# 147. Insertion Sort List

## Description

Given the head of a singly linked list, sort the list using insertion sort, and return the sorted list's head.

The steps of the insertion sort algorithm:

1. Insertion sort iterates, consuming one input element each repetition and growing a sorted output list.
2. At each iteration, insertion sort removes one element from the input data, finds the location it belongs within the sorted list and inserts it there.
3. It repeats until no input elements remain.

The following is a graphical example of the insertion sort algorithm. The partially sorted list (black) initially contains only the first element in the list. One element (red) is removed from the input data and inserted in-place into the sorted list with each iteration.

Example 1:

Input: head = [4,2,1,3]
Output: [1,2,3,4]


Example 2:

Input: head = [-1,5,3,4,0]
Output: [-1,0,3,4,5]


Constraints:

• The number of nodes in the list is in the range [1, 5000].
• -5000 <= Node.val <= 5000

## Solutions

Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. However, it has several advantages, such as simplicity and the ability to sort a list as it receives it.

### Code Explanation:

1. Base Case Check: If the list is empty (head is None) or contains only one element (head.next is None), it’s already sorted, so return head.

2. Dummy Head Initialization: A dummy node is created and pointed to the head of the list. This dummy node serves as an anchor and simplifies edge case handling, such as inserting elements at the head of the list.

3. Iteration Setup: Two pointers, pre and cur, are initialized to help traverse the list. pre starts at the dummy node, and cur starts at the head of the list. The idea is to iterate through the list with cur, and for each node, find its correct position in the portion of the list before cur that has already been sorted.

4. Main Loop: The loop continues as long as cur is not None, indicating there are still elements to be sorted.

5. Direct Append Check: If the current element pointed by pre is less than or equal to cur, it means cur is already in the correct position relative to pre, so move both pointers forward.

6. Finding Insertion Point: If cur needs to be moved to an earlier position to maintain sorting, start from the dummy node with a pointer p and move forward until finding the insertion point where p.next.val > cur.val. This indicates that cur should be inserted between p and p.next.

7. Re-linking: Once the insertion point is found:
• Temporarily store cur.next in t, as the next element to sort after reinserting cur.
• Insert cur between p and p.next by setting cur.next = p.next and p.next = cur.
• Update pre.next to t because cur has been moved out of its original position.
• Move cur to t, preparing for the next iteration.
8. Return: Once all elements have been correctly positioned, return dummy.next, which points to the head of the newly sorted list.

### Important Points:

• The use of a dummy head node simplifies edge cases, especially when inserting at the beginning of the list.
• The algorithm iteratively takes each element from the unsorted portion of the list and finds its correct position in the sorted portion, effectively extending the sorted portion one element at a time.
• The while loop that moves pointer p is crucial for maintaining the sorted order by finding the correct insertion point for each element in cur.
• /**
* public class ListNode {
*     int val;
*     ListNode next;
*     ListNode() {}
*     ListNode(int val) { this.val = val; }
*     ListNode(int val, ListNode next) { this.val = val; this.next = next; }
* }
*/
class Solution {
}
ListNode pre = dummy, cur = head;
while (cur != null) {
if (pre.val <= cur.val) {
pre = cur;
cur = cur.next;
continue;
}
ListNode p = dummy;
while (p.next.val <= cur.val) {
p = p.next;
}
ListNode t = cur.next;
cur.next = p.next;
p.next = cur;
pre.next = t;
cur = t;
}
return dummy.next;
}
}

• # Definition for singly-linked list.
# class ListNode:
#     def __init__(self, val=0, next=None):
#         self.val = val
#         self.next = next
class Solution:
def insertionSortList(self, head: ListNode) -> ListNode:
while cur:
if pre.val <= cur.val:
pre, cur = cur, cur.next
continue
p = dummy
while p.next.val <= cur.val:
p = p.next
t = cur.next
cur.next = p.next
p.next = cur
pre.next = t
cur = t
return dummy.next


• /**
* function ListNode(val, next) {
*     this.val = (val===undefined ? 0 : val)
*     this.next = (next===undefined ? null : next)
* }
*/
/**
* @return {ListNode}
*/
var insertionSortList = function (head) {
let prev = dummy,
while (cur != null) {
if (prev.val <= cur.val) {
prev = cur;
cur = cur.next;
continue;
}
let p = dummy;
while (p.next.val <= cur.val) {
p = p.next;
}
let t = cur.next;
cur.next = p.next;
p.next = cur;
prev.next = t;
cur = t;
}
return dummy.next;
};