198. House Robber -Easy

Question

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.

假设你计划在一条街上抢劫房子。为了防止触发安全系统，你不能抢劫相邻的两间房间，否则它会自动报警。给出一个非负整数列表，它代表每间房能够抢劫的钱，请你确定在不触发安全系统的前提下，你能够获得的最多的钱是多少？

Example

None

Solution

• 动态规划解。这道题很好解，既然不能抢劫相邻的房间，那么定义dp[i]：抢到第i间房时所能抢到的最多的钱，递推式为：dp[i] = max(dp[i - 1], dp[i - 2] + nums[i])。因为到达第i个房间前的最大收益只可能是dp[i - 1]或者dp[i - 2]

  class Solution(object):    def rob(self, nums):        """        :type nums: List[int]        :rtype: int        """        if len(nums) == 0:            return 0        dp = [0] * len(nums)        for index in range(len(nums)):            if index == 0:                dp[index] = nums[index]            elif index == 1:                dp[index] = max(nums[index], nums[index - 1])            else:                dp[index] = max(dp[index - 2] + nums[index], dp[index - 1])        return dp[-1]