# How to find the middle of a linked list

Just like my post on
How to find the kth last node of a linked list,
there are some boring ways to find the middle of a linked list,
but at least one exciting way,
and it again uses a trick called the “runner”.
We set up *two* pointers into the linked list,
`fast`

and `slow`

.
They will both iterate over the list,
but for each jump made by the `slow`

pointer,
the `fast`

pointer will make two jumps.
Then, when `fast`

reaches the end of the list,
`slow`

will be half-way through!

Note that a list only has a “middle” element
if there are an odd number of nodes!
When we try to skip the `fast`

pointer by 2,
but there’s only one node left,
we know that the list has an odd number of nodes,
and we can return the `slow`

pointer.
Otherwise,
we return `NULL`

.

Here’s an implementation in C:

```
#include <stdlib.h>
#include <stdarg.h>
#include <assert.h>
typedef struct Node {
int val;
struct Node * next;
} Node;
Node* find_middle(Node* head) {
Node* fast = head;
Node* slow = head;
while (fast != NULL && fast->next != NULL) {
fast = fast->next->next;
slow = slow->next;
}
if (fast == NULL) {
// Even number of nodes, so no middle node
return NULL;
}
return slow;
}
// ----------------------------------------------------
// --------------------- TESTS ------------------------
Node* mk_node(int val, Node* next) {
Node* node = malloc(sizeof(Node));
node->val = val;
node->next = next;
return node;
}
Node* mk_list(int len, ...) {
Node* list_start = NULL;
Node* list_end = NULL;
va_list argp;
va_start(argp, len);
for (int i = 0; i < len; i++) {
Node* node = mk_node(va_arg(argp, int), NULL);
if (list_start == NULL) {
list_start = node;
list_end = node;
} else {
list_end->next = node;
list_end = node;
}
}
va_end(argp);
return list_start;
}
int main(int argc, char** argv) {
assert(find_middle(mk_list(0))== NULL);
assert(find_middle(mk_list(1, 42))->val == 42);
assert(find_middle(mk_list(4, 1,2,3,4)) == NULL);
assert(find_middle(mk_list(5, 1,2,3,4,5))->val == 3);
return 0;
}
```

Here’s a similar implementation in Haskell:

```
module Runner where
middle :: [a] -> Maybe a
middle xs = g xs xs where
g (slow:slows) (fast1:fast2:fasts) = g slows fasts
g slows [_] = Just $ head slows
g _ _ = Nothing
main = print $
middle ([] :: [Int]) == Nothing &&
middle [1] == Just 1 &&
middle [1,2] == Nothing &&
middle [1,2,3] == Just 2 &&
middle [1,2,3,4] == Nothing &&
middle [1,2,3,4,5] == Just 3
```

Tagged #programming, #c. All content copyright James Fisher 2020. This post is not associated with my employer.