<p>You are given an integer array <code>jobs</code>, where <code>jobs[i]</code> is the amount of time it takes to complete the <code>i<sup>th</sup></code> job.</p>

<p>There are <code>k</code> workers that you can assign jobs to. Each job should be assigned to <strong>exactly</strong> one worker. The <strong>working time</strong> of a worker is the sum of the time it takes to complete all jobs assigned to them. Your goal is to devise an optimal assignment such that the <strong>maximum working time</strong> of any worker is <strong>minimized</strong>.</p>

<p><em>Return the <strong>minimum</strong> possible <strong>maximum working time</strong> of any assignment. </em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> jobs = [3,2,3], k = 3
<strong>Output:</strong> 3
<strong>Explanation:</strong> By assigning each person one job, the maximum time is 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> jobs = [1,2,4,7,8], k = 2
<strong>Output:</strong> 11
<strong>Explanation:</strong> Assign the jobs the following way:
Worker 1: 1, 2, 8 (working time = 1 + 2 + 8 = 11)
Worker 2: 4, 7 (working time = 4 + 7 = 11)
The maximum working time is 11.</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= jobs.length &lt;= 12</code></li>
	<li><code>1 &lt;= jobs[i] &lt;= 10<sup>7</sup></code></li>
</ul>

class Solution:
    def __init__(self):
        self.min_max_time = float('inf')
    def bt(self, idx, jobs, workers, k, e):
        if idx == len(jobs):
            self.min_max_time = min(self.min_max_time, max(workers))
            return
        for i in range(0,k):
            if i > 0 and workers[i] == workers[i-1]:
                continue
            if workers[i] + jobs[idx] > self.min_max_time:
                continue
            if workers[i] > e:
                continue
            
            workers[i] += jobs[idx]
            self.bt(idx + 1, jobs, workers, k, e)
            workers[i] -= jobs[idx]

    def minimumTimeRequired(self, jobs: List[int], k: int) -> int:
        jobs.sort()
        workers = [0] * k
        e = sum(jobs) / k
        self.bt(0, jobs, workers, k, e)
        return self.min_max_time
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