Problem Description
You are given an array nums of length n and an integer m. You need to determine if it is possible to split the array into n arrays of size 1 by performing a series of steps.
An array is called good if:
- The length of the array is one, or
- The sum of the elements of the array is greater than or equal to
m.
In each step, you can select an existing array (which may be the result of previous steps) with a length of at least two and split it into two arrays, if both resulting arrays are good.
Return true if you can split the given array into n arrays, otherwise return false.
Key Insights
- An array of size 1 is always good.
- To split an array into two good arrays, both resulting parts must either be of size 1 or have a sum greater than or equal to
m. - The total sum of all elements in the array plays a crucial role in determining the possibility of splits.
- If the total sum of the array is less than
m, it is impossible to split into good arrays.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
The solution involves calculating the total sum of the array. If the total sum is less than m, we immediately return false. Otherwise, we check if there are enough elements that can be split into good arrays. We can utilize a greedy approach to determine if we can keep splitting elements while ensuring each split results in good arrays.