Introduction

In this blog post, we will explore how to solve the LeetCode problem "517" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You have n super washing machines on a line. Initially, each washing machine has some dresses or is empty. For each move, you could choose any m (1 <= m <= n) washing machines, and pass one dress of each washing machine to one of its adjacent washing machines at the same time. Given an integer array machines representing the number of dresses in each washing machine from left to right on the line, return the minimum number of moves to make all the washing machines have the same number of dresses. If it is not possible to do it, return -1. Example 1: Input: machines = [1,0,5] Output: 3 Explanation: 1st move: 1 0 <-- 5 => 1 1 4 2nd move: 1 <-- 1 <-- 4 => 2 1 3 3rd move: 2 1 <-- 3 => 2 2 2 Example 2: Input: machines = [0,3,0] Output: 2 Explanation: 1st move: 0 <-- 3 0 => 1 2 0 2nd move: 1 2 --> 0 => 1 1 1 Example 3: Input: machines = [0,2,0] Output: -1 Explanation: It's impossible to make all three washing machines have the same number of dresses. Constraints: n == machines.length 1 <= n <= 104 0 <= machines[i] <= 105

Explanation

Here's the breakdown of the solution:

• Check Feasibility: Determine if an equal distribution is even possible by checking if the total number of dresses is divisible by the number of machines. If not, return -1.
• Calculate Target: Calculate the target number of dresses each machine should have after the distribution.

• Track Imbalance: Iterate through the machines, tracking the cumulative imbalance (prefix sum of machines[i] - target). At each machine, the absolute value of the imbalance indicates the number of dresses that need to "pass through" this machine from the left side. Simultaneously keep track of the max absolute imbalance, and the maximum number of dresses being moved on any machine. The maximum of these two is the answer.

• Complexity:

  • Runtime: O(n)
  • Storage: O(1)

Code

    def find_min_moves(machines):
    """
    Calculates the minimum number of moves to make all washing machines have the same number of dresses.

    Args:
        machines: A list of integers representing the number of dresses in each washing machine.

    Returns:
        The minimum number of moves, or -1 if it's impossible to have an equal distribution.
    """

    n = len(machines)
    total_dresses = sum(machines)

    if total_dresses % n != 0:
        return -1

    target = total_dresses // n
    prefix_sum = 0
    max_sum = 0
    max_machines = 0

    for dresses in machines:
        prefix_sum += dresses - target
        max_sum = max(max_sum, abs(prefix_sum))
        max_machines = max(max_machines, dresses - target)

    return max(max_sum, max_machines)