846. Hand of Straights - Explanation

Description

You are given an integer array hand where hand[i] is the value written on the ith card and an integer groupSize.

You want to rearrange the cards into groups so that each group is of size groupSize, and card values are consecutively increasing by 1.

Return true if it's possible to rearrange the cards in this way, otherwise, return false.

Example 1:

Input: hand = [1,2,4,2,3,5,3,4], groupSize = 4

Output: true

Explanation: The cards can be rearranged as [1,2,3,4] and [2,3,4,5].

Example 2:

Input: hand = [1,2,3,3,4,5,6,7], groupSize = 4

Output: false

Explanation: The closest we can get is [1,2,3,4] and [3,5,6,7], but the cards in the second group are not consecutive.

Constraints:

1 <= hand.length <= 1000
0 <= hand[i] <= 1000
1 <= groupSize <= hand.length

Topics

Recommended Time & Space Complexity

You should aim for a solution as good or better than O(nlogn) time and O(n) space, where n is the size of the input array.

Hint 1

It is observed that to form a group, the minimum value should be the starting value of the group. Additionally, the minimum value in the array serves as the starting value for one or more groups based on its frequency. Can you think of an efficient way to determine the frequencies of array elements? Maybe a specific data structure can be useful here.

Hint 2

We can use a hash map to store the elements along with their frequencies. Additionally, we sort the given array. Then, we iterate through the sorted array and try to form groups by decrementing the frequency count. If we fail to form a group at any step, we immediately return false. Can you think why this works?

Hint 3

Sorting ensures we start with the smallest available value, while the hash map helps track element availability using frequency counts. At each step, we pick the smallest available value x and attempt to form a group from x to x + groupSize - 1. If all elements are present based on their frequency counts, we decrement their counts as we iterate. If we successfully form all groups, we return true; otherwise, we return false.

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Prerequisites

Before attempting this problem, you should be comfortable with:

Hash Maps - Using frequency maps to count occurrences and track available elements
Sorting - Processing elements in sorted order to greedily form consecutive groups
Greedy Algorithms - Always starting groups from the smallest available element to ensure valid consecutive sequences
Heaps (Priority Queues) - Efficiently retrieving and removing the minimum element when forming groups

1. Sorting

Intuition

We are given a hand of cards and a group size. The goal is to check whether we can divide all cards into groups of size groupSize such that:

each group consists of consecutive numbers
every card is used exactly once

A simple and intuitive way to approach this is:

always try to form groups starting from the smallest available card
once we start a group at a number x, we must also have x + 1, x + 2, ..., x + groupSize - 1

Sorting the hand helps because it ensures we always process cards in increasing order, which naturally enforces the consecutive requirement.

A frequency map count helps us track how many times each card is still available.

Algorithm

If the total number of cards is not divisible by groupSize:
- return false immediately (grouping is impossible)
Count the frequency of each card value using a map.
Sort the hand in increasing order.
Iterate through each card value in the sorted hand:
- If the current card is already used up (its count is 0), skip it
- Otherwise, try to form a group starting from this card
To form a group starting at num:
- For every value from num to num + groupSize - 1:
  - If that value does not exist in the count map, return false
  - Otherwise, decrement its count by 1
If all cards are successfully grouped without failure:
- return true

class Solution:
    def isNStraightHand(self, hand, groupSize):
        if len(hand) % groupSize:
            return False

        count = Counter(hand)
        hand.sort()
        for num in hand:
            if count[num]:
                for i in range(num, num + groupSize):
                    if not count[i]:
                        return False
                    count[i] -= 1
        return True

public class Solution {
    public boolean isNStraightHand(int[] hand, int groupSize) {
        if (hand.length % groupSize != 0) return false;

        Map<Integer, Integer> count = new HashMap<>();
        for (int num : hand) {
            count.put(num, count.getOrDefault(num, 0) + 1);
        }

