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Some algorithms on linked lists are conveniently expressed as loops. Let's use conceptual lists to plan a loop to compute the length of a list L. We need to keep track of two variables: count (the number of values skipped over) and p (the remainder of the list). As an example, suppose L = [2, 4, 6, 8].
| p | count | |
|---|---|---|
| [2, 4, 6, 8] | 0 | |
| [4, 6, 8] | 1 | |
| [6, 8] | 2 | |
| [8] | 3 | |
| [ ] | 4 |
The loop ends when p is an empty list; variable count is the length of L. Notice that this loop has an invariant: at each line shown,
| (length-invariant) | count + length(p) = length(L). |
When p is an empty list, length(p) = 0. Substituting 0 for length(p) in (length-invariant) gives
count + 0 = length(L).
That is, when p = [ ], count must be length(L).
Putting that plan into code gives the following definition of length(L).
int length(ConstList L) { ConstList p = L; int count = 0; while(p != NULL) { count++; p = p->tail; } return count; }That can be made shorter by using a for-loop.
int length(ConstList L) { int count = 0; for(ConstList p = L; p != NULL; p = p->tail) { count++; } return count; }Look at the for-loop heading. That is a boilerplate way to loop over all of the cells in a linked list L. Memorize it.
Using a loop, write a C++ definition of function smallest(L), which returns the smallest number in nonempty list L. Answer
Using a loop, write a C++ definition of function firstEven(L), which returns the first even number in list L. If L does not contain an even number, then firstEven(L) should return −1. Answer
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