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991. Broken Calculator

Difficulty Topics

Description

There is a broken calculator that has the integer startValue on its display initially. In one operation, you can:

  • multiply the number on display by 2, or
  • subtract 1 from the number on display.

Given two integers startValue and target, return the minimum number of operations needed to display target on the calculator.

 

Example 1:

Input: startValue = 2, target = 3
Output: 2
Explanation: Use double operation and then decrement operation {2 -> 4 -> 3}.

Example 2:

Input: startValue = 5, target = 8
Output: 2
Explanation: Use decrement and then double {5 -> 4 -> 8}.

Example 3:

Input: startValue = 3, target = 10
Output: 3
Explanation: Use double, decrement and double {3 -> 6 -> 5 -> 10}.

 

Constraints:

  • 1 <= startValue, target <= 109

Solution

broken-calculator.py
class Solution:
    def brokenCalc(self, startValue: int, target: int) -> int:
        if startValue == target: return 0
        if startValue > target: return startValue - target

        if target % 2 == 0:
            return self.brokenCalc(startValue, target // 2) + 1
        else:
            return self.brokenCalc(startValue, target + 1) + 1