Find if a number is part of AP whose first element and difference are given

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Given three non-negative integers a, d and x. Here, a is the first element, d is the difference of an AP (Arithmetic Progression). We need to find if x is part of the given AP or not.

Examples :

Input : a = 1, d = 3, x = 7
Output : Yes
7 is part of given AP, 1 + 3 + 3 = 7

Input : a = 10, d = 0, x = 10
Output : Yes

Firstly, in case d = 0, we should output Yes if a = x else answer is No. For non-zero d, if x belongs to sequence x = a + n * d where n is non-negative integer, only if (n – a) / d is non-negative integer.

C++

// C++ program to check if x exist 
// or not in the given AP. 
#include <bits/stdc++.h> 
using namespace std; 
  
// returns yes if exist else no. 
bool isMember(int a, int d, int x) 
{ 
  
    // If difference is 0, then x must 
    // be same as a. 
    if (d == 0) 
        return (x == a); 
  
    // Else difference between x and a 
    // must be divisible by d. 
    return ((x - a) % d == 0 && (x - a) / d >= 0); 
} 
  
// Driver code. 
int main() 
{ 
    int a = 1, x = 7, d = 3; 
    if (isMember(a, d, x)) 
        cout << "Yes"; 
    else
        cout << "No"; 
    return 0; 
} 

Java

// Java program to check if x exist 
// or not in the given AP. 
class GFG { 
  
    // returns yes if exist else no. 
    static boolean isMember(int a, int d, int x) 
    { 
  
        // If difference is 0, then x must 
        // be same as a. 
        if (d == 0) 
            return (x == a); 
  
        // Else difference between x and a 
        // must be divisible by d. 
        return ((x - a) % d == 0 && (x - a) / d >= 0); 
    } 
  
    // Driver code. 
    public static void main(String args[]) 
    { 
        int a = 1, x = 7, d = 3; 
        if (isMember(a, d, x)) 
            System.out.println("Yes"); 
        else
            System.out.println("No"); 
    } 
} 
  
// This code is contributed by Nikita Tiwari 

Python3

# Python3 code to check if x exist  
# or not in the given AP. 
  
def isMember(a, d, x): 
      
    # If difference is 0, then x 
    # must be same as a. 
    if d == 0: 
        return x == a 
      
    # Else difference between x  
    # and a must be divisible by d. 
    return ((x - a) % d == 0 and 
        int((x - a) / d) >= 0) 
  
# Driver code 
a = 1
x = 7
d = 3
  
if isMember(a, d, x): 
    print( "Yes") 
else: 
    print("No") 
  
# This code is contributed by "Abhishek Sharma 44"

C#

// C# program to check if x exist 
// or not in the given AP. 
using System; 
class GFG { 
  
    // returns yes if exist else no. 
    static bool isMember(int a, int d, int x) 
    { 
        // If difference is 0, then x must 
        // be same as a. 
        if (d == 0) 
            return (x == a); 
  
        // Else difference between x and a 
        // must be divisible by d. 
        return ((x - a) % d == 0 && (x - a) / d >= 0); 
    } 
  
    // Driver code. 
    public static void Main() 
    { 
        int a = 1, x = 7, d = 3; 
        if (isMember(a, d, x)) 
            Console.WriteLine("Yes"); 
        else
            Console.WriteLine("No"); 
    } 
} 
  
// This code is contributed by vt_m. 

PHP

<?php 
// PHP program to check   
// if x exist or not in  
// the given AP. 
  
// returns yes if exist  
// else no. 
function isMember($a, $d, $x) 
{ 
  
    // If difference is 0, then  
    // x must be same as a 
    if ($d == 0) 
    return ($x == $a); 
      
// Else difference between x 
// and a must be divisible by d.  
return (($x - $a) % $d == 0 &&  
        ($x - $a) / $d >= 0); 
} 
  
// Driver code. 
$a = 1; $x = 7; $d = 3; 
if (isMember($a, $d, $x)) 
    echo "Yes"; 
else
    echo "No"; 
  
// This code is contributed by aj_36 
?> 

Javascript

<script> 
    // Javascript program to check if x exist 
    // or not in the given AP. 
      
    // returns yes if exist else no. 
    function isMember(a, d, x) 
    { 
  
        // If difference is 0, then x must 
        // be same as a. 
        if (d == 0) 
            return (x == a); 
  
        // Else difference between x and a 
        // must be divisible by d. 
        return ((x - a) % d == 0 && (x - a) / d >= 0); 
    } 
      
    let a = 1, x = 7, d = 3; 
    if (isMember(a, d, x)) 
        document.write("Yes"); 
    else
        document.write("No"); 
      
    // This code is contributed by divyeshrabadiya07. 
</script>

Output

Yes

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

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