        Arrays.sort(hand);
        for (int num : hand) {
            if (count.get(num) > 0) {
                for (int i = num; i < num + groupSize; i++) {
                    if (count.getOrDefault(i, 0) == 0) return false;
                    count.put(i, count.get(i) - 1);
                }
            }
        }
        return true;
    }
}

class Solution {
public:
    bool isNStraightHand(vector<int>& hand, int groupSize) {
        if (hand.size() % groupSize != 0) return false;

        unordered_map<int, int> count;
        for (int num : hand) count[num]++;

        sort(hand.begin(), hand.end());
        for (int num : hand) {
            if (count[num] > 0) {
                for (int i = num; i < num + groupSize; i++) {
                    if (count[i] == 0) return false;
                    count[i]--;
                }
            }
        }
        return true;
    }
};

class Solution {
    /**
     * @param {number[]} hand
     * @param {number} groupSize
     * @return {boolean}
     */
    isNStraightHand(hand, groupSize) {
        if (hand.length % groupSize !== 0) {
            return false;
        }

        const count = {};
        for (const num of hand) {
            count[num] = (count[num] || 0) + 1;
        }

        hand.sort((a, b) => a - b);
        for (const num of hand) {
            if (count[num] > 0) {
                for (let i = num; i < num + groupSize; i++) {
                    if (!count[i]) return false;
                    count[i] -= 1;
                }
            }
        }
        return true;
    }
}

public class Solution {
    public bool IsNStraightHand(int[] hand, int groupSize) {
        if (hand.Length % groupSize != 0) return false;

        var count = new Dictionary<int, int>();
        foreach (var num in hand) {
            count[num] = count.GetValueOrDefault(num, 0) + 1;
        }

        Array.Sort(hand);
        foreach (var num in hand) {
            if (count[num] > 0) {
                for (int i = num; i < num + groupSize; i++) {
                    if (!count.ContainsKey(i) || count[i] == 0) {
                        return false;
                    }
                    count[i]--;
                }
            }
        }
        return true;
    }
}

func isNStraightHand(hand []int, groupSize int) bool {
    if len(hand)%groupSize != 0 {
        return false
    }

    count := map[int]int{}
    for _, num := range hand {
        count[num]++
    }

    sort.Ints(hand)
    for _, num := range hand {
        if count[num] > 0 {
            for i := num; i < num+groupSize; i++ {
                if count[i] == 0 {
                    return false
                }
                count[i]--
            }
        }
    }
    return true
}

class Solution {
    fun isNStraightHand(hand: IntArray, groupSize: Int): Boolean {
        if (hand.size % groupSize != 0) return false

        val count = HashMap<Int, Int>()
        hand.forEach { count[it] = count.getOrDefault(it, 0) + 1 }
        hand.sort()

        for (num in hand) {
            if (count[num]!! > 0) {
                for (i in num until num + groupSize) {
                    if (count.getOrDefault(i, 0) == 0) {
                        return false
                    }
                    count[i] = count[i]!! - 1
                }
            }
        }
        return true
    }
}

class Solution {
    func isNStraightHand(_ hand: [Int], _ groupSize: Int) -> Bool {
        if hand.count % groupSize != 0 {
            return false
        }

        var count = [Int: Int]()
        for num in hand {
            count[num, default: 0] += 1
        }

        let sortedHand = hand.sorted()
        for num in sortedHand {
            if let freq = count[num], freq > 0 {
                for i in num..<(num + groupSize) {
                    if let f = count[i], f > 0 {
                        count[i] = f - 1
                    } else {
                        return false
                    }
                }
            }
        }

        return true
    }
}

Time & Space Complexity

Time complexity: $O(n \log n)$
Space complexity: $O(n)$

2. Heap

Intuition

We need to split the cards into groups of size groupSize, where each group is made of consecutive numbers, and every card is used exactly once.

A good strategy is to always start building a group from the smallest card value that is still available.
If we can always extend that smallest value into a full consecutive group, then the hand is valid.

To do this efficiently:

we store frequencies of each card in a map count
we keep a min-heap of the available card values so we can always get the current smallest value quickly

When we start a group from first (the smallest value in the heap), we must use:
first, first+1, ..., first+groupSize-1

If at any point a required value is missing, grouping is impossible.

The heap also helps ensure we remove values in the correct order when their count reaches zero.

