Minimum Fuel Cost to Report to the Capital
A medium-tier problem at 64% community acceptance, tagged with Tree, Depth-First Search, Breadth-First Search. Reported in interviews at American Express and 1 others.
You're on a tree where every node needs to report to the capital, and fuel cost scales with the number of people in each group traveling together. American Express and DRW have asked this one. The trap is obvious: greedy won't work, and a naive depth-first pass will miss the optimization window where you decide who travels with whom. The trick is tree DP, where you compute the minimum cost for each subtree and then decide optimally when to merge groups heading upward. If this problem hits your live assessment and you blank on the state transitions, StealthCoder runs invisibly and surfaces a working solution in seconds.
Companies that ask "Minimum Fuel Cost to Report to the Capital"
Minimum Fuel Cost to Report to the Capital 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 StealthCoderThis is a tree traversal problem where the greedy instinct (everyone travels alone, or merge everything) both fail. You need to use DFS to compute costs bottom-up, tracking the cost of having k people travel together from each subtree. The key insight is that merging groups reduces cost nonlinearly because fuel cost per person drops as group size rises. Common mistakes: treating it as a simple path-sum problem, not realizing the group-size dependency, or failing to prune the DP state space. The structure is classic tree DP, but the cost function is the wrinkle that trips candidates. BFS alone won't solve it; you need DFS with a recurrence relation. On a live OA, if you see a tree problem and hear 'minimize cost with group dynamics,' this pattern should fire. StealthCoder covers the exact state transitions and memoization shape, so even if you haven't drilled this exact variant, you're covered.
Pattern tags
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Make sure you actually pass it.
Minimum Fuel Cost to Report to the Capital recycles across companies for a reason. It's medium-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.
Minimum Fuel Cost to Report to the Capital interview FAQ
Is this actually a medium problem, or does it feel harder?+
It sits at 64% acceptance, which is right for medium, but it's a high medium. The tree traversal is straightforward; the DP formulation is the wall. Most candidates can code the DFS structure fast but get stuck on the recurrence relation and how to track group sizes efficiently.
Do I need to use both DFS and BFS, or just one?+
DFS is your core tool here. BFS doesn't help much because you need to compute optimal costs bottom-up, not layer-by-layer. DFS with memoization is the standard approach. Some solutions use DFS to build the tree, then DFS again to compute costs, but it's still depth-first thinking.
What's the real trick that makes this non-greedy?+
The cost per person decreases as your group size grows, but only if people travel together. A greedy 'always merge' fails on certain tree shapes. You have to compute the actual cost of each split and merge decision bottom-up, which is why DP is mandatory.
Are American Express and DRW the only companies asking this?+
They're the reported sources in the data, but that doesn't mean others haven't asked it. It's a solid tree DP problem, so expect it at other mid-tier tech and finance firms that value algorithmic depth.
How long should I spend on this in a real assessment?+
If you know the tree DP pattern, 15 to 25 minutes to code and test. If you don't, you'll thrash on the state definition. That's where StealthCoder saves you: it shows the exact memoization shape and transitions, so you're not guessing on the OA clock.
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