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Solution: Minimum Operations to Make the Integer Zero

Explore how to determine the minimum number of operations needed to reduce an integer to zero by repeatedly subtracting a sum involving powers of two and another integer. Understand the use of bitwise properties and conditions to verify if a target number can be expressed as a sum of exact powers of two within operation limits. This lesson equips you with a methodical approach to solve this problem efficiently using bitwise manipulation.

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 ...