Algorithm

If the total number of cards is not divisible by groupSize, return false.
Build a frequency map count where count[x] is how many times card x appears.
Put all distinct card values into a min-heap minH.
While the heap is not empty:
- Let first be the smallest available value (minH[0])
- Try to build one group starting at first
For every value i from first to first + groupSize - 1:
- If i is not in count, return false (missing a needed card)
- Decrease count[i] by 1 because we use one card of value i
- If count[i] becomes 0:
  - it must be the smallest value currently in the heap
  - otherwise, we are trying to remove numbers out of order, which means grouping breaks
  - pop it from the heap
If we process all groups successfully, return true

class Solution:
    def isNStraightHand(self, hand: List[int], groupSize: int) -> bool:
        if len(hand) % groupSize:
            return False

        count = {}
        for n in hand:
            count[n] = 1 + count.get(n, 0)

        minH = list(count.keys())
        heapq.heapify(minH)
        while minH:
            first = minH[0]
            for i in range(first, first + groupSize):
                if i not in count:
                    return False
                count[i] -= 1
                if count[i] == 0:
                    if i != minH[0]:
                        return False
                    heapq.heappop(minH)
        return True

public class Solution {
    public boolean isNStraightHand(int[] hand, int groupSize) {
        if (hand.length % groupSize != 0)
            return false;

        Map<Integer, Integer> count = new HashMap<>();
        for (int n : hand)
            count.put(n, 1 + count.getOrDefault(n, 0));

        PriorityQueue<Integer> minH = new PriorityQueue<>(count.keySet());
        while (!minH.isEmpty()) {
            int first = minH.peek();
            for (int i = first; i < first + groupSize; i++) {
                if (!count.containsKey(i))
                    return false;
                count.put(i, count.get(i) - 1);
                if (count.get(i) == 0) {
                    if (i != minH.peek())
                        return false;
                    minH.poll();
                }
            }
        }
        return true;
    }
}

class Solution {
public:
    bool isNStraightHand(vector<int>& hand, int groupSize) {
        if (hand.size() % groupSize != 0)
            return false;

        unordered_map<int, int> count;
        for (int n : hand)
            count[n] = 1 + count[n];

        priority_queue<int, vector<int>, greater<int>> minH;
        for (auto& pair : count)
            minH.push(pair.first);

        while (!minH.empty()) {
            int first = minH.top();
            for (int i = first; i < first + groupSize; i++) {
                if (count.find(i) == count.end())
                    return false;
                count[i] -= 1;
                if (count[i] == 0) {
                    if (i != minH.top())
                        return false;
                    minH.pop();
                }
            }
        }
        return true;
    }
};

/**
 * const { MinPriorityQueue } = require('@datastructures-js/priority-queue');
 */

class Solution {
    /**
     * @param {number[]} hand
     * @param {number} groupSize
     * @return {boolean}
     */
    isNStraightHand(hand, groupSize) {
        if (hand.length % groupSize !== 0) {
            return false;
        }

        const count = {};
        for (const n of hand) {
            count[n] = (count[n] || 0) + 1;
        }

        const minPQ = new MinPriorityQueue();
        for (const key in count) {
            minPQ.push(Number(key));
        }

        while (!minPQ.isEmpty()) {
            const first = minPQ.front();
            for (let i = first; i < first + groupSize; i++) {
                if (!(i in count) || count[i] === 0) {
                    return false;
                }
                count[i] -= 1;
                if (count[i] === 0) {
                    if (i !== minPQ.front()) {
                        return false;
                    }
                    minPQ.pop();
                }
            }
        }
        return true;
    }
}

public class Solution {
    public bool IsNStraightHand(int[] hand, int groupSize) {
        if (hand.Length % groupSize != 0)
            return false;

        var count = new Dictionary<int, int>();
        foreach (int num in hand) {
            if (count.ContainsKey(num))
                count[num]++;
            else
                count[num] = 1;
        }

        var minH = new PriorityQueue<int, int>();
        foreach (var num in count.Keys)
            minH.Enqueue(num, num);

        while (minH.Count > 0) {
            int first = minH.Peek();
            for (int i = first; i < first + groupSize; i++) {
                if (!count.ContainsKey(i) || count[i] == 0)
                    return false;

                count[i]--;
                if (count[i] == 0) {
                    if (i != minH.Peek())
                        return false;
                    minH.Dequeue();
                }
            }
        }
        return true;
    }
}

