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House Robber
172 浏览 | 2020-04-27 | 分类:动态规划,数据结构与算法 | 标签:

House Robber

Summary

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 system connected and it will automatically contact the police if two adjacent houses were broken into on the same night.

Given a list of non-negative integers representing the amount of money of each house, determine the maximum amount of money you can rob tonight without alerting the police.

My approuch

class Solution:
    def rob(self, nums: List[int]) -> int:
        if not nums:
            return 0
        dp0 = 0
        dp1 = nums[0]
        for d in range(1, len(nums)):
            tmp = dp1
            dp1 = dp0 + nums[d]
            dp0 = max(dp0, tmp)
        return max(dp1, dp0)

Other approuch

class Solution:
    def rob(self, nums: List[int]) -> int:
        
        # if we have no houses to rob, we can't get any money
        if not nums:
            return 0
        
        # if we only have 1 or 2 houses to rob, we take the max
        if len(nums) <= 2:
            return max(nums)
    
        # else we create a state array to hold the max amount
        # of money that we can accumulat at each house
        state = [0 for _ in range(len(nums))]
        
        # we can memoize our first two houses
        state[0] = nums[0]
        state[1] = nums[1]
        
        # for each house after our first 2, the max amount we can take
        # is equal to the max amount found in our state array, plus the
        # amount of the current house
        for i in range(2, len(nums)):
            
            # we use i-1 because we cannot rob houses adjacent to the 
            # one we are currently robbing
            state[i] = max(state[:i-1]) + nums[i]
            
        return max(state)

House Robber II

Summary

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 security system connected and it will automatically contact the police if two adjacent houses were broken into on the same night.

Given a list of non-negative integers representing the amount of money of each house, determine the maximum amount of money you can rob tonight without alerting the police.

My approuch

class Solution:
    def rob(self, nums: List[int]) -> int:
        n = len(nums)
        if not nums:
            return 0
        if n < 4:
            return max(nums)
        dp0 = [nums[1], nums[0]]
        dp1 = [nums[2], nums[0] + nums[2]]
        for d in range(3, n):
            tmp1 = dp1[0]
            tmp2 = dp1[1]
            if d < n - 1:
                dp1[1] = dp0[1] + nums[d]
            else:
                dp1[1] = dp0[1]
            dp1[0] = dp0[0] + nums[d]
            dp0[0] = max(dp0[0], tmp1)
            dp0[1] = max(dp0[1], tmp2)
        return max(dp1 + dp0)

House Robber III

Summary

The thief has found himself a new place for his thievery again. There is only one entrance to this area, called the "root." Besides the root, each house has one and only one parent house. After a tour, the smart thief realized that "all houses in this place forms a binary tree". It will automatically contact the police if two directly-linked houses were broken into on the same night.

Determine the maximum amount of money the thief can rob tonight without alerting the police.

My approuch

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
    def rob(self, root: TreeNode) -> int:
        dp = [0, 0]
        return max(self.calRob(root, dp))
        
    def calRob(self, root, dp):
        if not root:
            return (0, 0)
        dp[0], dp[1] = max(dp[0], dp[1]), dp[0] + root.val
        left = self.calRob(root.left, dp)
        right = self.calRob(root.right, dp)

        return (max(left) + max(right) ,root.val + left[0] + right[0])
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