How do you solve Minimum Operations to Reduce an Integer to 0 on LeetCode?

Minimum Operations to Reduce an Integer to 0 (LeetCode #2571) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(log n) time complexity and O(1) space complexity. Key insight: Understanding binary representation is crucial for optimizing operations.

What is the time complexity of Minimum Operations to Reduce an Integer to 0?

The optimal solution for Minimum Operations to Reduce an Integer to 0 runs in O(log n) time and uses O(1) space. The time complexity is O(log n) because we only need to examine the bits of n, which is proportional to the number of bits in its binary representation.

What is the brute force solution for Minimum Operations to Reduce an Integer to 0?

The brute force approach for Minimum Operations to Reduce an Integer to 0 is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves trying all possible combinations of adding or subtracting powers of 2 to reduce the number to 0. This method is straightforward but inefficient, as it explores every possible path. The optimal Optimal Solution approach improves this to O(log n).

What algorithm or data structure is used to solve Minimum Operations to Reduce an Integer to 0?

Minimum Operations to Reduce an Integer to 0 uses the following concepts: Dynamic Programming, Greedy, Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Dynamic Programming.

What are the interview tips for Minimum Operations to Reduce an Integer to 0?

Always think about the binary representation of numbers when dealing with powers of 2. Practice breaking down the problem into smaller parts, such as counting bits. Be prepared to explain your thought process clearly, especially when optimizing.

What are common mistakes when solving Minimum Operations to Reduce an Integer to 0?

Not considering the binary representation of numbers. Overlooking the effect of adjacent '1's on the number of operations.

#2571

Minimum Operations to Reduce an Integer to 0

Medium

Dynamic ProgrammingGreedyBit ManipulationBit ManipulationDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(log n)Space O(1)

The optimal solution leverages the binary representation of the number. Each bit in the binary form can be treated as a power of 2. The key is to count the number of '1's in the binary representation and handle adjacent '1's efficiently.

⚙️

Algorithm

3 steps

1Step 1: Convert n to its binary representation.
2Step 2: Count the number of '1's in the binary representation.
3Step 3: If there are adjacent '1's, they can be handled in fewer operations, so adjust the count accordingly.

solution.py2 lines

1def minOperations(n):
2    return bin(n).count('1') + (bin(n).count('11')) // 2

ℹ

Complexity note: The time complexity is O(log n) because we only need to examine the bits of n, which is proportional to the number of bits in its binary representation.

1Understanding binary representation is crucial for optimizing operations.
2Adjacent '1's in binary can be handled together, reducing the number of operations.

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