func isNStraightHand(hand []int, groupSize int) bool {
    if len(hand)%groupSize != 0 {
        return false
    }

    count := map[int]int{}
    for _, n := range hand {
        count[n]++
    }

    minH := priorityqueue.NewWith(utils.IntComparator)
    for k := range count {
        minH.Enqueue(k)
    }

    for !minH.Empty() {
        first, _ := minH.Peek()
        firstKey := first.(int)
        for i := firstKey; i < firstKey+groupSize; i++ {
            if count[i] == 0 {
                return false
            }
            count[i]--
            if count[i] == 0 {
                if val, _ := minH.Peek(); val.(int) != i {
                    return false
                }
                minH.Dequeue()
            }
        }
    }
    return true
}

class Solution {
    fun isNStraightHand(hand: IntArray, groupSize: Int): Boolean {
        if (hand.size % groupSize != 0) return false

        val count = mutableMapOf<Int, Int>()
        for (n in hand) {
            count[n] = count.getOrDefault(n, 0) + 1
        }

        val minH = PriorityQueue(count.keys)
        while (minH.isNotEmpty()) {
            val first = minH.peek()
            for (i in first until first + groupSize) {
                if (count.getOrDefault(i, 0) == 0) return false
                count[i] = count[i]!! - 1
                if (count[i] == 0) {
                    if (i != minH.peek()) return false
                    minH.poll()
                }
            }
        }
        return true
    }
}

class Solution {
    func isNStraightHand(_ hand: [Int], _ groupSize: Int) -> Bool {
        if hand.count % groupSize != 0 {
            return false
        }

        var count = [Int: Int]()
        for n in hand {
            count[n, default: 0] += 1
        }

        var minH = Heap<Int>(Array(count.keys))

        while !minH.isEmpty {
            guard let first = minH.min else { return false }

            for i in first..<(first + groupSize) {
                guard let freq = count[i] else { return false }
                count[i] = freq - 1
                if count[i] == 0 {
                    if i != minH.min {
                        return false
                    }
                    minH.removeMin()
                }
            }
        }

        return true
    }
}

Time & Space Complexity

Time complexity: $O(n \log n)$
Space complexity: $O(n)$

3. Ordered Map

Intuition

We want to check if the cards can be divided into groups of size groupSize, where each group consists of consecutive numbers and every card is used exactly once.

Instead of explicitly forming each group, we can think in terms of how many groups are currently “open” and waiting to be extended.

As we process card values in increasing order:

some groups may already be open and expect the current number next
the current number can either:
- extend existing open groups
- or start new groups

The key idea is:

if there are open_groups waiting for the current number, we must have at least that many cards of the current value
any extra cards beyond extending existing groups will start new groups
each group must close exactly after groupSize consecutive numbers

A queue is used to remember how many new groups were started at each step, so we can close them after groupSize steps.

Algorithm

If the total number of cards is not divisible by groupSize, return false.
Count the frequency of each card using a map.
Iterate over the card values in sorted order.
Maintain:
- open_groups: number of groups currently waiting to be extended
- last_num: previous card value processed
- a queue q to track how many groups were started at each value
For each card value num:
- If there are open groups and num is not consecutive to last_num, return false
- If open_groups > count[num], return false (not enough cards to extend groups)
Calculate how many new groups start at num:
- new_groups = count[num] - open_groups
- Push new_groups into the queue
Update:
- last_num = num
- open_groups = count[num]
If the queue size reaches groupSize:
- pop from the queue and subtract that value from open_groups
- this closes groups that have reached length groupSize
After processing all numbers:
- return true only if open_groups == 0

class Solution:
    def isNStraightHand(self, hand, groupSize):
        if len(hand) % groupSize != 0:
            return False

        count = Counter(hand)
        q = deque()
        last_num, open_groups = -1, 0

        for num in sorted(count):
            if ((open_groups > 0 and num > last_num + 1) or
                open_groups > count[num]
            ):
                return False

            q.append(count[num] - open_groups)
            last_num = num
            open_groups = count[num]

            if len(q) == groupSize:
                open_groups -= q.popleft()

        return open_groups == 0

public class Solution {
    public boolean isNStraightHand(int[] hand, int groupSize) {
        if (hand.length % groupSize != 0) return false;

