Arithmetic Number

Problem Description

Given three integers 'A' denoting the first term of an arithmetic sequence , 'C' denoting the common difference of an arithmetic sequence and an integer 'B'. you need to tell whether 'B' exists in the arithmetic sequence or not. Return 1 if B is present in the sequence. Otherwise, returns 0.

Examples

Example 1:

Input: A = 1, B = 3, C = 2
Output: 1
Explaination: 3 is the second term of the 
sequence starting with 1 and having a common 
difference 2.

Example 2:

Input: A = 1, B = 2, C = 3
Output: 0
Explaination: 2 is not present in the sequence.

Your Task

You do not need to read input or print anything. Your task is to complete the function inSequence() which takes A, B and C and returns 1 if B is present in the sequence. Otherwise, returns 0.

Expected Time Complexity: $O(1)$

Expected Auxiliary Space: $O(1)$

Constraints

• -10^9 ≤ A, B, C ≤ 10^9

Problem Explanation

Given three integers 'A' denoting the first term of an arithmetic sequence , 'C' denoting the common difference of an arithmetic sequence and an integer 'B'. you need to tell whether 'B' exists in the arithmetic sequence or not. Return 1 if B is present in the sequence. Otherwise, returns 0.

Code Implementation

Python

Written by @Ishitamukherjee2004

def is_present(A, C, B):
if (B - A) % C == 0 and (B - A) / C >= 0:
  return 1
return 0

C++

Written by @Ishitamukherjee2004

int isPresent(int A, int C, int B) {
if ((B - A) % C == 0 && (B - A) / C >= 0) {
  return 1;
}
return 0;
}

Javascript

Written by @Ishitamukherjee2004

function isPresent(A, C, B) {
if ((B - A) % C === 0 && (B - A) / C >= 0) {
  return 1;
}
return 0;
}

Typescript

Written by @Ishitamukherjee2004

function isPresent(A, C, B) {
if ((B - A) % C === 0 && (B - A) / C >= 0) {
  return 1;
}
return 0;
}

Java

Written by @Ishitamukherjee2004

public int isPresent(int A, int C, int B) {
if ((B - A) % C == 0 && (B - A) / C >= 0) {
  return 1;
}
return 0;
}

Solution Logic:

The solution checks if the difference between B and A is a multiple of C (the common difference) and if the result is non-negative. If both conditions are true, it means that B is present in the arithmetic sequence.

Time Complexity

• The time complexity is $O(1)$, because it only involves simple arithmetic operations.

Space Complexity

• The auxiliary space complexity is $O(1)$ because we are not using any extra space proportional to the size of the input array.