## Climbing Stairs

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

\begin{aligned} f(1) &= 1\\ f(0) &= 1\\ f(n) &= f(n-1)+f(n-2) \end{aligned}

## Unique Binary Search Trees

\begin{aligned} f(1) &= 1\\ f(0) &= 1\\ f(2) &= 2\\ f(n) &= \sum_{i=1}^{n}{f(i-1) \cdot f(n-i)} \end{aligned}

《编程珠玑》8.4 节上有。