title: minimum number of steps to reduce number to 1
body: <p>Given any number n, and three operations on n:</p>
  
  <ol>
  <li>add 1</li>
  <li>subtract 1</li>
  <li>divide by 2 if the number is even</li>
  </ol>
  
  <p>I want to find the minimum number of the above operations to reduce n to 1. I have tried dynamic progamming approach, also BFS with pruning, but n can be very large (10^300) and I do not know how to make my algorithm faster. The greedy approach (divide by 2 if even and subtract 1 if odd) also does not give the optimal result. Is another solution exists?</p>