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This technique uses two pointers, 'slow' and 'fast'. Both start at the head of the list. The 'slow' pointer progresses one node at a time while the 'fast' pointer moves two nodes at a time. When the 'fast' pointer reaches the end of the list, the 'slow' pointer will be at the middle node. This works because the 'fast' pointer traverses the list twice as fast as the 'slow' pointer, thus splitting the path lengthwise in half.
Time Complexity: O(n), where n is the number of nodes in the list, because we are iterating through the list once.
Space Complexity: O(1), since we are using a constant amount of space.
1#include <iostream>
2using namespace std;
3
4struct ListNode {
5 int val;
6 ListNode *next;
7 ListNode(int x) : val(x), next(NULL) {}
8};
9
10ListNode* middleNode(ListNode* head) {
11 ListNode* slow = head;
12 ListNode* fast = head;
13 while (fast != NULL && fast->next != NULL) {
14 slow = slow->next;
15 fast = fast->next->next;
16 }
17 return slow;
18}C++ utilizes similar logic as C, managing pointers 'slow' and 'fast' moving at different speeds to pinpoint the middle node. The ListNode construction ensures linked list nodes are initialized with a value and a default 'next' pointer of NULL.
This approach involves two passes over the list. The first pass calculates the total number of nodes. In the second pass, we traverse halfway through the list to reach the middle node by stopping at n/2, where n is the number of nodes. This explicitly determines the node that marks the middle of the list.
Time Complexity: O(n) for two full passes through the list.
Space Complexity: O(1) as only a few extra variables are used.
1
This C implementation counts the nodes in a linked list using an initial loop, then follows a second traversal that stops at the mid-point to return the middle node.