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 = 1x = 7d = 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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