I remember vividly Jon Bentley's first Algorithms lecture at CMU, where he asked all of us incoming Ph.D. students to write a binary search, and then dissected one of our implementations in front of the class. Of course it was broken, as were most of our implementations. This made a real impression on me, as did the treatment of this material in his wonderful Programming Pearls (Addison-Wesley, 1986; Second Edition, 2000). The key lesson was to carefully consider the invariants in your programs....