Hard
Maximum Profit from Valid Topological Order in DAG — C++
Full explanation · Time O(n * 2^n) · Space O(2^n)
// Time: O(n * 2^n)
// Space: O(2^n)
// dp, bitmasks
class Solution {
public:
int maxProfit(int n, vector<vector<int>>& edges, vector<int>& score) {
vector<int> adj(n);
for (const auto& e : edges) {
adj[e[1]] |= 1 << e[0];
}
vector<int> dp(1 << n, -1);
dp[0] = 0;
for (int mask = 0; mask < size(dp); ++mask) {
if (dp[mask] == -1) {
continue;
}
const int l = __builtin_popcount(mask) + 1;
for (int i = 0; i < n; ++i) {
if (mask & (1 << i)) {
continue;
}
if ((mask & adj[i]) == adj[i]) {
dp[mask | (1 << i)] = max(dp[mask | (1 << i)], dp[mask] + l * score[i]);
}
}
}
return dp.back();
}
};