LeetCode OJ 198 House Robber

最新推荐文章于 2020-01-12 09:11:44 发布

原创最新推荐文章于 2020-01-12 09:11:44 发布 · 526 阅读

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本文通过动态规划方法探讨了如何在不触发相邻房屋警报的情况下，最大化抢劫收益的问题。详细介绍了动态规划的思路、核心方程以及具体实现代码。

题目：

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.

思路：

典型的动态规划问题。假设OPT（i）为输入数据规模为i时的最优界，有如下方程。

OPT（1）=nums[1]

OPT(2)=max(nums[1],nums[2]).

OPT(n)=max(nums[n-1],nums[n-2]+wn) for n>=2

代码

class Solution {
public:
    int rob(vector<int>& nums) {
        if(nums.empty())
            return 0;
        unsigned long length = nums.size();
        vector<int> opt;
        for(int i=0;i<length;i++)
        {
            if(i==0)
                opt.push_back(nums[0]);
            if(i==1)
                opt.push_back(max(nums[0],nums[1]));
            if(i>=2)
                opt.push_back(max(opt[i-1],opt[i-2]+nums[i]));
        }
        return opt[length-1];
    }
    
};