Leetcode House Robber

最新推荐文章于 2024-01-18 14:02:27 发布

fight_to_dead

最新推荐文章于 2024-01-18 14:02:27 发布

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分类专栏： LeetCode 文章标签：动态规划 DP

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本文通过动态规划的方法解决了一个关于相邻房屋抢劫问题，其中相邻房屋设有联动报警系统，旨在最大化抢劫金额而不触发警报。分析了动态规划的四个步骤，并提供了Java代码实现。

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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.

分析：

这道题属于动态规划中求最大值的问题。用动态规划的四个步骤进行分析：

1. 状态n代表到第n个房子时最大的钱数

2. 状态转移方程： f[n] = max(f[n-2]+nums[n], f[n-1])，拿n-1的钱和不拿两种情况中取收益最大的

3. 初始状态： f[1] = nums[1] f[2] = max(nums[1], nums[2])

4. 答案为第n个房子时的最大收入

Java代码实现：

public class Solution {
    public int rob(int[] nums) {
        if(nums==null || nums.length==0)
            return 0;
        if(nums.length==1)
            return nums[0];
        if(nums.length==2)
            return Math.max(nums[0], nums[1]);
        
        int size = nums.length;
        int[] max = new int[size];
        max[0] = nums[0];
        max[1] = Math.max(nums[0], nums[1]);
        
        for(int i=2;i<size;i++)
        {
            max[i] = Math.max(max[i-2]+nums[i], max[i-1]);
        }
        
        return max[size-1];
    }
}