<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 minimumTimeRequired(vector<int>& jobs, int k) {
        int n = jobs.size();
        int u = (1 << n) - 1;
        vector<vector<int>> dp(1 << n, vector<int>(k + 1, INT_MAX));
        vector<int> s(1 << n, 0);

        for (int i = 0; i < n; ++i) {
            int bit = 1 << i;
            for (int j = 0; j < bit; ++j) {
                s[bit | j] = s[j] + jobs[i];
            }
        }

        // Initialize the subset array
        vector<vector<int>> subset(1 << 12);
        for (int mask = 0; mask < (1 << 12); ++mask) {
            int s = mask;
            while (s > 0) {
                subset[mask].push_back(s);
                s = (s - 1) & mask;
            }
        }

        for (int mask = 0; mask < (1 << n); ++mask) {
            for (int i = 1; i <= k; ++i) {
                if (i == 1) dp[mask][i] = s[mask];
                for (int g : subset[mask]) {
                    int ne = max(dp[mask ^ g][i - 1], s[g]);
                    dp[mask][i] = min(dp[mask][i], ne);
                }
            }
        }

        return dp[u][k];
    }
};


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