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You are given an array of positive integers nums.You need to select a subset of nums which satisfies the following condition:You can place the selected elements in a 0-indexed array such that it follows the pattern: [x, x2, x4, ..., xk/2, xk, xk/2, ..., x4, x2, x] (Note that k can be be any non-negative power of 2). For example, [2, 4, 16, 4, 2] and [3, 9, 3] follow the pattern while [2, 4, 8, 4, 2] does not.Return the maximum number of elements in a subset that satisfies these conditions.

Question

You are given an array of positive integers nums.You need to select a subset of nums which satisfies the following condition:You can place the selected elements in a 0-indexed array such that it follows the pattern: [x, x2, x4, ..., xk/2, xk, xk/2, ..., x4, x2, x] (Note that k can be be any non-negative power of 2). For example, [2, 4, 16, 4, 2] and [3, 9, 3] follow the pattern while [2, 4, 8, 4, 2] does not.Return the maximum number of elements in a subset that satisfies these conditions.

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Solution

The problem can be solved by using a hash map and a greedy algorithm. Here are the steps:

  1. Initialize a hash map to count the frequency of each number in the array.

  2. Sort the array in ascending order.

  3. Initialize a variable maxCount to 0. This variable will keep track of the maximum number of elements that can be included in the subset.

  4. Iterate over the sorted array. For each number x, check if x/2 is present in the hash map. If it is, then x can be included in the subset. Update the hash map by decrementing the count of x/2 and incrementing the count of x. Also, update maxCount to be the maximum of maxCount and the count of x.

  5. After iterating over the array, maxCount will be the maximum number of elements that can be included in the subset.

Here is a Python code snippet that implements the above steps:

def maxElements(nums):
    count = collections.Counter(nums)
    nums.sort()
    maxCount = 0
    for x in nums:
        if x % 2 == 0 and count[x // 2] > 0:
            count[x // 2] -= 1
            count[x] += 1
        maxCount = max(maxCount, count[x])
    return maxCount

This function takes as input a list of positive integers nums and returns the maximum number of elements that can be included in a subset that satisfies the given conditions. The time complexity of this function is O(n log n) due to the sorting operation, where n is the length of the input array. The space complexity is O(n) for storing the count of each number in the hash map.

This problem has been solved

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