You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed. All houses at this place are arranged in a circle. That means the first house is the neighbor of the last one. Meanwhile, 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.

Example 1:

Input: [2,3,2]
Output: 3
Explanation: You cannot rob house 1 (money = 2) and then rob house 3 (money = 2),
             because they are adjacent houses.

Example 2:

Input: [1,2,3,1]
Output: 4
Explanation: Rob house 1 (money = 1) and then rob house 3 (money = 3).
             Total amount you can rob = 1 + 3 = 4.

方法：計算兩次最大值

• dp1: largest sum when remove the last house (nums[0] to nums[nums.length-2])
• dp2: largest sum when remove
   the first house (nums[1] to nums[nums.length-1])
• return the larger sum (Math.max(dp1[dp1.length-1]. dp2[dp2.length-1]))
• edge cases
  • empty -> 0
  • only has one house -> nums[0]
  • only has two houses -> Math.max(nums[0], nums[1])

程式碼：

/**
 * <p>Title: </p>
 * <p>Description: </p>
 *
 * @CreateTime 2018/12/27 22:08
 */
public class Leetcode_213_HouseRobberII {

    public int rob(int[] nums) {
        if (nums.length == 0) return 0;
        if (nums.length == 1) return nums[0];
        if (nums.length == 2) return Math.max(nums[0], nums[1]);

        int[] dp1 = new int[nums.length - 1];
        int[] dp2 = new int[nums.length - 1];

        dp1[0] = nums[0];
        dp2[0] = nums[1];

        dp1[1] = Math.max(nums[0], nums[1]);
        dp2[1] = Math.max(nums[1], nums[2]);

        for (int i = 2; i < nums.length - 1; i++) {
            dp1[i] = Math.max(dp1[i - 2] + nums[i], dp1[i - 1]);
            dp2[i] = Math.max(dp2[i - 2] + nums[i + 1], dp2[i - 1]);
        }
        return Math.max(dp1[nums.length - 2], dp2[nums.length - 2]);
    }

    public static void main(String[] args) {
        Leetcode_213_HouseRobberII leetcode_213_houseRobberII = new Leetcode_213_HouseRobberII();
        System.out.println(leetcode_213_houseRobberII.rob(new int[]{2, 7, 9, 3, 1}));
        //11
    }
}

end