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Three-way Decisions

You might wonder about the restriction that an if statement makes only two-way decisions. Surely you must sometimes pick from more than just two branches?

We ran into this problem with a previous example program that divided integers into negative and positive. It really should pick one of three choices:

• ... -3 -2 -1 — negative
• 0 — neither
• +1 +2 +3 ... — positive

Two-way decisions can do this. First divide the integers into two groups (using a two-way decision):

• ... -3 -2 -1 — negative
• 0 +1 +2 +3 ... — zero and positive

Then further further divide the second group (by using another two-way decision):

• ... -3 -2 -1 — negative
• zero and positive:
  • 0 — neither
  • +1 +2 +3 ... — positive

By repeatedly splitting groups into two subgroups, you can split a collection into any number of fine divisions.