Note: This is an extension of House Robber.
After robbing those houses on that street, the thief has found himself a new place for his thievery so that he will not get too much attention. This time, all houses at this place are arranged in a circle. That means the first house is the neighbor of the last one. Meanwhile, the security system for these houses remain the same as for those in the previous street.
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 @Freezen for adding this problem and creating all test cases.
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题目

在上次打劫完一条街道之后，窃贼又发现了一个新的可以打劫的地方，但这次所有的房子围成了一个圈，这就意味着第一间房子和最后一间房子是挨着的。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。
注意事项
这题是House Robber的扩展，只不过是由直线变成了圈
样例
给出nums = [3,6,4], 返回　6，　你不能打劫3和4所在的房间，因为它们围成一个圈，是相邻的．

分析

打劫房屋问题的扩展，要求首尾不能相连，那就调用上一题中的方法两次，第一次不包括尾，第二次不包括首，最后求出最大就可以了

代码

public class Solution {
    public int rob(int[] nums) {
            if (nums.length == 0) {
                return 0;
            }
            if (nums.length == 1) {
                return nums[0];
            }
            return Math.max(robber1(nums, 0, nums.length - 2), robber1(nums, 1, nums.length - 1));
        }
        public int robber1(int[] nums, int start, int end) {
            if(start == end)
                return nums[start];
            if(end == start+1)
                return Math.max(nums[start], nums[start+1]);
            int[] dp = new int[end-start+2];
            dp[start] = nums[start];
            dp[start+1] = Math.max(nums[start], nums[start+1]);
            
            for(int i=start+2;i<=end;i++)
                dp[i] = Math.max(dp[i-1], dp[i-2] + nums[i]);
            
            return dp[end];
        }
}

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方法二

public class Solution {
    public int rob(int[] nums) {
            if (nums.length == 1) return nums[0];
    return Math.max(rob(nums, 0, nums.length - 2), rob(nums, 1, nums.length - 1));
        }
    private int rob(int[] num, int lo, int hi) {
    int include = 0, exclude = 0;
    for (int j = lo; j <= hi; j++) {
        int i = include, e = exclude;
        include = e + num[j];
        exclude = Math.max(e, i);
    }
    return Math.max(include, exclude);
}
}

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