What is the optimal time complexity of solving House Robber?

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 House Robber?

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 House Robber?

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 House Robber?

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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House Robber

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

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Problem Statement

Medium

You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed, the only constraint stopping you from robbing each of them is that adjacent houses have security systems connected and it will automatically contact the police if two adjacent houses were broken into on the same night.

Given an integer array nums representing the amount of money of each house, return the maximum amount of money you can rob tonight without alerting the police.

Write a function rob(nums: List[int]) -> int.

Constraints

•1 <= len(nums) <= 100
•0 <= nums[i] <= 400

Examples

Example 1

Input

nums = [1,2,3,1]

Output

Explanation

Rob house 1 (money = 1) then rob house 3 (money = 3). Total = 1 + 3 = 4.

Example 2

Input

nums = [2,7,9,3,1]

Output

Explanation

Rob house 1 (money = 2), rob house 3 (money = 9) and rob house 5 (money = 1). Total = 12.

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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