What is the optimal time complexity of solving Decimal to Binary conversion?

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 Decimal to Binary conversion?

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 Decimal to Binary conversion?

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 Decimal to Binary conversion?

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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Python BasicsEasy

Decimal to Binary conversion

Learn how to solve the 'Decimal to Binary conversion' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function decimal_to_binary(n) that takes a non-negative integer n and returns a string representing its binary (base-2) equivalent. Do not include leading zeros (except for the input 0, which should return '0').

To convert decimal to binary, repeatedly divide the number by 2 and collect the remainders in reverse order.

Constraints

•0 <= n <= 10^6

Examples

Example 1

Input

decimal_to_binary(10)

Output

'1010'

Explanation

10 ÷ 2 = 5 remainder 0, 5 ÷ 2 = 2 remainder 1, 2 ÷ 2 = 1 remainder 0, 1 ÷ 2 = 0 remainder 1. Reading remainders bottom-up: 1010.

Example 2

Input

decimal_to_binary(255)

Output

'11111111'

Explanation

255 in binary is eight 1s: 128+64+32+16+8+4+2+1 = 255.

Example 3

Input

decimal_to_binary(0)

Output

'0'

Explanation

0 in any base is 0.

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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