LeetCode-House Robber

##题目

####House Robber

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.

##解题思路
这道题的本质相当于在一列数组中取出一个或多个不相邻数，使其和最大。
这是一道动态规划问题。
我们维护一个一位数组dp，其中dp[i]表示到i位置时不相邻数能形成的最大和。
状态转移方程：

dp[0] = num[0] （当i=0时）
dp[1] = max(num[0], num[1]) （当i=1时）
dp[i] = max(num[i] + dp[i - 2], dp[i - 1])   （当i !=0 and i != 1时）(num[i]抢还是不抢两种情况)

##算法代码
代码采用JAVA实现：

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public class Solution {
    public int rob(int[] num) {
        //定义dp[i]表示抢到第i个房间的时候没有惊动警察的最大钱数
        if(num==null || num.length==0)
        	return 0;
        if(num.length==1)
        	return num[0];
        int[] dp=new int[num.length];
        dp[0]=num[0];
        dp[1]=Math.max(num[0],num[1]);
        for(int i=2;i<num.length;i++)
        	dp[i]=Math.max(dp[i-1],dp[i-2]+num[i]);
        return dp[num.length-1];
    }
}