Split Array Into Maximum Number of Subarrays

Problem Description

You are given an array nums consisting of non-negative integers. We define the score of subarray nums[l..r] as nums[l] AND nums[l + 1] AND ... AND nums[r], where AND is the bitwise AND operation. Consider splitting the array into one or more subarrays such that the following conditions are satisfied:

• Each element of the array belongs to exactly one subarray.
• The sum of scores of the subarrays is the minimum possible.

Return the maximum number of subarrays in a split that satisfies the conditions above.

Key Insights

• The score of a subarray is determined by the bitwise AND operation.
• A score of 0 can be achieved by including any zero in the subarray.
• The goal is to maximize the number of subarrays while keeping the total score as low as possible.
• Each time a subarray is formed with a score of 0, it can potentially increase the count of subarrays.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

The approach involves iterating through the array and maintaining the current score of the subarray using the bitwise AND operation. Whenever the score becomes zero, it's optimal to start a new subarray. This greedy approach ensures that we maximize the number of subarrays while keeping the total score at a minimum.

1. Initialize a counter for subarrays and a variable to store the current AND score as the first element of the array.
2. Loop through each element in the array starting from the second element.
3. For each element, update the current AND score.
4. If the current AND score becomes zero, increment the subarray counter and reset the current AND score to the current element.
5. After the loop, increment the counter for the last remaining subarray if it exists.
6. Return the total count of subarrays.

Code Solutions