<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();
        vector<vector<int>>dp((1<<n),vector<int>(k+1,INT_MAX));
        for(int i=0;i<(1<<n);i++){
            for(int j=0;j<k+1;j++){
                if(i==0){
                    dp[i][j]=0;
                    continue;
                }
                else if(j==0) continue;
                int sz = __builtin_popcount(i);
                if(sz < j) break;
                for(int submask = i;submask;submask = (submask-1)&i){
                    if(__builtin_popcount(i^submask) < (j-1)) continue;
                    int sum=0;
                    for(int l=0;l<n;l++) if(submask&(1<<l)) sum+=jobs[l];
                    sum = max(sum,dp[i^submask][j-1]);
                    dp[i][j] = min(dp[i][j],sum);
                }
            }
        }
        return dp[(1<<n)-1][k];
    }
};
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