# How to partition a linked list

Question 2.4 of *Cracking the Coding Interview*:

Write code to partition a linked list around a value

`x`

, such that all nodes less than`x`

come before all nodes greater than or equal to`x`

.

My first approach built two new lists:
one for values less than `x`

,
and another for values greater than or equal to `x`

.
When we’re done, I returned the concatenation of these lists.
To concatenate the two lists efficiently,
I remembered the tail of the first list.

Then I read the answer,
and found a simpler implementation:
you only have to build one new list!
When you find a value less than `x`

,
you put the node at the head of the list;
otherwise,
you append the node at the tail.
To make append constant-time,
you keep a pointer to the `tail`

.
This runs in `O(length of input)`

,
which is optimal.

Here’s an implementation in C:

```
#include <stdlib.h>
#include <assert.h>
#include <stdarg.h>
typedef struct Node {
int val;
struct Node * next;
} Node;
Node* partition(int x, Node* list) {
if (list == NULL) return NULL;
Node* head = list;
Node* tail = list;
Node* n = list->next;
list->next = NULL;
while (n != NULL) {
Node* next = n->next;
if (n->val < x) {
n->next = head;
head = n;
} else {
n->next = NULL;
tail->next = n;
tail = n;
}
n = next;
}
return head;
}
// ----------------------------------------------------
// --------------------- TESTS ------------------------
Node* mk_node(int val, Node* next) {
Node* node = malloc(sizeof(Node));
node->val = val;
node->next = next;
return node;
}
void assert_lists_eq(Node* actual, Node* expected) {
while (actual != NULL) {
assert(expected != NULL);
assert(actual->val == expected->val);
actual = actual->next;
expected = expected->next;
}
assert(expected == NULL);
}
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_lists_eq(
partition(5, mk_list(7, 2,6,3,7,5,3,6)),
mk_list(7, 3,3,2,6,7,5,6));
assert_lists_eq(
partition(1, mk_list(7, 2,6,3,7,5,3,6)),
mk_list(7, 2,6,3,7,5,3,6));
assert_lists_eq(
partition(42, mk_list(7, 2,6,3,7,5,3,6)),
mk_list(7, 6,3,5,7,3,6,2));
assert_lists_eq(
partition(5, mk_list(0)),
mk_list(0));
return 0;
}
```

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