House Robber II: the idea to remember.

The core insight

Solve two linear ranges: exclude the last house, or exclude the first house.

Why it works

The first and last houses cannot both be chosen. Every valid solution belongs to at least one of those two ranges.

The mistake to avoid

Handle a one house circle separately; otherwise both excluded ranges would be empty.

Commented Java solution

Use java.util.* imports and a surrounding solution class. Tree snippets assume the standard TreeNode definition; linked lists use ListNode and Clone Graph uses a Node with val and neighbors; Copy Random List uses Node with val, next and random. Read the input assumptions above.

int rob(int[] nums) {
    if (nums.length == 1) return nums[0];
    return Math.max(linear(nums, 0, nums.length - 1), linear(nums, 1, nums.length));
}
int linear(int[] nums, int start, int end) {
    int two = 0, one = 0;
    for (int i = start; i < end; i++) {
        int next = Math.max(one, two + nums[i]);
        two = one; one = next;
    }
    return one;
}

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