Problem Description

Given an array nums of length n, the task is to return an array answer of length n - 1 such that answer[i] = nums[i] | nums[i + 1], where | denotes the bitwise OR operation. Basically, for each pair of consecutive elements in the nums array, compute their bitwise OR and form the resultant array answer.

Intuition

The core idea behind this solution is rooted in understanding how the bitwise OR operation functions. The bitwise OR operation between two integers results in a new integer having bits set wherever either of the input integers has a bit set. Therefore, computing nums[i] | nums[i + 1] for each i means producing a new sequence where each element captures the "combined" presence of set bits in two consecutive elements of the original array.

To solve the problem, you iterate through the nums array, excluding the last element to avoid going out of bounds while accessing the next element. During each iteration, compute the OR between the current element and the next, and append the result to the answer list. The process is repeated for all pairs of consecutive elements in nums.

Solution Approach

To implement the solution, the approach involves iterating through the nums array and computing the bitwise OR for each pair of consecutive elements. This operation is very efficient with a time complexity of O(n) where n is the length of the nums array. This is because it involves a single loop that processes every element once.

Here's a step-by-step breakdown of the process:

1. Initialize: Start by creating an empty list answer to store the results of the OR operations.

2. Iterate: Use a loop to go through the list nums from the first element to the second-to-last element. For each index i, compute the result of nums[i] | nums[i + 1] and add it to the answer list.

3. Return: Once the loop completes, the answer list will contain the desired results, so return this list.

The solution can be implemented succinctly in Python using list comprehension. The pairwise function helps to generate pairs of consecutive elements from the nums array. Here's the implementation:

class Solution:
    def orArray(self, nums: List[int]) -> List[int]:
        return [a | b for a, b in pairwise(nums)]

This code uses pairwise from the itertools module in Python for generating consecutive element pairs, then performs the OR operation on each pair, and collects the results in a list.

Example Walkthrough

Let's consider a simple example where the input array nums is [1, 2, 3, 4]. We need to compute the result array answer, where each element is the bitwise OR of consecutive elements in nums.

1. Initialize: Start with an empty list for the result, answer = [].

2. Iterate through nums:

   • For i = 0, compute nums[0] | nums[1] which is 1 | 2 = 3. Append this to answer, resulting in answer = [3].
   • For i = 1, compute nums[1] | nums[2] which is 2 | 3 = 3. Append this to answer, updating it to answer = [3, 3].
   • For i = 2, compute nums[2] | nums[3] which is 3 | 4 = 7. Append this, yielding answer = [3, 3, 7].

3. Return answer: After processing all consecutive pairs, the final answer array is [3, 3, 7].

This step-by-step walk-through demonstrates the procedure of using bitwise OR on consecutive elements as specified in solving the problem. The efficiency comes from the ability to transform the entire array using a single loop with constant time operations per element pair.

Solution Implementation

Time and Space Complexity

The time complexity of the code is O(n), where n is the length of the input list nums. This is because the pairwise operation and list comprehension iterate through the list a single time to generate the result.

The space complexity is O(1), ignoring the space required for the output list. This assumes that no additional space proportional to the input size is being used other than the list to store the results.

Learn more about how to find time and space complexity quickly.