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By Thomas H. Cormen

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N/ Input and Output: Same as FACTORIAL. 1. If n D 0, then return 1 as the output. 2. n C 1/. 3/, and so on, never getting down to the base case when n equals 0. ” We can often rewrite algorithms that use a loop in a recursive style. A; n; i; x/ Inputs: Same as L INEAR -S EARCH, but with an added parameter i. Output: The index of an element equaling x in the subarray from AŒi through AŒn, or NOT- FOUND if x does not appear in this subarray. 1. If i > n, then return NOT- FOUND. 2. Otherwise (i Ä n), if AŒi D x, then return i.

0 scale. ”: the way that you might “sort” clothing for example, with shirts in one place, pants in another place, and so on. ” Binary search Before we see some sorting algorithms, let’s visit binary search, which requires the array being searched to be already sorted. lg n/ time to search an n-element array. In our bookshelf example, we start with the books already sorted by author name, left to right on the shelf. We’ll use the author name as the key, and let’s search for any book by Jonathan Swift.

When elements are some other form of data, then we have to define what “less than” means. As long as we have some clear notion of “less than,” we can determine whether an array is sorted. Recalling the example of books on a bookshelf from Chapter 2, we could sort the books alphabetically by author, alphabetically by title, or, if in a library, by call number. In this chapter, we’ll say that the books are sorted on the shelf if they appear in alphabetical order by author, reading from left to right.