Count All Valid Pickup and Delivery Options
A hard-tier problem at 65% community acceptance, tagged with Math, Dynamic Programming, Combinatorics. Reported in interviews at Acko and 1 others.
You've got n pickup-delivery pairs and you need to count all valid orderings where each pickup comes before its delivery. This is a combinatorics problem hidden as a DP question, and it hits different when you realize the brute force enumeration won't scale. DoorDash and Acko both ask this. The acceptance rate is solid at 65 percent, but that masks a trick: most people either overthink it with full state DP or miss the mathematical pattern entirely. If this problem lands in your assessment and you freeze on the formula, StealthCoder surfaces the working solution in seconds, invisible to the proctor.
Companies that ask "Count All Valid Pickup and Delivery Options"
Count All Valid Pickup and Delivery Options is the kind of problem that decides whether you pass. StealthCoder reads the problem on screen and surfaces a working solution in under 2 seconds. Invisible to screen share. The proctor sees nothing. Built by an engineer at a top-10 tech company who can solve these problems cold but didn't want to trust himself in a 90-minute screen share.
Get StealthCoderThe naive approach tries to track which pickups and deliveries have been used, leading to exponential branching. The real insight is combinatorial: at each step, you have a fixed number of valid next moves based on open pickups and complete pairs, and the answer follows a clean mathematical pattern involving factorials and products. Dynamic programming works here, but only if you recognize that the state can collapse into a simple count of open pickups rather than a bitmask of all pairs. Most candidates either implement the expensive bitmask DP or attempt to derive the formula by hand and mess up the algebra. When the time pressure hits and the pattern isn't obvious, StealthCoder is the hedge for the live OA.
Pattern tags
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Make sure you actually pass it.
Count All Valid Pickup and Delivery Options recycles across companies for a reason. It's hard-tier, and most candidates blank under the timer. StealthCoder is the hedge: an AI overlay invisible during screen share. It reads the problem and surfaces a working solution in under 2 seconds. Built by an engineer at a top-10 tech company who can solve these problems cold but didn't want to trust himself in a 90-minute screen share. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Count All Valid Pickup and Delivery Options interview FAQ
Is this just 'arrange objects with constraints' or something deeper?+
It's both. The constraint that each pickup precedes its delivery creates a dependency graph. You can solve it with DP on open pickup count, or recognize it reduces to a product formula. Either way, you need to see the structure, not brute force it. The 65 percent acceptance rate includes people who found the pattern fast.
How much harder is this than standard DP problems?+
The difficulty spike comes from state compression. Most DP problems give you an obvious state. Here, you must realize that open pickup count is sufficient, not bitmask. If you don't see that, the code explodes. That's why it's rated HARD and not MEDIUM.
Do DoorDash and Acko ask this because it's relevant to their actual product?+
Delivery platforms do care about order sequencing and combinatorial counting. Whether the problem maps directly to production code is unclear, but both companies have posted it. It signals comfort with math and pattern recognition under time pressure.
What's the most common wrong approach?+
Trying to enumerate all permutations and filter. That's O(factorial) and times out instantly. The second trap is a DP with a bitmask state instead of collapsing to open count, which is correct but slow. The clean solution is much smaller.
Is combinatorics knowledge required or can I derive it in the interview?+
You can derive it if you see the pattern fast. Knowing factorial-based combinatorics helps you recognize the structure quickly. At HARD difficulty with 65 percent acceptance, most who pass either knew the pattern or reverse-engineered it from small examples. The math isn't obscure, just non-obvious under time pressure.
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