Check if it is possible to move from (0, 0) to (x, y) in N steps

Given a point (x, y). Find whether it is possible or not to move from (0, 0) to (x, y) in exactly n steps. 4 types of steps are valid, you can move from a point (a, b) to either of (a, b+1), (a, b-1), (a-1, b), (a+1, b)
Examples: 

Input: x = 0, y = 0, n = 2
Output: POSSIBLE

Input: x = 1, y = 1, n = 3 
Output: IMPOSSIBLE

Approach : 

In the shortest path, one can move from (0, 0) to (x, y) in |x| + |y|. So, it is not possible to move from (0, 0) to (x, y) in less than |x| + |y| steps. After reaching one can take two more steps as (x, y) -> (x, y+1) -> (x, y). 

So, it is possible if 

n >= |x| + |y| and ( n-( |x| + |y| ) ) % 2 = 0.

Below is the implementation of the above approach: 

C++

// CPP program to check whether it is possible
// or not to move from (0, 0) to (x, y)
// in exactly n steps
#include <bits/stdc++.h>
using namespace std;

// Function to check whether it is possible
// or not to move from (0, 0) to (x, y)
// in exactly n steps
bool Arrive(int a, int b, int n)
{
    if (n >= abs(a) + abs(b) and (n - (abs(a) + abs(b))) % 2 == 0)
        return true;

    return false;
}

// Driver code
int main()
{
    int a = 5, b = 5, n = 11;

    if (Arrive(a, b, n))
        cout << "Yes";
    else
        cout << "No";

    return 0;
}

C

// C program to check whether it is possible
// or not to move from (0, 0) to (x, y)
// in exactly n steps
#include <stdio.h>
#include <stdbool.h>

int abs(int a)
{
  int abs = a;
  if(abs < 0)
    abs = abs * (-1);
  return abs;
}

// Function to check whether it is possible
// or not to move from (0, 0) to (x, y)
// in exactly n steps
bool Arrive(int a, int b, int n)
{
    if (n >= abs(a) + abs(b) && (n - (abs(a) + abs(b))) % 2 == 0)
        return true;

    return false;
}

// Driver code
int main()
{
    int a = 5, b = 5, n = 11;

    if (Arrive(a, b, n))
        printf("Yes");
    else
        printf("No");

    return 0;
}

// This code is contributed by kothavvsaakash.

Java

// Java program to check whether it is possible
// or not to move from (0, 0) to (x, y)
// in exactly n steps
import java.io.*;

public class GFG {

// Function to check whether it is possible
// or not to move from (0, 0) to (x, y)
// in exactly n steps
static boolean Arrive(int a, int b, int n)
{
    if (n >= Math.abs(a) + Math.abs(b) && (n - (Math.abs(a) + Math.abs(b))) % 2 == 0)
        return true;

    return false;
}

// Driver code
int main()
{

    return 0;
}

    public static void main (String[] args) {

    int a = 5, b = 5, n = 11;

    if (Arrive(a, b, n))
        System.out.println( "Yes");
    else
        System.out.println( "No");
    }
}
//This code is contributed by shs..

Python3

# Python3 program to check whether
# it is possible or not to move from
# (0, 0) to (x, y) in exactly n steps

# Function to check whether it is
# possible or not to move from
# (0, 0) to (x, y) in exactly n steps
def Arrive(a, b, n):

    if (n >= abs(a) + abs(b) and
       (n - (abs(a) + abs(b))) % 2 == 0):
        return True

    return False

# Driver code
a = 5
b = 5
n = 11

if (Arrive(a, b, n)):
    print("Yes")
else:
    print("No")

# This code is contributed
# by Yatin Gupta

C#

// C# program to check whether
// it is possible or not to
// move from (0, 0) to (x, y)
// in exactly n steps
using System;

class GFG
{

// Function to check whether it
// is possible or not to move
// from (0, 0) to (x, y) in
// exactly n steps
static bool Arrive(int a, int b, int n)
{
    if (n >= Math.Abs(a) + Math.Abs(b) &&
       (n - (Math.Abs(a) + Math.Abs(b))) % 2 == 0)
        return true;

    return false;
}

// Driver code
public static void Main ()
{
    int a = 5, b = 5, n = 11;

    if (Arrive(a, b, n))
        Console.WriteLine( "Yes");
    else
        Console.WriteLine( "No");
    }
}

// This code is contributed by shashank

PHP

<?php
// PHP program to check whether
// it is possible or not to move
// from (0, 0) to (x, y) in exactly n steps

// Function to check whether it
// is possible or not to move
// from (0, 0) to (x, y) in exactly n steps
function Arrive($a, $b, $n)
{
    if ($n >= abs($a) + abs($b) and
       ($n - (abs($a) + abs($b))) % 2 == 0)
        return true;

    return false;
}

// Driver code
$a = 5; $b = 5; $n = 11;

if (Arrive($a, $b, $n))
    echo "Yes";
else
    echo "No";

// This code is contributed
// by Akanksha Rai(Abby_akku)

Javascript

<script>

// JavaScript program to check whether it is
// possible or not to move from (0, 0) to (x, y)
// in exactly n steps

// Function to check whether it is possible
// or not to move from (0, 0) to (x, y)
// in exactly n steps
function Arrive(a, b, n)
{
    if (n >= Math.abs(a) + Math.abs(b) &&
       (n - (Math.abs(a) + Math.abs(b))) % 2 == 0)
        return true;

    return false;
}

// Driver code
var a = 5, b = 5, n = 11;

if (Arrive(a, b, n))
    document.write("Yes");
else
    document.write("No");

// This code is contributed by Ankita saini

</script>

Output:

No

Time Complexity: O(1)
Auxiliary Space: O(1) because using constant space.