What is the time complexity of Apply Operations on Array to Maximize Sum of Squares?

The optimal solution for Apply Operations on Array to Maximize Sum of Squares runs in O(n log n) time and uses O(1) space. The time complexity is O(n log n) due to the sorting step, which is much more efficient than the O(n²) of the brute force approach.

What is the brute force solution for Apply Operations on Array to Maximize Sum of Squares?

The brute force approach for Apply Operations on Array to Maximize Sum of Squares is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves trying all possible pairs of indices to apply the AND and OR operations. This will allow us to explore all potential outcomes of the array, but it's inefficient due to the large number of operations. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Apply Operations on Array to Maximize Sum of Squares?

Apply Operations on Array to Maximize Sum of Squares uses the following concepts: Array, Hash Table, Greedy, Bit Manipulation. The recommended patterns to study are: Greedy Algorithms, Sorting, Array Manipulation.

What are the interview tips for Apply Operations on Array to Maximize Sum of Squares?

Always think about how to maximize or minimize values in array problems. Consider edge cases, such as when k equals the length of the array. Practice explaining your thought process clearly, as this is often as important as the solution itself.

What are common mistakes when solving Apply Operations on Array to Maximize Sum of Squares?

Not considering the impact of the AND and OR operations on the overall array. Failing to sort the array before selecting the k largest elements.

#2897

Apply Operations on Array to Maximize Sum of Squares

Hard

ArrayHash TableGreedyBit ManipulationGreedy AlgorithmsSortingArray Manipulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(1)

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Intuition

Time O(n log n)Space O(1)

Instead of brute-forcing through all pairs, we can recognize that the AND and OR operations can be used to maximize individual elements. The goal is to maximize the largest k elements in the array, which can be achieved by applying the operations strategically.

⚙️

Algorithm

3 steps

1Step 1: Identify the maximum element in the array, as it will contribute the most to the sum of squares.
2Step 2: Use the AND and OR operations to combine elements to maximize the largest values.
3Step 3: After maximizing, sort the array and select the k largest elements to compute their sum of squares.

solution.py3 lines

1def maxSumOfSquares(nums, k):
2    nums.sort(reverse=True)
3    return sum(x*x for x in nums[:k]) % (10**9 + 7)

ℹ

Complexity note: The time complexity is O(n log n) due to the sorting step, which is much more efficient than the O(n²) of the brute force approach.

1The AND and OR operations can be used to manipulate the bits of numbers to maximize their values.
2Greedily maximizing the largest elements in the array will yield the highest sum of squares.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.