        Map<Integer, Integer> count = new TreeMap<>();
        for (int num : hand) {
            count.put(num, count.getOrDefault(num, 0) + 1);
        }

        Queue<Integer> q = new LinkedList<>();
        int lastNum = -1, openGroups = 0;

        for (int num : count.keySet()) {
            if ((openGroups > 0 && num > lastNum + 1) ||
                 openGroups > count.get(num)) {
                return false;
            }

            q.add(count.get(num) - openGroups);
            lastNum = num;
            openGroups = count.get(num);

            if (q.size() == groupSize) {
                openGroups -= q.poll();
            }
        }
        return openGroups == 0;
    }
}

class Solution {
public:
    bool isNStraightHand(vector<int>& hand, int groupSize) {
        if (hand.size() % groupSize != 0) return false;

        map<int, int> count;
        for (int num : hand) count[num]++;

        queue<int> q;
        int lastNum = -1, openGroups = 0;

        for (auto& entry : count) {
            int num = entry.first;
            if ((openGroups > 0 && num > lastNum + 1) ||
                 openGroups > count[num]) {
                return false;
            }

            q.push(count[num] - openGroups);
            lastNum = num;
            openGroups = count[num];

            if (q.size() == groupSize) {
                openGroups -= q.front();
                q.pop();
            }
        }
        return openGroups == 0;
    }
};

class Solution {
    /**
     * @param {number[]} hand
     * @param {number} groupSize
     * @return {boolean}
     */
    isNStraightHand(hand, groupSize) {
        if (hand.length % groupSize !== 0) return false;

        let count = new Map();
        hand.forEach((num) => count.set(num, (count.get(num) || 0) + 1));

        let q = new Queue();
        let lastNum = -1,
            openGroups = 0;

        Array.from(count.keys())
            .sort((a, b) => a - b)
            .forEach((num) => {
                if (
                    (openGroups > 0 && num > lastNum + 1) ||
                    openGroups > count.get(num)
                ) {
                    return false;
                }

                q.push(count.get(num) - openGroups);
                lastNum = num;
                openGroups = count.get(num);

                if (q.size() === groupSize) {
                    openGroups -= q.pop();
                }
            });

        return openGroups === 0;
    }
}

public class Solution {
    public bool IsNStraightHand(int[] hand, int groupSize) {
        if (hand.Length % groupSize != 0) return false;

        var count = new SortedDictionary<int, int>();
        foreach (int num in hand) {
            if (!count.ContainsKey(num)) count[num] = 0;
            count[num]++;
        }

        var q = new Queue<int>();
        int lastNum = -1, openGroups = 0;

        foreach (int num in count.Keys) {
            if ((openGroups > 0 && num > lastNum + 1) ||
                 openGroups > count[num]) {
                return false;
            }

            q.Enqueue(count[num] - openGroups);
            lastNum = num;
            openGroups = count[num];

            if (q.Count == groupSize) {
                openGroups -= q.Dequeue();
            }
        }
        return openGroups == 0;
    }
}

func isNStraightHand(hand []int, groupSize int) bool {
    if len(hand)%groupSize != 0 {
        return false
    }

    count := make(map[int]int)
    for _, num := range hand {
        count[num]++
    }

    keys := make([]int, 0, len(count))
    for k := range count {
        keys = append(keys, k)
    }
    sort.Ints(keys)

    q := []int{}
    lastNum, openGroups := -1, 0

    for _, num := range keys {
        if (openGroups > 0 && num > lastNum+1) ||
            openGroups > count[num] {
            return false
        }

        q = append(q, count[num]-openGroups)
        lastNum = num
        openGroups = count[num]

        if len(q) == groupSize {
            openGroups -= q[0]
            q = q[1:]
        }
    }
    return openGroups == 0
}

class Solution {
    fun isNStraightHand(hand: IntArray, groupSize: Int): Boolean {
        if (hand.size % groupSize != 0) return false

        val count = TreeMap<Int, Int>()
        for (num in hand) {
            count[num] = count.getOrDefault(num, 0) + 1
        }

        val q: Queue<Int> = LinkedList()
        var lastNum = -1
        var openGroups = 0

        for (num in count.keys) {
            if ((openGroups > 0 && num > lastNum + 1) ||
                 openGroups > count[num]!!) {
                return false
            }

            q.add(count[num]!! - openGroups)
            lastNum = num
            openGroups = count[num]!!

