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Find if there exists multiple ways to draw line through (x, y) to cut rectangle in equal halfs

  • Last Updated : 23 Apr, 2021

Given four integers W, H, x, and y. The task is to find if there exist multiple ways to draw a line through (x, y) to cut the rectangle into two equal parts. If there are multiple ways print Yes otherwise print No. The co-ordinates of rectangle are (0, 0), (W, 0), (W, H) and (0, H)
Note: The point (x, y) always lies inside or above the rectangle.
Examples: 
 

Input: W = 2, H = 2, x = 1, y = 1 
Output: Yes 
Line segment joining the points (0, 0) and (2, 2) 
or (0, 2) and (2, 0) etc. are all valid ways.
Input: W = 1, H = 3, x = 1, y = 2 
Output: No 
 

 

Approach: The rectangle can be divided into two equal parts when the line is drawn vertically, horizontally, or diagonally through the center of the rectangle. So, the answer will be Yes only if the point (x, y) is the center of the rectangle i.e. (W / 2, H / 2) otherwise the answer will be No.
Below is the implementation of the above approach: 
 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function that returns true if multiple
// lines are possible passing through
// (x, y) that divide the given
// rectangle into two equal parts
int isPossible(int w, int h, int x, int y)
{
 
    // If the point (x, y) is the
    // centre of the rectangle
    if (x * 2 == w && y * 2 == h)
        return true;
 
    return false;
}
 
// Driver code
int main()
{
    int w = 1, h = 2, x = 1, y = 2;
 
    if (isPossible(w, h, x, y))
        cout << "Yes";
    else
        cout << "No";
 
    return 0;
}

Java




// Java implementation of the approach
class GFG
{
 
// Function that returns true if multiple
// lines are possible passing through
// (x, y) that divide the given
// rectangle into two equal parts
static boolean isPossible(int w, int h, int x, int y)
{
 
    // If the point (x, y) is the
    // centre of the rectangle
    if (x * 2 == w && y * 2 == h)
        return true;
 
    return false;
}
 
// Driver code
public static void main(String[] args)
{
    int w = 1, h = 2, x = 1, y = 2;
 
    if (isPossible(w, h, x, y))
        System.out.print("Yes");
    else
        System.out.print("No");
}
}
 
// This code contributed by PrinciRaj1992

Python 3




# Python 3 implementation of the approach
 
# Function that returns true if multiple
# lines are possible passing through
# (x, y) that divide the given
# rectangle into two equal parts
def isPossible(w, h, x, y):
     
    # If the point (x, y) is the
    # centre of the rectangle
    if (x * 2 == w and y * 2 == h):
        return True
 
    return False
 
# Driver code
if __name__ == '__main__':
    w = 1
    h = 2
    x = 1
    y = 2
 
    if (isPossible(w, h, x, y)):
        print("Yes")
    else:
        print("No")
 
# This code is contributed by Surendra_Gangwar

C#




// C# implementation of the approach
using System;
 
class GFG
{
     
// Function that returns true if multiple
// lines are possible passing through
// (x, y) that divide the given
// rectangle into two equal parts
static bool isPossible(int w, int h,
                       int x, int y)
{
 
    // If the point (x, y) is the
    // centre of the rectangle
    if (x * 2 == w && y * 2 == h)
        return true;
 
    return false;
}
 
// Driver code
static public void Main ()
{
    int w = 1, h = 2, x = 1, y = 2;
 
    if (isPossible(w, h, x, y))
        Console.Write("Yes");
    else
        Console.Write("No");
}
}
 
// This code is contributed by ajit.

Javascript




<script>
 
// Javascript implementation of the approach
 
// Function that returns true if multiple
// lines are possible passing through
// (x, y) that divide the given
// rectangle into two equal parts
function isPossible(w, h, x, y)
{
 
    // If the point (x, y) is the
    // centre of the rectangle
    if (x * 2 == w && y * 2 == h)
        return true;
 
    return false;
}
 
// Driver code
    let w = 1, h = 2, x = 1, y = 2;
 
    if (isPossible(w, h, x, y))
        document.write("Yes");
    else
        document.write("No");
 
</script>
Output: 
No

 

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