Day 321 #651

Good morning! Here's your coding interview problem for today.

This problem was asked by PagerDuty.

Given a positive integer N, find the smallest number of steps it will take to reach 1.

There are two kinds of permitted steps:

• You may decrement N to N - 1.
• If a * b = N, you may decrement N to the larger of a and b.
  For example, given 100, you can reach 1 in five steps with the following route: 100 -> 10 -> 9 -> 3 -> 2 -> 1.