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)
If you like neveropen and would like to contribute, you can also write an article using contribute.neveropen.co.uk or mail your article to review-team@neveropen.co.uk. See your article appearing on the neveropen main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!