Binary Searching (or Divide and Conquer)

Today we built towers for Donald Trump with legos. We tried to build them as efficiently as possible. Some of the groups took 39 weeks to build the tower and some were more efficient. One group only took 6 weeks.

We also looked at algorithms for searching and finding a word in the dictionary. First we tried to start at the beginning at turn each page until we found the word. This is a Linear Search, and it wasn't the most effect method, it took 700 page turns to find the word Walrus. If we divided the book in half each time we could find any word in a 1500 page dictionary in 6 or 7 page turns. That is what we call a Binary Search, where we cut the problem in half each time. That was much more efficient.

But we also learned that the Binary Search only works when the data is sorted, so sometimes you are stuck with the Linear Search.
How many different applications can you think of for the Binary Search where we solve the problem by cutting the problem in half each time?

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