Hand of Straights

Problem Description

Alice has some number of cards and she wants to rearrange the cards into groups so that each group is of size groupSize, and consists of groupSize consecutive cards. Given an integer array hand where hand[i] is the value written on the i-th card and an integer groupSize, return true if she can rearrange the cards, or false otherwise.

Key Insights

• The total number of cards must be divisible by groupSize to form complete groups.
• Using a frequency map (or hash table) helps count occurrences of each card value.
• Sorting the unique card values allows for efficient grouping of consecutive cards.
• A greedy approach is employed where we try to form groups starting from the smallest card available.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the hand array. Space Complexity: O(n) - for storing the frequency of card values.

Solution

To determine if the cards can be rearranged into groups of consecutive numbers, we can follow these steps:

1. Check if the length of the hand array is divisible by groupSize. If not, return false.
2. Create a frequency map to count occurrences of each card value.
3. Sort the unique card values from the frequency map.
4. Iterate through the sorted card values and attempt to form groups of size groupSize using the frequency map.
5. For each group, decrement the counts in the frequency map accordingly. If at any point we cannot form a complete group, return false.
6. If all groups are formed successfully, return true.

Code Solutions