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