Introduction

In this blog post, we will explore how to solve the LeetCode problem "1601" 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

We have n buildings numbered from 0 to n - 1. Each building has a number of employees. It's transfer season, and some employees want to change the building they reside in. You are given an array requests where requests[i] = [fromi, toi] represents an employee's request to transfer from building fromi to building toi. All buildings are full, so a list of requests is achievable only if for each building, the net change in employee transfers is zero. This means the number of employees leaving is equal to the number of employees moving in. For example if n = 3 and two employees are leaving building 0, one is leaving building 1, and one is leaving building 2, there should be two employees moving to building 0, one employee moving to building 1, and one employee moving to building 2. Return the maximum number of achievable requests. Example 1: Input: n = 5, requests = [[0,1],[1,0],[0,1],[1,2],[2,0],[3,4]] Output: 5 Explantion: Let's see the requests: From building 0 we have employees x and y and both want to move to building 1. From building 1 we have employees a and b and they want to move to buildings 2 and 0 respectively. From building 2 we have employee z and they want to move to building 0. From building 3 we have employee c and they want to move to building 4. From building 4 we don't have any requests. We can achieve the requests of users x and b by swapping their places. We can achieve the requests of users y, a and z by swapping the places in the 3 buildings. Example 2: Input: n = 3, requests = [[0,0],[1,2],[2,1]] Output: 3 Explantion: Let's see the requests: From building 0 we have employee x and they want to stay in the same building 0. From building 1 we have employee y and they want to move to building 2. From building 2 we have employee z and they want to move to building 1. We can achieve all the requests. Example 3: Input: n = 4, requests = [[0,3],[3,1],[1,2],[2,0]] Output: 4 Constraints: 1 <= n <= 20 1 <= requests.length <= 16 requests[i].length == 2 0 <= fromi, toi < n

Explanation

Here's the solution:

• Core Idea: Use bit manipulation to represent all possible combinations of requests. Iterate through each combination and check if the net change in employees for each building is zero.
• Optimization: For each combination, calculate the change in employee count for each building. If all buildings have a net change of zero, the combination is valid.

• Maximization: Keep track of the maximum number of requests that can be achieved in a valid combination.

• Runtime Complexity: O(2^m n), where m is the number of requests and n is the number of buildings. *Storage Complexity: O(n)

Code

    def maximumAchievableRequests(n, requests):
    m = len(requests)
    max_requests = 0

    for mask in range(2**m):
        changes = [0] * n
        count = 0

        for i in range(m):
            if (mask >> i) & 1:
                changes[requests[i][0]] -= 1
                changes[requests[i][1]] += 1
                count += 1

        valid = True
        for change in changes:
            if change != 0:
                valid = False
                break

        if valid:
            max_requests = max(max_requests, count)

    return max_requests