LeetCode198—House Robber

最新推荐文章于 2025-08-11 15:06:51 发布

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本文探讨了一种特殊情况下从一系列房屋中盗窃的问题，目标是在不触动报警系统的前提下获得最大金额。采用动态规划方法，通过定义状态转移方程来解决这一问题。

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原题

原题链接
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.

分析

题目这么长，其实很简单，在一个数组中找出和最大的子序列，子序列需要满足要求，任何两个元素不相邻。

动态规划问题，假设dp[i]表示在i时最大值，那么有下列方程：
$dp[i]=max(dp[i-2]+nums[i], dp[i-1])$

根据这个方程就很容易写代码了：

class Solution {
public:
    int rob(vector<int>& nums) {
        if (nums.size() == 0)
            return 0;
        if (nums.size() == 1)
            return nums[0];
        if (nums.size() == 2)
            return nums[0] > nums[1] ? nums[0] : nums[1];
        int length = nums.size();

        vector<int>dp(length);
        dp[0] = nums[0];
        dp[1] = nums[0] > nums[1] ? nums[0] : nums[1];

        for (int i = 2; i < length; ++i)
        {
            dp[i] = max(dp[i - 2] + nums[i], dp[i - 1]);
        }
        return dp[length - 1];
    }
};