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.
Credits:Special thanks to @ifanchu for adding this problem and creating all test cases. Also thanks to @ts for adding additional test cases.
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题目

假设你是一个专业的窃贼，准备沿着一条街打劫房屋。每个房子都存放着特定金额的钱。你面临的唯一约束条件是：相邻的房子装着相互联系的防盗系统，且 当相邻的两个房子同一天被打劫时，该系统会自动报警。
给定一个非负整数列表，表示每个房子中存放的钱， 算一算，如果今晚去打劫，你最多可以得到多少钱 在不触动报警装置的情况下。
样例
给定 [3, 8, 4], 返回 8.

分析

动态规划解决。
dp[i]:打劫前i个房子最多可以得到的钱
遇到第i个房子，两种选择打劫或者不打劫，所以
状态转移方程：
dp[i] = Max(dp[i-1],res[i-2]+A[i-1])
初始条件：
dp[0]= 0
dp[1] = A[0]

代码

public class Solution {
    /**
     * @param A: An array of non-negative integers.
     * return: The maximum amount of money you can rob tonight
     */
    //---方法一---
    public long houseRobber(int[] A) {
        // write your code here
        int n = A.length;
        if(n == 0)
            return 0;
        long []res = new long[n+1];
        
        
        res[0] = 0;
        res[1] = A[0];
        for(int i = 2; i <= n; i++) {
            res[i] = Math.max(res[i-1], res[i-2] + A[i-1]);
        }
        return res[n];
    }
    //---方法二---
    public long houseRobber(int[] A) {
        // write your code here
        int n = A.length;
        if(n == 0)
            return 0;
        long []res = new long[2];
        
        
        res[0] = 0;
        res[1] = A[0];
        for(int i = 2; i <= n; i++) {
            res[i%2] = Math.max(res[(i-1)%2], res[(i-2)%2] + A[i-1]);
        }
        return res[n%2];
    }
}

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方法二

同样的是动态规划，由于每个点只存在两个状态，即打劫或者不打劫，所以我们可以使用一个变量来保存这个状态，所以利用一个二维数组
dp[i][0]:表示不打劫第i个房屋的最大价值
dp[i][1]:表示打劫第i个房屋的最大价值

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

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