How do you solve Sort Integers by The Number of 1 Bits on LeetCode?

Sort Integers by The Number of 1 Bits (LeetCode #1356) 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: Understanding binary representation is crucial for bit manipulation problems.

What is the time complexity of Sort Integers by The Number of 1 Bits?

The optimal solution for Sort Integers by The Number of 1 Bits runs in O(n log n) time and uses O(n) space. The optimal solution has a time complexity of O(n log n) due to the sorting step. The space complexity is O(n) because we create a new sorted array.

What algorithm or data structure is used to solve Sort Integers by The Number of 1 Bits?

Sort Integers by The Number of 1 Bits uses the following concepts: Array, Bit Manipulation, Sorting, Counting. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Sort Integers by The Number of 1 Bits?

Always clarify the sorting criteria with the interviewer. Think about edge cases, such as all numbers being the same or having the same number of 1's. Practice counting bits using different methods to be comfortable with bit manipulation.

What are common mistakes when solving Sort Integers by The Number of 1 Bits?

Not considering the case where multiple integers have the same number of 1's. Overcomplicating the sorting logic instead of using built-in functions.

Sort Integers by The Number of 1 Bits — LeetCode #1356 (Easy)

Tags: Array, Bit Manipulation, Sorting, Counting

Related patterns: Hash Map, Array

Brute Force approach

Time complexity: O(n²). Space complexity: O(1).

The brute-force approach involves counting the number of 1's in the binary representation of each integer and then sorting the array based on these counts. If two integers have the same count, we sort them by their value.

The time complexity is O(n²) because we are sorting the array, and the sorting algorithm can take O(n log n) time. However, counting the bits for each element takes O(n) in the worst case, leading to an overall complexity of O(n²) when considering the sorting.

Step 1: Create a helper function to count the number of 1's in the binary representation of a number.
Step 2: For each integer in the array, use the helper function to get the count of 1's.
Step 3: Sort the array first by the count of 1's and then by the integer value in case of ties.

1. Input: [0,1,2,3,4,5,6,7,8] 2. Count of 1's: [0, 1, 1, 2, 1, 2, 2, 3, 1] 3. Pairing counts with values: [(0,0), (1,1), (1,2), (2,3), (1,4), (2,5), (2,6), (3,7), (1,8)] 4. Sort by counts and values: [(0,0), (1,1), (1,2), (1,4), (1,8), (2,3), (2,5), (2,6), (3,7)] 5. Output: [0,1,2,4,8,3,5,6,7]

Optimal Solution approach

Time complexity: O(n log n). Space complexity: O(n).

The optimal solution leverages built-in sorting functions that can handle custom sorting criteria efficiently. By using a tuple of (number of 1's, value) as the sorting key, we can achieve the desired order in a single pass.

The optimal solution has a time complexity of O(n log n) due to the sorting step. The space complexity is O(n) because we create a new sorted array.

Step 1: Use a sorting function that allows custom keys.
Step 2: For each integer, calculate the number of 1's in its binary representation.
Step 3: Sort the array using a tuple of (count of 1's, integer value) as the key.

Key Insights

Understanding binary representation is crucial for bit manipulation problems.
Sorting by multiple criteria can be efficiently handled using custom sorting keys.

Common Mistakes

Not considering the case where multiple integers have the same number of 1's.
Overcomplicating the sorting logic instead of using built-in functions.

Interview Tips

Always clarify the sorting criteria with the interviewer.
Think about edge cases, such as all numbers being the same or having the same number of 1's.
Practice counting bits using different methods to be comfortable with bit manipulation.

#1356

Sort Integers by The Number of 1 Bits

Easy

Array↗Bit Manipulation↗Sorting↗Counting↗Hash Map↗Array↗

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)

⚙️

Algorithm

3 steps

1Step 1: Use a sorting function that allows custom keys.
2Step 2: For each integer, calculate the number of 1's in its binary representation.
3Step 3: Sort the array using a tuple of (count of 1's, integer value) as the key.

solution.py8 lines

1# Full working Python code
2
3def sortByBits(arr):
4    return sorted(arr, key=lambda x: (bin(x).count('1'), x))
5
6# Example usage
7arr = [0,1,2,3,4,5,6,7,8]
8print(sortByBits(arr))

ℹ

Complexity note: The optimal solution has a time complexity of O(n log n) due to the sorting step. The space complexity is O(n) because we create a new sorted array.

1Understanding binary representation is crucial for bit manipulation problems.
2Sorting by multiple criteria can be efficiently handled using custom sorting keys.

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