Given an integer S, the task is to find the coordinates of a triangle whose area is (S / 2).
Examples:
Input: S = 4
Output:
(0, 0)
(1000000000, 1)
(999999996, 1)Input: S = 15
Output:
(0, 0)
(1000000000, 1)
(999999985, 1)
Approach:
- It is known than the area of the triangle whose coordinates are (X1, Y1), (X2, Y2) and (X3, Y3) is given by A = ((X1 * Y2) + (X2 * Y3) + (X3 * Y1) – (X1 * Y3) – (X2 * Y1) – (X3 * Y2)) / 2.
- Now fixing (X1, Y1) to (0, 0) gives A = ((X2 * Y3) – (X3 * Y2)) / 2.
- It is given that A = S / 2 which implies S = (X2 * Y3) – (X3 * Y2).
- Now fix (X2, Y2) to (109, 1) and the equation becomes S = 109 * Y3 – X3 which can be solved by taking an integer value of a variable that given the integer value for the other variable.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std;
const long MAX = 1000000000;
// Function to find the triangle // with area = (S / 2) void findTriangle( long S)
{ // Fix the two pairs of coordinates
long X1 = 0, Y1 = 0;
long X2 = MAX, Y2 = 1;
// Find (X3, Y3) with integer coordinates
long X3 = (MAX - S % MAX) % MAX;
long Y3 = (S + X3) / MAX;
cout << "(" << X1 << ", " << Y1 << ")\n" ;
cout << "(" << X2 << ", " << Y2 << ")\n" ;
cout << "(" << X3 << ", " << Y3 << ")" ;
} // Driver code int main()
{ long S = 4;
findTriangle(S);
return 0;
} |
Java
// Java implementation of the approach class GFG
{ static final long MAX = 1000000000 ;
// Function to find the triangle
// with area = (S / 2)
static void findTriangle( long S)
{
// Fix the two pairs of coordinates
long X1 = 0 , Y1 = 0 ;
long X2 = MAX, Y2 = 1 ;
// Find (X3, Y3) with integer coordinates
long X3 = (MAX - S % MAX) % MAX;
long Y3 = (S + X3) / MAX;
System.out.println( "(" + X1 +
", " + Y1 + ")" );
System.out.println( "(" + X2 +
", " + Y2 + ")" );
System.out.println( "(" + X3 +
", " + Y3 + ")" );
}
// Driver code
public static void main (String[] args)
{
long S = 4 ;
findTriangle(S);
}
} // This code is contributed by AnkitRai01 |
Python3
# Python3 implementation of the approach MAX = 1000000000 ;
# Function to find the triangle # with area = (S / 2) def findTriangle(S) :
# Fix the two pairs of coordinates
X1 = 0 ; Y1 = 0 ;
X2 = MAX ; Y2 = 1 ;
# Find (X3, Y3) with integer coordinates
X3 = ( MAX - S % MAX ) % MAX ;
Y3 = (S + X3) / MAX ;
print ( "(" , X1, "," , Y1, ")" );
print ( "(" , X2, "," , Y2, ")" );
print ( "(" , X3, "," , Y3, ")" );
# Driver code if __name__ = = "__main__" :
S = 4 ;
findTriangle(S);
# This code is contributed by kanugargng |
C#
// C# implementation of the above approach using System;
class GFG
{ static readonly long MAX = 1000000000;
// Function to find the triangle
// with area = (S / 2)
static void findTriangle( long S)
{
// Fix the two pairs of coordinates
long X1 = 0, Y1 = 0;
long X2 = MAX, Y2 = 1;
// Find (X3, Y3) with integer coordinates
long X3 = (MAX - S % MAX) % MAX;
long Y3 = (S + X3) / MAX;
Console.WriteLine( "(" + X1 +
", " + Y1 + ")" );
Console.WriteLine( "(" + X2 +
", " + Y2 + ")" );
Console.WriteLine( "(" + X3 +
", " + Y3 + ")" );
}
// Driver code
public static void Main (String[] args)
{
long S = 4;
findTriangle(S);
}
} // This code is contributed by PrinciRaj1992 |
Javascript
<script> // Javascript implementation of the approach let MAX = 1000000000; // Function to find the triangle // with area = (S / 2) function findTriangle( S)
{ // Fix the two pairs of coordinates
let X1 = 0, Y1 = 0;
let X2 = MAX, Y2 = 1;
// Find (X3, Y3) with integer coordinates
let X3 = (MAX - S % MAX) % MAX;
let Y3 = (S + X3) / MAX;
document.write( "(" + X1 + ", " + Y1 + ")<br/>" );
document.write( "(" + X2 + ", " + Y2 + ")<br/>" );
document.write( "(" + X3 + ", " + Y3 + ")<br/>" )
}
// Driver code let S = 4;
findTriangle(S);
// This code contributed by aashish1995 </script> |
Output:
(0, 0) (1000000000, 1) (999999996, 1)
Time Complexity: O(1)
Auxiliary Space: O(1)