What is the optimal time complexity of solving Harshad number?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Harshad number?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Harshad number?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Harshad number?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Harshad number

Learn how to solve the 'Harshad number' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function is_harshad(n) that takes a positive integer n and returns True if n is a Harshad (Niven) number, or False otherwise. A Harshad number is a number that is divisible by the sum of its digits. For example, 18 is a Harshad number because 1 + 8 = 9, and 18 is divisible by 9.

Constraints

•1 <= n <= 10^9

Examples

Example 1

Input

n = 18

Output

True

Explanation

Sum of digits = 1 + 8 = 9. Since 18 % 9 == 0, it is a Harshad number.

Example 2

Input

n = 21

Output

True

Explanation

Sum of digits = 2 + 1 = 3. Since 21 % 3 == 0, it is a Harshad number.

Example 3

Input

n = 14

Output

False

Explanation

Sum of digits = 1 + 4 = 5. Since 14 % 5 != 0, it is not a Harshad number.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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