Check whether a given point lies on or inside the rectangle | Set 3

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Given two numbers a and b where b < a form a rectangle with points (0, b), (b, 0), (a-b, b), (b, a-b). Given a point (x, y), the task is to check whether this point lies inside or on the rectangle or not.
Examples:

Input: a = 7, b = 2, x = 5, y = 2;
Output: Given point does not lie on the rectangle

Input: a = 7, b = 2, x = 4, y = 5;
Output: Given point lies inside the rectangle

Approach: An efficient way is to form 4 line’s equation of a rectangle. Then, if a given point lies in or on the rectangle if and only if, substituting the given point on:

The right sideline ( x-y-b = 0 ) must give the value less than or equals to zero.
The left sideline ( x-y+a = 0 ) must give the value greater than or equals to one.
The upper sideline ( x+y-2*a+b = 0 ) must give the value less than or equals to zero.
The lower sideline ( x+y-b = 0 ) must give the value greater than or equals to one.

C++

// C++ program to Check whether a given point
// lies inside or on the rectangle or not
#include <bits/stdc++.h>
using namespace std;
 
// function to Check whether a given point
// lies inside or on the rectangle or not
bool LiesInsieRectangle(int a, int b, int x, int y)
{
    if (x - y - b <= 0 && x - y + b >= 0
        && x + y - 2 * a + b <= 0 && x + y - b >= 0)
        return true;
 
    return false;
}
 
// Driver code
int main()
{
    int a = 7, b = 2, x = 4, y = 5;
 
    if (LiesInsieRectangle(a, b, x, y))
        cout << "Given point lies inside the rectangle";
    else
        cout << "Given point does not lie on the rectangle";
 
return 0;
}

C

// C program to Check whether a given point
// lies inside or on the rectangle or not
#include <stdio.h>
#include <stdbool.h>
 
// function to Check whether a given point
// lies inside or on the rectangle or not
bool LiesInsieRectangle(int a, int b, int x, int y)
{
    if (x - y - b <= 0 && x - y + b >= 0
        && x + y - 2 * a + b <= 0 && x + y - b >= 0)
        return true;
 
    return false;
}
 
// Driver code
int main()
{
    int a = 7, b = 2, x = 4, y = 5;
 
    if (LiesInsieRectangle(a, b, x, y))
        printf("Given point lies inside the rectangle");
    else
        printf("Given point does not lie on the rectangle");
 
return 0;
}
 
// This code is contributed by kothavvsaakash.

Java

// Java program to Check whether 
// a given point lies inside or
// on the rectangle or not
class GFG 
{
 
// function to Check whether 
// a given point lies inside 
// or on the rectangle or not
static boolean LiesInsieRectangle(int a, int b, 
                                  int x, int y)
{
if (x - y - b <= 0 && x - y + b >= 0 && 
    x + y - 2 * a + b <= 0 && x + y - b >= 0)
    return true;
 
return false;
}
 
// Driver code
public static void main(String[] args) 
{
    int a = 7, b = 2, x = 4, y = 5;
 
    if (LiesInsieRectangle(a, b, x, y))
        System.out.println("Given point lies " + 
                        "inside the rectangle");
    else
        System.out.println("Given point does not " + 
                            "lie on the rectangle");
}
}
 
// This code is contributed
// by ChitraNayal

Python3

# Python 3 program to Check whether 
# a given point lies inside or on
# the rectangle or not
 
# function to Check whether a given 
# point lies inside or on the
# rectangle or not 
def LiesInsieRectangle(a, b, x, y) :
 
    if(x - y - b <= 0 and
       x - y + b >= 0 and
       x + y - 2 * a + b <= 0 and
       x + y - b >= 0) :
        return True
     
    return False
 
# Driver code
if __name__ == "__main__" :
 
    # multiple assignments
    a, b, x, y = 7, 2, 4, 5
 
    if LiesInsieRectangle(a, b, x, y) :
        print("Given point lies inside"
                      " the rectangle")
    else :
        print("Given point does not lie"
                    " on the rectangle")
 
# This code is contributed by ANKITRAI1

C#

// C# program to Check whether 
// a given point lies inside 
// or on the rectangle or not
using System;
class GFG 
{
 
// function to Check whether 
// a given point lies inside 
// or on the rectangle or not
static bool LiesInsieRectangle(int a, int b, 
                               int x, int y)
{
if (x - y - b <= 0 &&
    x - y + b >= 0 && 
    x + y - 2 * a + b <= 0 && 
    x + y - b >= 0)
    return true;
 
return false;
}
 
// Driver code
public static void Main() 
{
    int a = 7, b = 2, x = 4, y = 5;
 
    if (LiesInsieRectangle(a, b, x, y))
        Console.Write("Given point lies " + 
                   "inside the rectangle");
    else
        Console.Write("Given point does not " + 
                       "lie on the rectangle");
}
}
 
// This code is contributed 
// by ChitraNayal

PHP

<?php
// PHP program to Check whether 
// a given point lies inside 
// or on the rectangle or not
 
// function to Check whether
// a given point lies inside 
// or on the rectangle or not
function LiesInsieRectangle($a, $b, 
                            $x, $y)
{
    if ($x - $y - $b <= 0 && 
        $x - $y + $b >= 0 &&
        $x + $y - 2 * $a + $b <= 0 && 
        $x + $y - $b >= 0)
        return true;
 
    return false;
}
 
// Driver code
$a = 7;
$b = 2;
$x = 4;
$y = 5;
 
if (LiesInsieRectangle($a, $b,
                       $x, $y))
    echo "Given point lies ". 
         "inside the rectangle";
else
    echo "Given point does not". 
        " lie on the rectangle";
 
// This code is contributed by mits
?>

Javascript

<script>
 
// Javascript program to Check whether a given point 
// lies inside or on the rectangle or not 
 
 
// function to Check whether a given point 
// lies inside or on the rectangle or not 
function LiesInsieRectangle(a, b, x, y) 
{ 
    if (x - y - b <= 0 && x - y + b >= 0 
        && x + y - 2 * a + b <= 0 && x + y - b >= 0) 
        return true; 
 
    return false; 
} 
 
// Driver code 
  
    let a = 7, b = 2, x = 4, y = 5; 
 
    if (LiesInsieRectangle(a, b, x, y)) 
        document.write("Given point lies inside the rectangle"); 
    else
        document.write("Given point does not lie on the rectangle"); 
 
// This code is contributed by Mayank Tyagi
 
</script>

Output:

Given point lies inside the rectangle

Time Complexity: O(1), since there is no loop or recursion.
Auxiliary Space: O(1), since no extra space has been taken.

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