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 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.

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.

Example 2:

Input: nums = [1,2,3,1]
Output: 4
Explanation: Rob house 1 (money = 1) and then rob house 3 (money = 3).
Total amount you can rob = 1 + 3 = 4.

Example 3:

Input: nums = [1,2,3]
Output: 3

Constraints:

• 1 <= nums.length <= 100
• 0 <= nums[i] <= 1000

解析

跟 198. House Robber 類似

題目給定一個陣列 nums ， 每個 nums[i] 該戶有的錢數目

相鄰的兩間如果連續拿錢就會啟動警報

而這題與198. House Robber 不同的是， 這題的第1間與最後一間是相鄰的是一個環狀結構

要求實做出一個演算法在不啟動警報的情況下 拿出最多錢

因為第0間與最後一間是相鄰的所以不能直接用上一題的解法

透過下圖

可以發現只要把所有用戶分成第 0 到 len(nums)-2 家與 第 1 到 len(nums)-1 家

分別去考慮這樣就可以把第0間 跟最後一間分開可以使用 198. House Robber 的解法

分別考慮 0 到 len(nums)-2 與 1 到 len(nums) -1 然後取最大值

就是結果

由於上一個 198. House Robber 的解為 O(n)

所以這題的時間複雜度也是 O(n)

程式碼

package sol

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}
func rob(nums []int) int {
	total := len(nums)

	var rob_with_range = func(start, end int) int {
		prevTwo := 0
		prevOne := nums[end]
		totalRob := 0
		for robIdx := end - 1; robIdx >= start; robIdx-- {
			totalRob = max(nums[robIdx]+prevTwo, prevOne)
			prevTwo = prevOne
			prevOne = totalRob
		}
		return max(prevOne, prevTwo)
	}
	if total == 1 {
		return nums[0]
	}

	return max(rob_with_range(0, total-2), rob_with_range(1, total-1))
}

困難點

1. 要看出可以把環狀結構拆分成兩個部份

Solve Point

• [x] 把 index 分成 前 n-2 個 與後 n-2 個 分別去呼叫 198. House Robber 的解法
• [x] 然後把兩個結果