            if (q.size == groupSize) {
                openGroups -= q.poll()
            }
        }
        return openGroups == 0
    }
}

class Solution {
    func isNStraightHand(_ hand: [Int], _ groupSize: Int) -> Bool {
        if hand.count % groupSize != 0 {
            return false
        }

        var count = [Int: Int]()
        for num in hand {
            count[num, default: 0] += 1
        }

        var queue = Deque<Int>()
        var lastNum = -1
        var openGroups = 0

        for (num, numCount) in count.sorted(by: { $0.key < $1.key }) {
            if (openGroups > 0 && num > lastNum + 1) || openGroups > numCount {
                return false
            }

            queue.append(numCount - openGroups)
            lastNum = num
            openGroups = numCount

            if queue.count == groupSize {
                openGroups -= queue.removeFirst()
            }
        }
        return openGroups == 0
    }
}

Time & Space Complexity

Time complexity: $O(n \log n)$
Space complexity: $O(n)$

4. Hash Map

Intuition

We need to split the hand into groups of size groupSize, where each group is made of consecutive numbers and every card is used exactly once.

This approach uses only a frequency map and a simple rule:

Any valid group must start at the beginning of a consecutive run
So for a given number num, we first walk left to find the earliest possible start of its run
(we keep moving left while start - 1 still exists in the hand)
Once we know a possible start, we try to repeatedly form consecutive groups starting from that start:
- while there are still cards at start, we build a group:
  start, start+1, ..., start+groupSize-1
- decrement counts as we use cards

By always forming groups from the earliest start in a run, we avoid skipping needed smaller cards and ensure groups remain consecutive.

Algorithm

If len(hand) is not divisible by groupSize, return false.
Build a frequency map count for all card values.
For each card value num in the hand:
- Find the earliest start of the consecutive run containing num:
  - set start = num
  - while count[start - 1] > 0, decrement start
For every possible start up to num:
- While count[start] > 0:
  - Try to create one full group starting at start
  - For each i from start to start + groupSize - 1:
    - If count[i] == 0, return false (missing a needed card)
    - Otherwise decrement count[i]
- Move start forward by 1 and continue
If all groups are formed successfully, return true.

class Solution:
    def isNStraightHand(self, hand: List[int], groupSize: int) -> bool:
        if len(hand) % groupSize != 0:
            return False

        count = Counter(hand)
        for num in hand:
            start = num
            while count[start - 1]:
                start -= 1
            while start <= num:
                while count[start]:
                    for i in range(start, start + groupSize):
                        if not count[i]:
                            return False
                        count[i] -= 1
                start += 1
        return True

public class Solution {
    public boolean isNStraightHand(int[] hand, int groupSize) {
        if (hand.length % groupSize != 0) return false;

        Map<Integer, Integer> count = new HashMap<>();
        for (int num : hand) {
            count.put(num, count.getOrDefault(num, 0) + 1);
        }

        for (int num : hand) {
            int start = num;
            while (count.getOrDefault(start - 1, 0) > 0) start--;
            while (start <= num) {
                while (count.getOrDefault(start, 0) > 0) {
                    for (int i = start; i < start + groupSize; i++) {
                        if (count.getOrDefault(i, 0) == 0) return false;
                        count.put(i, count.get(i) - 1);
                    }
                }
                start++;
            }
        }
        return true;
    }
}

class Solution {
public:
    bool isNStraightHand(vector<int>& hand, int groupSize) {
        if (hand.size() % groupSize != 0) return false;

        unordered_map<int, int> count;
        for (int num : hand) count[num]++;

        for (int num : hand) {
            int start = num;
            while (count[start - 1] > 0) start--;
            while (start <= num) {
                while (count[start] > 0) {
                    for (int i = start; i < start + groupSize; i++) {
                        if (count[i] == 0) return false;
                        count[i]--;
                    }
                }
                start++;
            }
        }
        return true;
    }
};

class Solution {
    /**
     * @param {number[]} hand
     * @param {number} groupSize
     * @return {boolean}
     */
    isNStraightHand(hand, groupSize) {
        if (hand.length % groupSize !== 0) return false;

