How do you solve Minimum Operations to Make the Integer Zero on LeetCode?

Minimum Operations to Make the Integer Zero (LeetCode #2749) 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 how binary representation works can significantly reduce the number of operations needed.

What is the time complexity of Minimum Operations to Make the Integer Zero?

The optimal solution for Minimum Operations to Make the Integer Zero runs in O(log n) time and uses O(1) space. The complexity is logarithmic because we only need to count the bits in num1, which is proportional to the number of bits in its binary representation.

What is the brute force solution for Minimum Operations to Make the Integer Zero?

The brute force approach for Minimum Operations to Make the Integer Zero is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves trying all possible combinations of operations to reduce num1 to zero. This means we will repeatedly subtract values derived from num2 and powers of 2 until we reach zero or determine it's impossible. The optimal Optimal Solution approach improves this to O(log n).

What algorithm or data structure is used to solve Minimum Operations to Make the Integer Zero?

Minimum Operations to Make the Integer Zero uses the following concepts: Bit Manipulation, Brainteaser, Enumeration. The recommended patterns to study are: Bit Manipulation, Dynamic Programming.

What are the interview tips for Minimum Operations to Make the Integer Zero?

Always clarify the problem constraints and edge cases before diving into coding. Think about how binary operations can simplify the problem, especially when dealing with powers of two. Practice explaining your thought process as you code, as this demonstrates your understanding and can help catch mistakes.

What are common mistakes when solving Minimum Operations to Make the Integer Zero?

Not considering the parity of (num1 + num2) when determining if reaching zero is possible. Failing to account for the minimum number of bits set in num1 as a lower bound for operations.

#2749

Minimum Operations to Make the Integer Zero

Medium

Bit ManipulationBrainteaserEnumerationBit ManipulationDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(log n)Space O(1)

The optimal solution leverages the properties of binary representation and the constraints of the problem. By focusing on the bits of num1 and how they interact with num2, we can minimize operations effectively.

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Algorithm

5 steps

1Step 1: Calculate the effective value of num2 as num2 + 1.
2Step 2: If num1 is less than or equal to num2, return -1 as we cannot reach zero.
3Step 3: Count the number of bits set in num1 (this gives a lower bound on operations).
4Step 4: Check if the sum of num1 and num2 is even; if not, return -1 since we cannot reach zero with odd adjustments.
5Step 5: Return the number of bits set in num1 as the minimum operations needed.

solution.py9 lines

1# Full working Python code
2
3def min_operations(num1, num2):
4    num2 += 1
5    if num1 <= num2:
6        return -1
7    if (num1 + num2) % 2 != 0:
8        return -1
9    return bin(num1).count('1')

ℹ

Complexity note: The complexity is logarithmic because we only need to count the bits in num1, which is proportional to the number of bits in its binary representation.

1Understanding how binary representation works can significantly reduce the number of operations needed.
2The relationship between num1 and num2 is crucial; if num1 is too small relative to num2, reaching zero becomes impossible.

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