What is the optimal time complexity of solving Permutations in which n people can occupy r seats?

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 Permutations in which n people can occupy r seats?

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 Permutations in which n people can occupy r seats?

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 Permutations in which n people can occupy r seats?

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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Permutations in which n people can occupy r seats

Learn how to solve the 'Permutations in which n people can occupy r seats' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function compute_nPr(n, r) that takes two non-negative integers n and r (where n >= r) and returns the number of permutations, i.e., the number of ways to arrange r items out of n items. The formula is nPr = n! / (n - r)!.

For example, if 5 people want to sit in 3 seats, the number of ways is 5P3 = 5! / 2! = 120 / 2 = 60.

Constraints

•0 <= r <= n <= 20

Examples

Example 1

Input

compute_nPr(5, 3)

Output

Explanation

5P3 = 5! / (5-3)! = 120 / 2 = 60.

Example 2

Input

compute_nPr(4, 2)

Output

Explanation

4P2 = 4! / 2! = 24 / 2 = 12.

Example 3

Input

compute_nPr(6, 6)

Output

Explanation

6P6 = 6! / 0! = 720 / 1 = 720.

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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