        const count = new Map();
        hand.forEach((num) => count.set(num, (count.get(num) || 0) + 1));

        for (const num of hand) {
            let start = num;
            while (count.get(start - 1) > 0) start--;
            while (start <= num) {
                while (count.get(start) > 0) {
                    for (let i = start; i < start + groupSize; i++) {
                        if (!count.get(i)) return false;
                        count.set(i, count.get(i) - 1);
                    }
                }
                start++;
            }
        }
        return true;
    }
}

public class Solution {
    public bool IsNStraightHand(int[] hand, int groupSize) {
        if (hand.Length % groupSize != 0) return false;

        Dictionary<int, int> count = new Dictionary<int, int>();
        foreach (int num in hand) {
            if (!count.ContainsKey(num)) count[num] = 0;
            count[num]++;
        }

        foreach (int num in hand) {
            int start = num;
            while (count.ContainsKey(start - 1) && count[start - 1] > 0) {
                start--;
            }
            while (start <= num) {
                while (count.ContainsKey(start) && count[start] > 0) {
                    for (int i = start; i < start + groupSize; i++) {
                        if (!count.ContainsKey(i) || count[i] == 0) {
                            return false;
                        }
                        count[i]--;
                    }
                }
                start++;
            }
        }
        return true;
    }
}

func isNStraightHand(hand []int, groupSize int) bool {
    if len(hand)%groupSize != 0 {
        return false
    }

    count := map[int]int{}
    for _, num := range hand {
        count[num]++
    }

    for _, num := range hand {
        start := num
        for count[start-1] > 0 {
            start--
        }

        for start <= num {
            for count[start] > 0 {
                for i := start; i < start+groupSize; i++ {
                    if count[i] == 0 {
                        return false
                    }
                    count[i]--
                }
            }
            start++
        }
    }
    return true
}

class Solution {
    fun isNStraightHand(hand: IntArray, groupSize: Int): Boolean {
        if (hand.size % groupSize != 0) return false

        val count = HashMap<Int, Int>()
        hand.forEach { count[it] = count.getOrDefault(it, 0) + 1 }

        for (num in hand) {
            var start = num
            while (count.getOrDefault(start - 1, 0) > 0) {
                start--
            }

            while (start <= num) {
                while (count.getOrDefault(start, 0) > 0) {
                    for (i in start until start + groupSize) {
                        if (count.getOrDefault(i, 0) == 0) {
                            return false
                        }
                        count[i] = count[i]!! - 1
                    }
                }
                start++
            }
        }
        return true
    }
}

class Solution {
    func isNStraightHand(_ hand: [Int], _ groupSize: Int) -> Bool {
        if hand.count % groupSize != 0 {
            return false
        }

        var count = [Int: Int]()
        for num in hand {
            count[num, default: 0] += 1
        }

        for num in hand {
            var start = num
            while (count[start - 1] ?? 0) > 0 {
                start -= 1
            }
            while start <= num {
                while (count[start] ?? 0) > 0 {
                    for i in start..<(start + groupSize) {
                        if (count[i] ?? 0) == 0 {
                            return false
                        }
                        count[i]! -= 1
                    }
                }
                start += 1
            }
        }

        return true
    }
}

Time & Space Complexity

Time complexity: $O(n)$
Space complexity: $O(n)$

Common Pitfalls

Forgetting to Check Divisibility First

If the total number of cards is not divisible by groupSize, it is impossible to form complete groups. Skipping this initial check wastes time processing the array and may lead to subtle bugs where the algorithm appears to succeed but produces an invalid grouping.

Not Starting Groups from the Smallest Available Card

Groups must be formed starting from the smallest available card value to ensure consecutive sequences work correctly. Starting from an arbitrary card can leave smaller cards stranded without enough consecutive neighbors to form a valid group. Always process cards in sorted order or use a min-heap to find the smallest available value.

Failing to Decrement Counts Properly

When forming a group, each card in the consecutive sequence must have its count decremented. A common bug is forgetting to decrement or decrementing the wrong key, which causes cards to be reused or leaves cards unused. Additionally, when a card's count reaches zero, it must be handled correctly to avoid checking for cards that no longer exist.