Description

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.

The original problem is here.

The original code is here.

My Solution

I solve this problem in C++, as below:

``````/*
*House Robber
*Author: shuaijiang
*Email: zhaoshuaijiang8@gmail.com
*/
#include<iostream>
#include<vector>
#include<stdlib.h>
using namespace std;

class Solution {
public:
int rob(vector<int>& nums) {
int size = nums.size();
if(size <= 0)
return 0;
if(size == 1)
return nums[0];
if(size == 2)
return max(nums[0], nums[1]);

vector<int> money = vector<int>(size, 0);
vector<int> index = vector<int>(size, 0);
//Dynamic programming
money[0] = nums[0];
index[0] = 1;
money[1] = max(nums[0],nums[1]);
if(nums[0] > nums[1])
index[1] = 1;
else
index[1] = 0;
for(int count=2;count<size;++count){
money[count] = max(money[count-1],money[count-2]+nums[count]);
if( money[count-1] >= money[count-2]+nums[count] ){
if(count == size-1)
return money[count];
index[count] = index[count-1];
}
else
index[count] = index[count-2];
}
if(index[size-1] == 0)
return money[size-1];
//The result without the last one
int max1 = money[size-2];

money[1] = nums[1];
money[2] = max(nums[1],nums[2]);
//Compute the result without the first one
for(int count=3;count<size;++count){
money[count] = max(money[count-1],money[count-2]+nums[count]);
}
//return the max of the two results
return max(money[size-1], max1);
}
};
``````

Note

To solve the problem, dynamic programming is used. Assume the robber get one house i, he just need to compute the maximum of the nums[i-1] and (nums[i-2]+nums[i]) as the money[i], this will not alert police. In the end, the robber can get the maximum of money[end-1]; Additionally, the first and the end of the house can’t be robbed at the same time.