diff --git a/dsa-solutions/gfg-solutions/Easy problems/Arithmetic-Number.md b/dsa-solutions/gfg-solutions/Easy problems/Arithmetic-Number.md new file mode 100644 index 000000000..689b508f8 --- /dev/null +++ b/dsa-solutions/gfg-solutions/Easy problems/Arithmetic-Number.md @@ -0,0 +1,146 @@ +--- +id: arithmetic-number +title: Arithmetic Number +sidebar_label: Arithmetic-Number +tags: + - Intermediate + - Array + - Mathematical + - GeeksforGeeks + - CPP + - Python + - DSA +description: "This tutorial covers the solution to the Find the Arithmetic Number problem from the GeeksforGeeks." +--- +## 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 + + + + + + ```py + def is_present(A, C, B): + if (B - A) % C == 0 and (B - A) / C >= 0: + return 1 + return 0 + + + ``` + + + + + + ```cpp + int isPresent(int A, int C, int B) { + if ((B - A) % C == 0 && (B - A) / C >= 0) { + return 1; + } + return 0; +} + + ``` + + + + + + + ```javascript + function isPresent(A, C, B) { + if ((B - A) % C === 0 && (B - A) / C >= 0) { + return 1; + } + return 0; +} + + + ``` + + + + + + + ```typescript +function isPresent(A, C, B) { + if ((B - A) % C === 0 && (B - A) / C >= 0) { + return 1; + } + return 0; +} + + ``` + + + + + + + ```java + 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. \ No newline at end of file