's possible
    // to rotate page or not
    static void possibleOrNot(long a1,long a2,
                              long b1,long b2,
                              long c1,long c2)
    {

        // Calculating distance b/w points
        long dis1 = (long)Math.Pow(b1 - a1, 2) +
                    (long) Math.Pow(b2 - a2, 2);
        long dis2 = (long)Math.Pow(c1 - b1, 2) +
                    (long)Math.Pow(c2 - b2, 2);

        // If distance is not equal
        if(dis1 != dis2)
            Console.Write("No");

        // If the points are in same line
        else if (b1 == ((a1 + c1) / 2.0) && b2 ==
                       ((a2 + c2) / 2.0))
            Console.Write("No");
        else
            Console.Write("Yes");
    }

    // Driver method
    public static void Main()
    {
        // Points a, b, and c
        long  a1 = 1, a2 = 0, b1 = 2,
                 b2 = 0, c1 = 3, c2 = 0;
        possibleOrNot(a1, a2, b1, b2, c1, c2);
    }
}
// This code is contributed by Anant Agarwal.

PHP

<?php
// PHP program to fill
// an array with frequencies.

// function to find if
// it's possible to
// rotate page or not
function possibleOrNot($a1, $a2, $b1,
                       $b2, $c1, $c2)
{

    // Calculating distance
    // b/w points
    $dis1 = pow($b1 - $a1, 2) +
            pow($b2 - $a2, 2);
    $dis2 = pow($c1 - $b1, 2) +
            pow($c2 - $b2, 2);

    // If distance
    // is not equal
    if($dis1 != $dis2)
        echo "No";

    // If the points
    // are in same line
    else if ($b1 == (($a1 + $c1) / 2.0) &&
             $b2 == (($a2 + $c2) / 2.0))
        echo "No";
    else
        echo "Yes";
}

// Driver Code

// Points a, b, and c
$a1 = 1;
$a2 = 0;
$b1 = 2;
$b2 = 0;
$c1 = 3;
$c2 = 0;
possibleOrNot($a1, $a2, $b1,
              $b2, $c1, $c2);

// This code is contributed by ajit
?>

Javascript

<script>

// javascript program to fill an array with frequencies.


    // function to find if it's possible
    // to rotate page or not

    function possibleOrNot( a1, a2, b1, b2, c1, c2)
    {

        // Calculating distance b/w points
        var dis1 = Math.pow(b1 - a1, 2) +  Math.pow(b2 - a2, 2);

        var dis2 = Math.pow(c1 - b1, 2) +  Math.pow(c2 - b2, 2);

        // If distance is not equal
        if(dis1 != dis2)
            document.write("No");

        // If the points are in same line
        else if (b1 == ((a1 + c1) / 2.0) && b2 == ((a2 + c2) / 2.0))
            document.write("No");
        else
            document.write("Yes");
    }

    // Driver method

        // Points a, b, and c

        var  a1 = 1, a2 = 0, b1 = 2, b2 = 0, c1 = 3, c2 = 0;

        possibleOrNot(a1, a2, b1, b2, c1, c2);


</script>

Output:

No

Time Complexity: O(logn)

Auxiliary Space: O(1)