IC210 Class 40: More Recursion
Review Section 13.1 of Problem Solving with C++
Lecture
This whole lecture is simply about looking at typical linked list problems and how they're solved. Both in the problem discussed in detail in the notes, and in the problems given at the end of the notes, we look at both iterative (i.e. using loops!) approaches and recursive approaches.
A typical linked list problem - compute the length
Here's a typical
example of a linked list problem: Write a function that determines the length
of a linked list - i.e. the number of nodes. Assuming that we have a Node struct like this:
struct Node{public: int data; Node *next;};
we know that our function's prototype should look like this:
int length(Node*);
It returns an int because, of
course, the length of a list is an integer. It takes a pointer to a Node, because we manipulate lists by manipulating pointers,
just like with arrays. The process we use to determine the length is
straightforward too: move through the list from front to back one node at a
time, keeping track of how many you visit in the process.
int length(Node *L){ // Initialize: curr points to the node we're about to visit Node *curr = L; int count = 0; while(????) { // record that we've visited the node pointed to by curr count++; // set curr to the next node to visit curr = curr->next; } return count;}
The only real difficulty is going to be this: How do we
know when we're done? What do we replace the ???? with? The easiest way to determine this is to work
through our current function as it operates on an example list:
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Before 1st loop iteration |
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Before 2nd loop iteration |
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Before 3rd loop iteration |
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From the preceding example, what was it that told us when
we should continue looping versus when it was time to stop? It was the value of
curr! Specifically, as long as curr isn't the null pointer we should continue looping! From
this, we see that our function's completed definition should be:
int length(Node *L){ // Initialize: curr points to the node we're about to visit Node *curr = L; int count = 0; while(curr != 0) { // record that we've visited the node pointed to by curr count++; // set curr to the next node to visit curr = curr->next; } return count;}
In general this way of writing functions for manipulating
linked lists is pretty good. It's usually questions like "when do we stop
this loop?" or "does this work with an empty list?" that cause
us problems. (Convince yourself that our length
implementation does work for the empty list!) Try applying the same technique
to the problems listed below.
A recursive approach to functions on lists
It turns out that a lot of linked list operations are
very easily accomplished with recursion. The reason for this is that there is
an essentially recursive way of looking at lists. Recall that "a
list" in our program is really a pointer to the first node in a linked
list. Suppose LIST is a variable of type Node* in our program, and suppose that it points to the list
87, 42, 53, 4 as illustrated in the following picture:
So, LIST is an object of
type Node* and therefore we say that it is a list. However, by
that same argument the next-field of the node with data-value 87 is a list.
After all, isn't it also of type Node*? It is the
list 42, 53, 4, i.e. everything but the first element of the list that LIST is. So, there is this natural way of looking at a
list as consisting of the first node and the list of everything else.
As far as the length problem is
concerned, we see that the length of LIST is one plus the length of the list given by the first
node's next pointer. So can't we say:
int length(Node *L){ return 1 + length(L->next);}
Well, this almost works. It only "almost" work because our recursive function has no base case. On the other hand, with every recursive call the list we look at is smaller and smaller. So we're naturally working towards the base case of a list of zero elements - the empty list! Therefore, a complete recursive function for computing the length of a list is:
int length(Node *L){ if (L == 0) return 0; else return 1 + length(L->next);}
That's pretty elegant. Compare that to the "slick" way of doing length iteratively:
int length(Node *L){ int count = 0; for(Node *p = L; p != 0; p = p->next) count++; return count;}
Which one you prefer is a matter of taste. However, there are some situations where the iterative approach is more natural and some where the recursive approach is more natural. Try doing the Problems below both ways:
Deleting a list
Since nodes in a linked list are each created dynamically
with "new", they live on in your program until they are each
individually destroyed with "delete". It is
often useful to have a function void deletelist(Node* L);
that deletes each of the nodes in a list. In good ol' top-down fashion, I'll
implement this function "wishing" that other functions were available
to me:
void deletelist(Node* L){ while(L != 0) deletefirstnode(L);}
So, you see that the real problem is deleting the first node in a list.
void deletefirstnode(Node* &L) // Assumes L is not the empty list!!{
Node *T = L;
L = L->next;
delete T;
}
Hopefully you see that L = L->next effectively removes the first node from L,
but that to actually give back the memory we allocated when creating that node
with new, we need to call delete.
Problems
1. Find the maximum value in a list of double's. Check out my recursive and iterative solutions
2.
Construct a copy of a list
of double's. Check out my recursive solution
to this problem. An iterative solution is tougher!
3.
Construct a reverse copy of
a list of double's. Check out my iterative solution
to this problem. A recursive solution is tougher!
Last modified by LT M. Johnson 11/26/2007 05:15:29 PM
11/26/2007 05:15:29 PM