<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 {
public:
int getTotalTime(int state, const std::vector<int>& jobs) {
    int n = jobs.size();
    int time = 0;
    for (int i = 0; i < n; i++) {
        if (state & (1 << i)) {
            time += jobs[i];
        }
    }
    return time;
}

int dfsMinimumTime(int worker, int jobsTaken, std::vector<std::vector<int>>& dp, int k, int n, const std::vector<int>& jobs) {
    if (worker == k) {
        return (jobsTaken == (1 << n) - 1) ? 0 : INT_MAX;
    }

    if (dp[worker][jobsTaken] != -1) {
        return dp[worker][jobsTaken];
    }

    int minTime = INT_MAX;
    for (int j = 1; j < (1 << n); j++) {
        if ((jobsTaken & j) == 0) {
            int time = getTotalTime(j, jobs);
            int maxTime = std::max(time, dfsMinimumTime(worker + 1, jobsTaken | j, dp, k, n, jobs));
            minTime = std::min(minTime, maxTime);
        }
    }

    dp[worker][jobsTaken] = minTime;
    return minTime;
}

int minimumTimeRequired(const std::vector<int>& jobs, int k) {
    int n = jobs.size();
    std::vector<std::vector<int>> dp(k, std::vector<int>(1 << n, -1));
    return dfsMinimumTime(0, 0, dp, k, n, jobs);
}
};
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