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4.2 Sequential Search with Sentinel

Try to think of some ways to improve the speed of sequential search. It should be clear that, to speed up a program, it pays to concentrate on the parts that use the most time to begin with. In this case, it's the loop.

Consider what happens each time through the loop:

  1. The loop counter i is incremented and compared against n.

  2. array[i] is compared against key.

If we could somehow eliminate one of these comparisons, the loop might be a lot faster. So, let's try... why do we need step 1? It's because, otherwise, we might run off the end of array[], causing undefined behavior, which is in turn because we aren't sure that key is in array[]. If we knew that key was in array[], then we could skip step 1.

But, hey! we can ensure that the item we're looking for is in the array. How? By putting a copy of it at the end of the array. This copy is called a sentinel (see sentinel), and the search technique as a whole is called sequential search with sentinel (see sequential search with sentinel). Here's the code:

 
/* Returns the smallest i such that array[i] == key, 
or -1 if key is not in array[]. array[] must be an modifiable array of n ints
with room for a (n + 1)th element. */ int
seq_sentinel_search (int array[], int n, int key)
{ int *p; array[n] = key; for (p = array; *p != key; p++) /* Nothing to do. */; return p - array < n ? p - array : -1; }
This code is included in @refalso{600

Notice how the code above uses a pointer, int *p, rather than a counter i as in &#60;@xref{\NODE\, , Sequentially search an array of int.&#62;s,16} earlier. For the most part, this is simply a style preference: for iterating through an array, C programmers usually prefer pointers to array indexes. Under older compilers, code using pointers often compiled into faster code as well, but modern C compilers usually produce the same code whether pointers or indexes are used.

The return statement in this function uses two somewhat advanced features of C: the conditional or "ternary" operator ?: and pointer arithmetic. The former is a bit like an expression form of an if statement. The expression a ? b : c first evaluates a. Then, if a != 0, b is evaluated and the expression takes that value. Otherwise, a == 0, c is evaluated, and the result is the expression's value.

Pointer arithmetic is used in two ways here. First, the expression p++ acts to advance p to point to the next int in array. This is analogous to the way that i++ would increase the value of an integer or floating point variable i by one. Second, the expression p - array results in the "difference" between p and array, i.e., the number of int elements between the locations to which they point. For more information on these topics, please consult a good C reference, such as [ Kernighan 1988].

Searching with a sentinel requires that the array be modifiable and large enough to hold an extra element. Sometimes these are inherently problematic--the array may not be modifiable or it might be too small--and sometimes they are problems because of external circumstances. For instance, a program with more than one concurrent thread (see thread) cannot modify a shared array for sentinel search without expensive locking.

Sequential sentinel search is an improvement on ordinary sequential search, but as it turns out there's still room for improvement--especially in the runtime for unsuccessful searches, which still always take n comparisons. In the next section, we'll see one technique that can reduce the time required for unsuccessful searches, at the cost of longer runtime for successful searches.

See also: [ Knuth 1998b], algorithm 6.1Q; [ Cormen 1990], section 11.2; [ Bentley 2000], section 9.2.


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