Check if it is possible to move from (a, 0) to (b, 0) with given jumps

Given two points, i.e. (a, 0) to (b, 0). The task is to check whether it is possible to move from (a,0) to (b,0) or not. One can move as (a, 0), (a+x, 0), (a+x+1, 0), (a, 2*x, 0), (a, 2*x+1, 0)……

Examples:

Input: a = 3, x = 10, b = 4
Output: No

Input: a = 3, x = 2, b = 5
Output: Yes

Approach: An answer will be possible if: 

1. a + n*x = b, where n is a non-negative integer.
2. a + n*x + 1 = b where n is a positive integer.

So, 
(b – a) / x is an integer or (b – a – 1) / x is an integer
(b – a) % x = 0 or (b – a – 1) % x = 0 

Below is the implementation of the above approach:  

C++

// CPP program to move form
// (a, 0) to (b, 0) with given jumps
#include <bits/stdc++.h>
using namespace std;

// Function to check if it is possible
bool Move(int a, int x, int b)
{
    if ((((b - a) % x == 0) || ((b - a - 1) % x == 0) && a + 1 != b) && b >= a)
        return true;

    return false;
}

// Driver code
int main()
{
    int a = 3, x = 2, b = 7;

    // function call
    if (Move(a, x, b))
        cout << "Yes";
    else
        cout << "No";
}

C

// C program to move form
// (a, 0) to (b, 0) with given jumps
#include <stdio.h>
#include <stdbool.h>

// Function to check if it is possible
bool Move(int a, int x, int b)
{
    if ((((b - a) % x == 0) || ((b - a - 1) % x == 0) && a + 1 != b) && b >= a)
        return true;

    return false;
}

// Driver code
int main()
{
    int a = 3, x = 2, b = 7;

    // function call
    if (Move(a, x, b))
        printf("Yes");
    else
        printf("No");
}

// This code is contributed by kothavvsaakash.

Java

// Java program to move form
// (a, 0) to (b, 0) with given jumps
import java.io.*;

class GFG {

// Function to check if it is possible
static boolean Move(int a, int x, int b)
{
    if ((((b - a) % x == 0) || ((b - a - 1) % x == 0) && a + 1 != b) && b >= a)
        return true;

    return false;
}

// Driver code
    public static void main (String[] args) {
            int a = 3, x = 2, b = 7;

    // function call
    if (Move(a, x, b))
        System.out.println( "Yes");
    else
        System.out.println( "No");
    }
}
//This code is contributed by shs..

Python 3

# Python 3 program to move form
# (a, 0) to (b, 0) with given jumps

# Function to check if it
# is possible
def Move(a, x, b):

    if ((((b - a) % x == 0) or
         ((b - a - 1) % x == 0) and
           a + 1 != b) and b >= a):
        return True

    return False

# Driver code
if __name__ == "__main__":
    a = 3
    x = 2
    b = 7

    # function call
    if (Move(a, x, b)):
        print("Yes")
    else:
        print("No")

# This code is contributed
# by ChitraNayal

C#

// C# program to move form
// (a, 0) to (b, 0) with given jumps
using System;

class GFG
{

// Function to check if it is possible
static bool Move(int a, int x, int b)
{
    if ((((b - a) % x == 0) ||
         ((b - a - 1) % x == 0) &&
           a + 1 != b) && b >= a)
        return true;

    return false;
}

// Driver code
public static void Main ()
{
    int a = 3, x = 2, b = 7;

    // function call
    if (Move(a, x, b))
        Console.WriteLine( "Yes");
    else
        Console.WriteLine( "No");
}
}

// This code is contributed
// by inder_verma

PHP

<?php
// PHP program to move form
// (a, 0) to (b, 0) with given jumps

// Function to check if it is possible
function Move($a, $x, $b)
{
    if (((($b - $a) % $x == 0) ||
         (($b - $a - 1) % $x == 0) &&
           $a + 1 != $b) && $b >= $a)
        return true;

    return false;
}

// Driver code
$a = 3; $x = 2; $b = 7;

// function call
if (Move($a, $x, $b))
    echo "Yes";
else
    echo"No";

// This code is contributed
// by anuj_67
?>

Javascript

<script>
// Javascript program to move form
// (a, 0) to (b, 0) with given jumps

    // Function to check if it is possible
    function Move(a,x,b)
    {
        if ((((b - a) % x == 0) || ((b - a - 1) % x == 0)
             && a + 1 != b) && b >= a)
            return true;

        return false;
    }

    // Driver code
    let a = 3, x = 2, b = 7;
    // function call
    if (Move(a, x, b))
        document.write( "Yes");
    else
        document.write( "No");


// This code is contributed by avanitrachhadiya2155
</script>

Output:

Yes

Time Complexity: O(1)
Auxiliary Space: O(1)