8.01 Triple step

[greencarlos]

What this PR does:

Triple Step Backtracking, Top-Down memo, Bottom-Up memo, and constant space solutions

Triple Step:

A child is running up a staircase with n steps and
can hop either 1 step, 2 steps, or 3 steps at a time.
Implement a method to count how many possible ways
the child can run up the stairs.

Recursion and Dynamic Programming (4 steps)

1. Start with the recursive backtracking solution
2. Optimize by using a memoization table (top-down dynamic programming)
3. Remove the need for recursion (bottom-up dynamic programming)
4. Apply final tricks to reduce the time/memory complexity

[profnandaa]

Other than deleting the previous soln, could you please add yours as a new alternative in a different file (*-v2)?

[greencarlos]

@profnandaa updated

[profnandaa]

Thanks!