problem report: sort list

quick sort version 1: 

　　quick sort 定义： https://en.wikipedia.org/wiki/Quicksort

　　quick sort 核心部分为partition（http://www.cnblogs.com/jiangchen/p/5398166.html），

　　　　　　　　　　　　取list中间点（http://www.cnblogs.com/jiangchen/p/5529704.html）

　　时间复杂度为o(nlgn)　　

public class Solution {
    //recursive partition list to left,middle,right 3 parts, use concat function to conntet 3 parts together at end of function 
    public ListNode sortList(ListNode head) {  
        if (head == null || head.next == null) {
            return head;
        }
        ListNode middle = findMedian(head);
        
        ListNode leftDummy = new ListNode(0), leftTail = leftDummy;
        ListNode rightDummy = new ListNode(0), rightTail = rightDummy;
        ListNode middleDummy = new ListNode(0), middleTail = middleDummy;
        
        while (head != null) {
            if (head.val < middle.val) {
                leftTail.next = head;
                leftTail = head;
            } else if(head.val == middle.val) {
                middleTail.next = head;
                middleTail = head;
            } else {
                rightTail.next = head;
                rightTail = head;
            }
            head = head.next;
        }
        leftTail.next = null;
        middleTail.next = null;
        rightTail.next = null;
        
        ListNode left = sortList(leftDummy.next);
        ListNode right = sortList(rightDummy.next);
        
        return concat(left, middleDummy.next, right);
    }
    // connect 3 part together
    private ListNode concat (ListNode left, ListNode mid, ListNode right) {
        ListNode dummy = new ListNode(0), tail = dummy;
        tail.next = left;
        tail = getTail(tail);//left 本身可能是一个空串，所以3次getTail都用tail作为起始点，而不用left，mid，right
        tail.next = mid;
        tail = getTail(tail);
        tail.next = right;
        tail = getTail(tail);
        return dummy.next;
    }
    //get end of current list 
    private ListNode getTail (ListNode current) {
        if (current == null) {
            return current;
        }
        while (current.next != null) {
            current = current.next;
        }
        return current;
    }
    
    private ListNode findMedian(ListNode head) {
        ListNode slow = head, fast = head.next;
        while (fast != null && fast.next != null) {
            slow = slow.next;
            fast = fast.next.next;
        }
        return slow;
    }
}

merge sort version 1: 

　　merge sort 定义： https://en.wikipedia.org/wiki/Merge_sort 

 　　merge sort 核心部分为 recusive devide linked list to two part

　　　　　　　　　　　　　　merge a list

public class Solution {            
    private ListNode findMiddle(ListNode head) {
        ListNode slow = head, fast = head.next;
        while (fast != null && fast.next != null) {
            fast = fast.next.next;
            slow = slow.next;
        }
        return slow;
    }    

    private ListNode merge(ListNode head1, ListNode head2) {
        ListNode  tail,dummy = new ListNode(0);
        tail = dummy;
        while (head1 != null || head2 != null) {
            if (head2 != null && (head1 == null || head1.val > head2.val)) {
                tail.next = head2;
                tail = head2;
                head2 = head2.next;
            } else  {
                tail.next = head1;
                tail = head1;
                head1 = head1.next;
            }
        }
       return dummy.next;
    }

    public ListNode sortList(ListNode head) {
        ListNode dummyHead1, dummyHead2;
        if (head == null || head.next == null) {
            return head;
        }
        ListNode head1, head2, mid;
        mid = findMiddle(head);
        head1 = head;
        head2 = mid.next;
        mid.next = null;
       // System.out.println(head1.val);
        //System.out.println(head2.val);

        head1 = sortList(head1);
        head2 = sortList(head2);
        
        return merge(head1,head2);
    }
}

// version 1: Merge Sort
public class Solution {            
    private ListNode findMiddle(ListNode head) {
        ListNode slow = head, fast = head.next;
        while (fast != null && fast.next != null) {
            fast = fast.next.next;
            slow = slow.next;
        }
        return slow;
    }    

    private ListNode merge(ListNode head1, ListNode head2) {
        ListNode dummy = new ListNode(0);
        ListNode tail = dummy;
        while (head1 != null && head2 != null) {
            if (head1.val < head2.val) {
                tail.next = head1;
                head1 = head1.next;
            } else {
                tail.next = head2;
                head2 = head2.next;
            }
            tail = tail.next;
        }
        if (head1 != null) {
            tail.next = head1;
        } else {
            tail.next = head2;
        }

        return dummy.next;
    }

    public ListNode sortList(ListNode head) {
        if (head == null || head.next == null) {
            return head;
        }

        ListNode mid = findMiddle(head);

        ListNode right = sortList(mid.next);
        mid.next = null;
        ListNode left = sortList(head);

        return merge(left, right);
    }
}