The answer is dp[full_mask] where all courses are taken.
Code

[{"language":"C++","code":"class Solution {\npublic:\n    int minNumberOfSemesters(int n, vector<vector<int>>& relations, int k) {\n        vector<int> pre(n, 0);\n        for (auto& r : relations) pre[r[1]-1] |= 1 << (r[0]-1);\n        vector<int> dp(1<<n, n+1);\n        dp[0] = 0;\n        for (int mask = 0; mask < (1<<n); ++mask) {\n            int avail = 0;\n            for (int i = 0; i < n; ++i)\n                if ((mask & (1<<i)) == 0 && (mask & pre[i]) == pre[i])\n                    avail |= 1<<i;\n            for (int sub = avail; sub; sub = (sub-1)&avail) {\n                if (__builtin_popcount(sub) > k) continue;\n                dp[mask|sub] = min(dp[mask|sub], dp[mask]+1);\n            }\n        }\n        return dp[(1<<n)-1];\n    }\n};","lang":"cpp","html":"<pre class=\"shiki shiki-themes github-light github-dark\" style=\"background-color:#fff;--shiki-dark-bg:#24292e;color:#24292e;--shiki-dark:#e1e4e8\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">class</span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\"> Solution</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\"> {</span></span>\n<span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">public:</span></span>\n<span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">    int</span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\"> minNumberOfSemesters</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">(</span><span style=\"color:#D73A49;--shiki-dark:#F97583\">int</span><span style=\"color:#E36209;--shiki-dark:#FFAB70\"> n</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">, </span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\">vector</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">&#x3C;</span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\">vector</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">&#x3C;</span><span style=\"color:#D73A49;--shiki-dark:#F97583\">int</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">>></span><span style=\"color:#D73A49;--shiki-dark:#F97583\">&#x26;</span><span style=\"color:#E36209;--shiki-dark:#FFAB70\"> relations</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">, </span><span style=\"color:#D73A49;--shiki-dark:#F97583\">int</span><span style=\"color:#E36209;--shiki-dark:#FFAB70\"> k</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">) {</span></span>\n<span class=\"line\"><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">        vector</span><span style=\"color:#D73A49;--shiki-dark:#F97583\">&#x3C;int></span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\"> pre</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">(n, </span><span style=\"color:#005CC5;--shiki-dark:#79B8FF\">0</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">);</span></span>\n<span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">        for</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\"> (</span><span style=\"color:#D73A49;--shiki-dark:#F97583\">auto&#x26;</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\"> r : relations) pre[r[</span><span style=\"color:#005CC5;--shiki-
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