Hand of Straights

Signal

"Split into consecutive-run groups" over a multiset of values is greedy by necessity: whatever the smallest remaining card is, it must be the start of some group — nothing smaller exists to pair it with a run beginning earlier.

Approach

Count each card's frequency. Repeatedly look at the smallest value that still has a positive count, and consume one card each of that value through value + W - 1 to form a group. If any of those W required values is missing (count is zero), the hand can't be split. Keep doing this until every count reaches zero.

Skeleton

counts = Counter(hand)
for start in sorted(counts):
    need = counts[start]
    if need <= 0: continue
    for v in range(start, start + W):
        if counts[v] < need: return False
        counts[v] -= need
return True

Solution

from collections import Counter

def is_n_straight_hand(hand: list[int], group_size: int) -> bool:
    if len(hand) % group_size != 0:
        return False

    counts = Counter(hand)
    for start in sorted(counts):
        need = counts[start]
        if need <= 0:
            continue
        for v in range(start, start + group_size):
            if counts[v] < need:
                return False
            counts[v] -= need
    return True

Complexity

O(n log n) time — dominated by sorting the distinct values; the group-forming sweep itself is O(n · W) in the worst case. O(n) space for the counts.

Pitfalls

• Iterating sorted(counts) once and using each value's current remaining count as need (rather than re-scanning for the global minimum each time) is what keeps this from becoming quadratic re-sorting.
• Forgetting the early len(hand) % group_size != 0 check wastes work — an uneven total can never split evenly, no matter what the values are.
• This greedily commits to using the smallest remaining card as a group start — that's provably safe here (no smaller card can ever need it later), which is exactly the kind of exchange-argument justification worth stating if an interviewer asks "why does greedy work here?"