House Robber IV

House Robber IV

What is this problem about?

In the House Robber IV interview question, you are given an array of integers representing money in houses and a target $k$. You need to rob at least $k$ houses without robbing adjacent ones. The goal is to minimize the maximum amount of money you rob from any single house. This is a "Min-Max" optimization problem.

Why is this asked in interviews?

This problem is a favorite at companies like Bloomberg and Amazon because it tests whether a candidate can recognize that a search problem can be solved by checking a condition. It requires the Binary Search on the Answer interview pattern. Instead of trying to find the optimal set of houses directly, you check: "Is it possible to rob $k$ houses if I am only allowed to take up to $X$ dollars from each?"

Algorithmic pattern used

1. Binary Search on Answer: The possible answer range is between the minimum and maximum house values.
2. Greedy Check: For a middle value mid, iterate through the houses. Use a greedy approach to pick as many houses as possible where value <= mid, ensuring no two are adjacent.
3. If the count of picked houses is $\ge k$, then mid is a potential answer, so try a smaller value. Otherwise, try a larger value.

Example explanation

houses = [2, 3, 5, 9], $k = 2$.

1. Try mid = 5.
2. Check: Can we pick 2 houses with value $\le 5$?
   • Pick index 0 (val 2).
   • Cannot pick index 1 (adjacent).
   • Pick index 2 (val 5).
3. Count = 2. Yes! Try smaller.
4. Try mid = 3.
5. Check: Can we pick 2 houses with value $\le 3$?
   • Pick index 0 (val 2).
   • Pick index 2 (val 5? No, 5 > 3).
   • Count = 1. No. Result: 5.

Common mistakes candidates make

• Trying DP: Attempting to solve this with standard House Robber DP, which becomes $O(N imes K)$ and is too slow.
• Incorrect Greedy logic: Failing to skip the adjacent house correctly during the validation step.
• Search Range: Starting the binary search from 0 instead of the minimum element in the array.

Interview preparation tip

Whenever you see a problem asking to "Minimize the Maximum" or "Maximize the Minimum," immediately think of Binary Search on the Answer. It is one of the most powerful and common optimizations in technical interviews.