# 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* tail = list;
Node* n = list->next;
list->next = NULL;
while (n != NULL) {
Node* next = n->next;
if (n->val < x) {
} else {
n->next = NULL;
tail->next = n;
tail = n;
}
n = next;
}

}

// ----------------------------------------------------
// --------------------- 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;
}
``````

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