How do you solve Find if Array Can Be Sorted on LeetCode?

Find if Array Can Be Sorted (LeetCode #3011) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Elements can only be swapped if they have the same number of set bits.

What is the time complexity of Find if Array Can Be Sorted?

The optimal solution for Find if Array Can Be Sorted runs in O(n log n) time and uses O(n) space. The sorting step dominates the complexity, making it O(n log n) due to the sort operation on the categorized list.

What is the brute force solution for Find if Array Can Be Sorted?

The brute force approach for Find if Array Can Be Sorted is Brute Force, with O(n²) time complexity and O(1) space complexity. We can try to sort the array by repeatedly swapping adjacent elements that have the same number of set bits. This approach is straightforward but inefficient as it checks every possible swap. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Find if Array Can Be Sorted?

Find if Array Can Be Sorted uses the following concepts: Array, Bit Manipulation, Sorting. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Find if Array Can Be Sorted?

Always clarify the problem constraints and requirements. Think about edge cases, such as already sorted arrays. Explain your thought process clearly while coding.

What are common mistakes when solving Find if Array Can Be Sorted?

Failing to correctly count the number of set bits. Not considering the order of elements after sorting.

#3011

Find if Array Can Be Sorted

Medium

ArrayBit ManipulationSortingHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

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

Instead of trying to sort the array through swaps, we can categorize the elements based on their set bits and check if we can arrange them in a sorted manner based on these categories.

⚙️

Algorithm

3 steps

1Step 1: Create a list of tuples where each tuple contains the number of set bits and the original value of the element.
2Step 2: Sort this list based on the number of set bits first and then by the original values.
3Step 3: Check if the sorted list maintains the order of the original values.

solution.py9 lines

1# Full working Python code
2
3def count_set_bits(n):
4    return bin(n).count('1')
5
6def can_sort(nums):
7    sorted_nums = sorted(nums)
8    categorized = sorted((count_set_bits(num), num) for num in nums)
9    return all(categorized[i][1] == sorted_nums[i] for i in range(len(nums)))

ℹ

Complexity note: The sorting step dominates the complexity, making it O(n log n) due to the sort operation on the categorized list.

1Elements can only be swapped if they have the same number of set bits.
2Sorting can be achieved by categorizing elements based on their set bits.

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