Divide Array in Sets of K Consecutive Numbers

Problem Description

Given an array of integers nums and a positive integer k, check whether it is possible to divide this array into sets of k consecutive numbers. Return true if it is possible. Otherwise, return false.

Key Insights

• The total number of elements in nums must be divisible by k.
• We can use a frequency map to count occurrences of each number.
• By repeatedly forming sets of k consecutive numbers from the smallest available number, we can determine if partitioning is possible.
• Sorting the unique numbers helps in easily grouping them into consecutive sets.

Space and Time Complexity

Time Complexity: O(N log N) - due to sorting the unique elements. Space Complexity: O(N) - for storing the frequency map.

Solution

To solve this problem, we utilize a frequency map (hash table) to count the occurrences of each number in the array. We then sort the unique numbers and attempt to form sets of k consecutive numbers starting from the smallest number available. If at any point we cannot form a complete set, we return false. If we can form all sets successfully, we return true.

Code Solutions