IPO
hardTime: O(n log n)Space: O(n)
Signals to notice
maximize capital after k investmentstwo heaps: affordable and profitablegreedy selection
Brute force first
Try all combinations — O(C(n,k)).
The key insight
Min-heap by capital, max-heap by profit. Each round: move newly affordable projects to profit heap, pick most profitable. O(n log n).
What must stay true
As capital grows, more projects become affordable. The profit heap always picks the best available option.
Easy way to go wrong
Not pre-sorting by capital — the min-heap feeds the profit heap efficiently as budget increases.