Building a PTO Optimizer with JavaScript: The Algorithm Explained

How do you maximize consecutive days off using the fewest PTO days possible? It turns out this is a surprisingly fun combinatorial optimization problem. Here is how I solved it — and built a free tool anyone can use. The Problem Given: A list of public holidays (fixed dates) A number of available PTO days A year calendar Find: The optimal placement of PTO days that maximizes consecutive days off. Sounds simple? It is — if you only look at one holiday at a time. But when you consider all possible placements across an entire year, the search space explodes. Why Brute Force Doesn't Work A naive approach would be to try every possible combination of PTO day placements. With 260 working days in a year and, say, 10 PTO days to place, you're looking at C(260, 10) — roughly 4.2 trillion combinations. Even if you could check 1 million combinations per second, that would take about 49 days. Not exactly instant feedback. We need a smarter approach. The Greedy Algorithm The key insight: public hol