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Given an array arr, you need to find the number of distinct values that can be obtained by taking the bitwise OR of all possible subarrays (non-empty) of arr.

Clarifying Questions

1. What is the range of the array arr?
   • The array can have a length n where 1 <= n <= 50000.
2. What are the constraints on the elements of the array?
   • Each element of the array will be an integer in the range from 0 to 10^9.
3. Do we need to return the count or the distinct values themselves?
   • We need to return the count of distinct values.

Strategy

1. Understanding the Bitwise OR:
   • The bitwise OR of two integers is a binary operation that results in a number where each bit is set to 1 if at least one of the corresponding bits of the operands is 1.
2. Generate Subarrays and Compute OR:
   • Instead of generating all possible subarrays explicitly, we can use a more efficient approach by maintaining a set of results from the previous iteration and only extending these to new subarrays by including the current element.
3. Efficient Calculation:
   • For each new element in the array, combine it with all results obtained from the previous elements using the OR operation.
   • Keep a set to track the values generated in the current iteration, then merge this into a global set of all possible results.

Implementation

Here’s how you can implement this strategy:

def subarrayBitwiseORs(arr):
    res = set()  # To hold all distinct OR results
    cur = set()  # Current set of OR results
    
    for num in arr:
        cur = {num | x for x in cur} | {num}  # Include the number itself and OR with all previous results
        res |= cur  # Merge current OR results into the global set of results
        
    return len(res)  # Return the count of distinct OR results

# Example usage:
# arr = [1, 2, 4]
# print(subarrayBitwiseORs(arr))  # Output should be the count of distinct bitwise OR results

Time Complexity

• Time Complexity: The worst-case scenario involves creating up to O(n) new OR results at each step, leading to a total complexity of O(n^2). However, the union operations with sets help reduce redundancy.

• Space Complexity: The space required is O(n) for tracking current OR results, but the total space utilized can grow due to the set of distinct results.

The strategy and approach ensure that the problem is dealt with in an efficient manner, suitable for the given constraints.

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