Problem Statement
House Robber II
You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed. All houses at this place are arranged in a circle. That means the first house is the neighbor of the last one. Meanwhile, adjacent houses have a security system connected, and it will automatically contact the police if two adjacent houses were broken into on the same night.
Given an array nums representing the amount of money of each house, return the maximum amount of money you can rob tonight without alerting the police.
Examples
Example 1:
Input: nums = [2, 3, 2]
Output: 3
Explanation: You cannot rob house 1 (money = 2) and then rob house 3 (money = 2), because they are adjacent houses (circular arrangement).
Example 2:
Input: nums = [1, 2, 3, 1]
Output: 4
Explanation: Rob house 1 (money = 1) and then rob house 3 (money = 3).
Example 3:
Input: nums = [1, 2, 3]
Output: 3
Explanation: Rob house 3 (money = 3).
Constraints
- 1 <= nums.length <= 100
- 0 <= nums[i] <= 1000
Problem Breakdown
To solve this problem, we need to:
- This problem is a variation of the House Robber problem with a circular arrangement.
- Since the houses are arranged in a circle, the first and last houses are adjacent, so you can't rob both of them.
- You can solve this by considering two cases: (1) excluding the first house, and (2) excluding the last house, and then taking the maximum of these two cases.
- For each case, you can use the same dynamic programming approach as in the original House Robber problem.
String Problems
Learning Objective
Apply string manipulation concepts to solve a real-world problem.
House Robber II
You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed. All houses at this place are arranged in a circle. That means the first house is the neighbor of the last one. Meanwhile, adjacent houses have a security system connected, and it will automatically contact the police if two adjacent houses were broken into on the same night.
Given an array nums representing the amount of money of each house, return the maximum amount of money you can rob tonight without alerting the police.
Examples
Example 1:
You cannot rob house 1 (money = 2) and then rob house 3 (money = 2), because they are adjacent houses (circular arrangement).
Example 2:
Rob house 1 (money = 1) and then rob house 3 (money = 3).
Example 3:
Rob house 3 (money = 3).
Problem Breakdown
Constraints:
- 1 <= nums.length <= 100
- 0 <= nums[i] <= 1000
Key Insights:
This problem is a variation of the House Robber problem with a circular arrangement.
Since the houses are arranged in a circle, the first and last houses are adjacent, so you can't rob both of them.
You can solve this by considering two cases: (1) excluding the first house, and (2) excluding the last house, and then taking the maximum of these two cases.
For each case, you can use the same dynamic programming approach as in the original House Robber problem.
Real-World Application
This problem has several practical applications:
Resource Allocation
Optimizing the allocation of resources in a circular arrangement where adjacent resources cannot be selected together.
Financial Planning
Maximizing returns in investment strategies where certain combinations of investments cannot be made simultaneously.
Security Systems
Designing optimal security coverage for a circular arrangement of buildings or areas.