Minimum Number of Taps to Open to Water a Garden
A hard-tier problem at 51% community acceptance, tagged with Array, Dynamic Programming, Greedy. Reported in interviews at Intuit and 8 others.
You're standing at position 0 in a garden. Each tap at index i can water plants in a range. You need the minimum number of taps to water all plants from 0 to n. Intuit, DE Shaw, Uber, and Salesforce all ask this. The trap: the greedy path feels right but leaves gaps. The DP path feels slow but locks in. The clever path borrows from jump-game and crushes both. Only 51% pass on first submission. If this lands in your live OA and you freeze on the transition, StealthCoder reads the screen and surfaces the working solution in seconds while the proctor sees nothing.
Companies that ask "Minimum Number of Taps to Open to Water a Garden"
Minimum Number of Taps to Open to Water a Garden 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. Made by an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too.
Get StealthCoderThe problem is a range-covering variant of dynamic programming, not a pure greedy problem. At each position, a tap extends left and right by its range value. Your job is to select the minimum set of taps that covers index 0 to n with no gaps. The standard greedy approach (pick the tap that reaches furthest at each step) fails because you can't always move forward without backtracking or jumping ahead. The DP approach recasts it as: dp[i] = minimum taps to water up to position i. For each position, check all taps that can reach it and take the minimum. This works but scales poorly on large n. The key insight is to transform it into a jump-game problem: convert ranges into the maximum reach from each position, then find minimum jumps needed. This is O(n) and catches the greedy pattern that actually works here. Array manipulation, DP state transition, and greedy re-framing all meet at one solution. Companies like Akuna Capital and BNY Mellon ask this to see if you can spot the transformation. When you're stuck during the assessment, StealthCoder runs invisibly and shows you the solution.
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Minimum Number of Taps to Open to Water a Garden 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. Made by an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Minimum Number of Taps to Open to Water a Garden interview FAQ
Is this just a greedy problem like Jump Game II?+
It borrows from greedy but isn't pure greedy. The range-covering twist means you can't always pick the furthest-reaching tap first without creating unreachable gaps. The insight is to recast it as 'maximum reach from each index' (like Jump Game II), then apply greedy jumps. That's where the transformation lives.
Why does a simple greedy approach fail here?+
Greedy alone picks the tap with maximum range, but taps overlap and aren't sorted by range. You might pick a far tap and skip nearer ones that bridge gaps. You need to track the furthest position reachable from your current coverage zone, then jump to the best next tap. That's the DP-greedy hybrid.
Do I need DP or can I solve this with just greedy and ranges?+
You need both concepts. DP guarantees correctness by exploring all combinations. Greedy optimizes it by always picking the tap that extends coverage furthest. The trick is recognizing that after converting ranges to reachability, the jump-game greedy strategy applies cleanly here.
Why do 49% of submissions fail if it's asked at Intuit, Uber, and Salesforce so often?+
Most candidates misunderstand the range model (tap at i waters from max(0, i-range[i]) to min(n, i+range[i])). Others try pure DP without optimization or pure greedy without covering gaps. The gap-detection step trips up half. It's not algorithmic complexity, it's the range semantics.
How does this relate to the broader Array and DP topics?+
This combines interval coverage (Array concept), state transitions (DP backbone), and optimal selection under constraints (Greedy layer). It's a capstone problem that synthesizes all three. That's why companies like DE Shaw and Akuna Capital ask it in later-round interviews.
Want the actual problem statement? View "Minimum Number of Taps to Open to Water a Garden" on LeetCode →