leetcode 213. House Robber II

https://leetcode.com/problems/house-robber-ii/

Description

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.

Note

variation of https://leetcode.com/problems/house-robber/
newly added constraint: arranged in a circle
I just splitted the possible cases not voilating the contraint.

case 1. case of nums which reduced to [1:]
case 2. case of nums which recuded to [:-1]

And then take the maxium value in case 1 and case 2.

Dynamic programming solution

class Solution:
    def f(self, memo, i, nums, n):
        if (i >= n):
            return 0
        if (i in memo): return memo[i]
        ans = max(
            nums[i] + self.f(memo, i+2, nums, n), 
            self.f(memo, i+1, nums, n) 
        )
        memo[i] = ans
        return ans
    
    def rob(self, nums: List[int]) -> int:
        n = len(nums)
        if n == 1: return nums[0]
            
        ans1 = self.f({}, 0, nums[1:], n-1)
        ans2 = self.f({}, 0, nums[:-1], n-1)
        return max(ans1, ans2)