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 (x – 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. |
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> |
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 ?> |
Output
Yes
Time Complexity: O(1)
Auxiliary Space: O(1)