Lab 02 - Debugging

Thanks for my Lab Tutor Zhang Puyu!

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Lab 2 Slides

Selected Problems from Exercise 1

Wishful Thinking

Before we talk about the wishful thinking, let's get a quick review of the Mathematical Induction

Mathematical Induction

Suppose we want to find the value of $P(n)$ for any non-negative interger $n$, we only need to do two things:

1. Find $P(0)$.

2. Find a way to get $P(k+1)$ based on the value of $P(k)$.

The so called "Wishful Thinking" is just the reverse of above!

Wishful Thinking

Suppose we already know:

1. How to compute $P(k+1)$ using $P(k)$;

2. The value of $P(0)$, i.e., "the base case" (or terminating condition)

Now we want to find $P(n)$, and so we can just find $P(n-1)$ first. To find $P(n-1)$, we just need to find $P(n-2)$ first... the cycle goes on until we reach $P(0)$ where the recursion terminates.