The Super Washing Machines coding problem is a unique and challenging array problem. You have n washing machines arranged in a line, each containing a certain number of dresses. In each move, you can choose any number of machines and transfer one dress from each chosen machine to one of its adjacent machines. The goal is to find the minimum number of moves to make all washing machines have the same number of dresses. If it is impossible, return -1.
This problem is often asked by Amazon and Google to test a candidate's ability to apply "Greedy" logic and prefix sum concepts to a complex scenario. It requires thinking about the "flow" of items across a line. It’s not just about the total number of items, but about the bottlenecks that occur at specific points in the array. Solving this shows that you can reduce a physical movement problem into a mathematical bottleneck analysis.
The primary pattern used is the Greedy and Prefix Sum interview pattern. First, check if the total number of dresses is divisible by n. If not, return -1. Then, calculate the "balance" at each machine: balance = current_dresses - average. The key observation is that the maximum number of moves is determined by two factors:
Machines: [1, 0, 5]. Total = 6, n = 3, target = 2.
Balances: [1-2, 0-2, 5-2] = [-1, -2, 3].
Running Prefix Sums: [-1, -3, 0].
A common error is thinking that only the prefix sum matters. In a machine where you need to move dresses to both sides, the prefix sum doesn't fully capture the bottleneck because you can only move one dress per turn from that machine. Another mistake is overcomplicating the simulation instead of looking for the mathematical constraints.
To excel in the Super Washing Machines interview question, practice thinking about "flow" and "net change" in array problems. Prefix sums are incredibly powerful for problems involving range sums or net balances. Understanding the Greedy interview pattern will help you identify that the local bottlenecks dictate the global minimum time.
