DSA interview question

Hand of Straights

Medium · Data structures · Topics: heap, greedy, hash map

The problem

A card game deals a hand of numbered cards, and the player wants to split the whole hand into groups of exactly W cards, where each group is a run of consecutive numbers, like 3-4-5. Is it possible? Greedy works because the choice is forced: the smallest card left can't be in the middle or at the end of any run (nothing smaller remains), so it must start a run. Take it and the next W − 1 consecutive values, fail if any is missing, and repeat. An ordered map of counts makes "smallest card left" and "is x + 1 available?" cheap.

Example: [1, 2, 3, 6, 2, 3, 4, 7, 8], W = 3 → true ([1,2,3] [2,3,4] [6,7,8]).

Function signature

bool isNStraightHand(const vector<int>& hand, int groupSize);

Test cases

Input `(hand, W)`	Output	Explanation
`([1, 2, 3, 6, 2, 3, 4, 7, 8], 3)`	`true`	[1,2,3] [2,3,4] [6,7,8]
`([1, 2, 3, 4, 5], 4)`	`false`	5 cards can't form groups of 4
`([1, 1, 2, 2, 3, 3], 3)`	`true`	Two runs of 1-2-3
`([1, 2, 4], 3)`	`false`	The size fits, but 3 is missing
`([1], 1)`	`true`

(Confirm: every card must be used; groups are runs of consecutive values of length exactly W.)

How interviewers phrase it

"Return true if the hand can be rearranged into groups of groupSize consecutive cards" (LeetCode 846; the same as LeetCode 1296 "Divide Array in Sets of K Consecutive Numbers").

Clarifying questions to ask

Must every card be used? (Yes.)
Can cards repeat? (Yes.)
How large are the values? (Up to 10⁹, so use a map, not an array.)

Follow-ups to expect

"Why must the smallest card start a group?"
"What's the quick rejection?"
"How does a min-heap version work?"
"Can it be O(n)-ish after sorting?"
"Complexity?"

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