3.1: Updating Variables

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In Exercise 2.2 of Section 2.9, I asked you to write a program that models a bike-share system with bikes moving between two stations. Each day 5 percent of the bikes in Boston are dropped off in Cambridge, and 3 percent of the bikes in Cambridge get dropped off in Boston.

To update the state of the system, you might have been tempted to write something like

b = b - 0.05*b + 0.03*c
c = c + 0.05*b - 0.03*c

But that would be wrong, so very wrong. Why? The problem is that the first line changes the value of b, so when the second line runs, it gets the old value of c and the new value of b. As a result, the change in b is not always the same as the change in c, which violates the Principle of Conservation of Bikes!

One solution is to use temporary variables like b_new and c_new:

b_new = b - 0.05*b + 0.03*c
c_new = c + 0.05*b - 0.03*c
b = b_new
c = c_new

This has the effect of updating the variables simultaneously; that is, it reads both old values before writing either new value.

The following is an alternative solution that has the added advantage of simplifying the computation:

b_to_c = 0.05*b - 0.03*c
b = b - b_to_c
c = c + b_to_c

It’s easy to look at this code and confirm that it obeys Conservation of Bikes. Even if the value of b_to_c is wrong, at least the total number of bikes is right. And that brings us to the Fifth Theorem of Debugging:

The best way to avoid a bug is to make it impossible.

In this case, removing redundancy also eliminates the opportunity for a bug.