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Solution: Minimum Operations to Make the Integer Zero

Explore a bitwise manipulation technique to determine the minimum operations needed to reduce an integer to zero. Understand how to express the target number as sums of powers of two with consideration of constraints. This lesson guides you through the approach, step-by-step reasoning, and efficient checks to solve related algorithmic challenges.

Statement

You are given two integers num1 and num2.

In a single operation, you may select any integer i within the range [0,60][0, 60] and subtract (2i+‘num2‘)(2^i + \text{`num2`}) from num1.

Determine the minimum number of operations required to reduce num1 to exactly 00.

If it is not possible to make num1 equal to 00, return 1-1.

Note: In each operation, you are free to choose a different value of i.

Constraints:

  • 11 \leq num1 109 ...