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Program to find number of given operations required to reach Target in Python

Suppose we have two values start and end, we have to find the minimum number of operations needed to convert start to end by using these operations −

  • Decrement by 1

  • Multiply by 2

So, if the input is like start = 2, end = 7, then the output will be 3, as we can multiply 2 to get 4, then multiply 2 to get 8 and then subtract 1 to get 7.

To solve this, we will follow these steps −

  • ans := 0

  • Do the following infinitely, do

    • if end <= start, then

      • return ans + start − end

    • otherwise when end is odd, then

      • end := end + 1, ans := ans + 1

    • otherwise,

      • end := quotient of end / 2

      • ans := ans + 1

Let us see the following implementation to get better understanding −

Example

class Solution:
   def solve(self, start, end):
      ans = 0
      while True:
         if end <= start:
            return ans + start - end
         elif end % 2:
            end += 1
            ans += 1
         else:
            end //= 2
            ans += 1
ob1 = Solution()
start = 2
end = 7
print(ob1.solve(start, end))

Input

2, 7

Output

3