### Problem statement

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 a security system connected, and **it will automatically contact the police if two adjacent houses were broken into on the same night**.

Given an integer array *nums* representing the amount of money of each house, return *the maximum amount of money you can rob tonight **without alerting the police***.

Problem statement taken from: https://leetcode.com/problems/house-robber-ii/

**Example 1:**

```
Input: nums = [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: nums = [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.
```

**Example 3:**

```
Input: nums = [1,2,3]
Output: 3
```

**Constraints:**

```
- 1 <= nums.length <= 100
- 0 <= nums[i] <= 1000
```

### Explanation

This problem is an extension of our old blog post House Robber. The tricky part of the problem is the houses are arranged in a circle. The first house is the neighbor of the last one, which means one of the houses cannot be robbed.

We need to run two cases here:

- Select the first house and ignore the last one. We calculate the max amount that can be looted from nums[0] to nums[len - 2].
- Select the last house and ignore the first one. We calculate the max amount that can be looted from nums[1] to nums[len - 1].

Let's check the algorithm here:

```
// rob(nums) method
- set n = nums.size();
// for empty array.
- if n == 0
- return 0
// for an array of size 1
- if n == 1
- return nums[0]
- return max(robHelper(nums, 0, n - 2), robHelper(nums, 1, n - 1))
// robHelper(nums, l, r)
- set include = 0
exclude = 0
tmp = 0
- loop for i = l; i <= r; i++
- set tmp = max(include, exclude)
- update include = exclude + nums[i]
- set exclude = tmp
- return max(include, exclude)
```

Let's check our solutions in **C++**, **Golang**, and **Javascript**.

#### C++ solution

```
class Solution {
public:
int robHelper(vector<int>& nums, int l, int r) {
int include = 0, exclude = 0, tmp;
for(int i = l ; i <= r ; i++) {
tmp = max(include , exclude);
include = exclude + nums[i];
exclude = tmp;
}
return max(include , exclude);
}
int rob(vector<int>& nums) {
int n = nums.size();
if(n == 0) {
return 0;
}
if(n == 1) {
return nums[0];
}
return max(robHelper(nums, 0, n - 2) , robHelper(nums, 1, n - 1));
}
};
```

#### Golang solution

```
func max(a, b int) int {
if a > b {
return a
}
return b
}
func robHelper(nums []int, l, r int) int {
include, exclude, tmp := 0, 0, 0
for i := l; i <= r; i++ {
tmp = max(include, exclude)
include = exclude + nums[i]
exclude = tmp
}
return max(include, exclude)
}
func rob(nums []int) int {
n := len(nums)
if n == 0 {
return 0
}
if n == 1 {
return nums[0]
}
return max(robHelper(nums, 0, n - 2), robHelper(nums, 1, n - 1))
}
```

#### Javascript solution

```
var robHelper = function(nums, l, r) {
let include = 0, exclude = 0, tmp;
for(let i = l; i <= r; i++) {
tmp = Math.max(include, exclude);
include = exclude + nums[i];
exclude = tmp;
}
return Math.max(include, exclude);
}
var rob = function(nums) {
let n = nums.length;
if(n == 0) {
return 0;
}
if(n == 1) {
return nums[0];
}
return Math.max(robHelper(nums, 0, n - 2), robHelper(nums, 1, n - 1));
};
```

Let's dry run our algorithm for a given input.

```
Input: nums = [1, 3, 2, 6, 8, 4]
// rob(vector<int>& nums)
Step 1: n = nums.size()
= 6
Step 2: n == 0
6 == 0
false
Step 3: n == 1
6 == 1
false
Step 4: return max(robHelper(nums, 0, n - 2), robHelper(nums, 1, n - 1))
return max(robHelper(nums, 0, 4), robHelper(nums, 1, 5))
First call for robHelper(nums, 0, 4)
Step 5: include = 0
exclude = 0
tmp
Step 6: loop for i = l; i <= r
i = 0
0 <= 4
true
tmp = max(include , exclude)
= max(0, 0)
= 0
include = exclude + nums[i]
= 0 + nums[0]
= 0 + 1
= 1
exclude = tmp
= 0
i++
i = 1
Step 7: loop for i <= r
1 <= 4
true
tmp = max(include , exclude)
= max(1, 0)
= 1
include = exclude + nums[i]
= 0 + nums[1]
= 0 + 3
= 3
exclude = tmp
= 1
i++
i = 2
Step 8: loop for i <= r
2 <= 4
true
tmp = max(include , exclude)
= max(3, 1)
= 3
include = exclude + nums[i]
= 1 + nums[2]
= 1 + 2
= 3
exclude = tmp
= 3
i++
i = 3
Step 9: loop for i <= r
3 <= 4
true
tmp = max(include , exclude)
= max(3, 3)
= 3
include = exclude + nums[i]
= 3 + nums[3]
= 3 + 6
= 9
exclude = tmp
= 3
i++
i = 4
Step 10: loop for i <= r
4 <= 4
true
tmp = max(include , exclude)
= max(9, 3)
= 9
include = exclude + nums[i]
= 3 + nums[4]
= 3 + 8
= 11
exclude = tmp
= 9
i++
i = 5
Step 11: loop for i <= r
5 <= 4
false
Step 12: return max(include, exclude)
max(11, 9)
We return 11
// we come back to step 4 and compute robHelper(nums, 1, 5)
Step 13: return max(11, robHelper(nums, 1, 5))
call for robHelper(nums, 1, 5)
Step 14: include = 0
exclude = 0
tmp
Step 15: loop for i = l; i <= r
i = 1
1 <= 5
true
tmp = max(include , exclude)
= max(0, 0)
= 0
include = exclude + nums[i]
= 0 + nums[1]
= 0 + 3
= 3
exclude = tmp
= 0
i++
i = 2
Step 16: loop for i <= r
i = 2
2 <= 5
true
tmp = max(include , exclude)
= max(3, 0)
= 3
include = exclude + nums[i]
= 0 + nums[2]
= 0 + 2
= 2
exclude = tmp
= 3
i++
i = 3
Step 17: loop for i <= r
i = 3
3 <= 5
true
tmp = max(include , exclude)
= max(2, 3)
= 3
include = exclude + nums[i]
= 3 + nums[3]
= 3 + 6
= 9
exclude = tmp
= 3
i++
i = 4
Step 18: loop for i <= r
i = 4
4 <= 5
true
tmp = max(include , exclude)
= max(9, 3)
= 9
include = exclude + nums[i]
= 3 + nums[4]
= 3 + 8
= 11
exclude = tmp
= 9
i++
i = 5
Step 19: loop for i <= r
i = 5
5 <= 5
true
tmp = max(include , exclude)
= max(11, 9)
= 11
include = exclude + nums[i]
= 9 + nums[5]
= 9 + 4
= 13
exclude = tmp
= 11
i++
i = 6
Step 20: loop for i <= r
i = 6
6 <= 5
false
We return to step 13
Step 21: return max(11, robHelper(nums, 1, 5))
return max(11, 13)
We return the answer as 13.
```

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