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Briefcase Lock

A briefcase has a 4-digit rolling-lock. Each digit is a number from 0-9 that can be rolled either forwards or backwards.

Create a function that returns the smallest number of turns it takes to transform the lock from the current combination to the target combination. One turn is equivalent to rolling a number forwards or backwards by one.

To illustrate:

  • current-lock: 4089
  • target-lock: 5672

What is the minimum number of turns it takes to transform 4089 to 5672?

4 ➞ 5
4 ➞ 5  // Forward Turns: 1 <- Min
4 ➞ 3 ➞ 2 ➞ 1 ➞ 0 ➞ 9 ➞ 8 ➞ 7 ➞ 6 ➞ 5  // Backward Turns: 9

0 ➞ 6
0 ➞ 1 ➞ 2 ➞ 3 ➞ 4 ➞ 5 ➞ 6  // Forward Turns: 6
0 ➞ 9 ➞ 8 ➞ 7 ➞ 6  // Backward Turns: 4  <- Min

8 ➞ 7
8 ➞ 9 ➞ 0 ➞ 1 ➞ 2 ➞ 3 ➞ 4 ➞ 5 ➞ 6 ➞ 7  // Forward Turns: 9
8 ➞ 7  // Backward Turns: 1  <- Min

9 ➞ 2
9 ➞ 0 ➞ 1 ➞ 2  // Forward Turns: 3  <- Min
9 ➞ 8 ➞ 7 ➞ 6 ➞ 5 ➞ 4 ➞ 3 ➞ 2  // Backward Turns: 7

It takes 1 + 4 + 1 + 3 = 9 minimum turns to change the lock from 4089 to 5672.

Example

MinTurns("4089", "5672") ➞ 9

MinTurns("1111", "1100") ➞ 2

MinTurns("2391", "4984") ➞ 10

Notes

  • Both locks are in string format.
  • A 9 rolls forward to 0, and a 0 rolls backwards to a 9.