What is the optimal time complexity of solving Non decreasing numbers with n digits?

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 Non decreasing numbers with n digits?

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 Non decreasing numbers with n digits?

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 Non decreasing numbers with n digits?

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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Competitive ProgrammingEasy

Non decreasing numbers with n digits

Learn how to solve the 'Non decreasing numbers with n digits' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function count_non_decreasing(n) that returns the count of non-decreasing numbers with n digits. A number is non-decreasing if every digit is greater than or equal to the digit to its left. Leading zeros are allowed (e.g. 012 is non-decreasing).

Constraints

•1 <= n <= 20

Examples

Example 1

Input

count_non_decreasing(1)

Output

Explanation

All single digit numbers (0 to 9) are non-decreasing.

Example 2

Input

count_non_decreasing(2)

Output

Explanation

There are 55 non-decreasing numbers of 2 digits (like 00, 01, ..., 11, 12, ..., 99).

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

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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