Sunday, November 29, 2015

Sort LinkedList


http://yuanhsh.iteye.com/blog/2186111
http://www.cnblogs.com/TenosDoIt/p/3666585.html
归并排序(算法交换链表节点,时间复杂度O(nlogn),不考虑递归栈空间的话空间复杂度是O(1)) 
首先用快慢指针的方法找到链表中间节点,然后递归的对两个子链表排序,把两个排好序的子链表合并成一条有序的链表。归并排序应该算是链表排序最佳的选择了,保证了最好和最坏时间复杂度都是nlogn,而且它在数组排序中广受诟病的空间复杂度在链表排序中也从O(n)降到了O(1)
    ListNode *mergeSortList(ListNode *head) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        //链表归并排序
        if(head == NULL || head->next == NULL)return head;
        else
        {
            //快慢指针找到中间节点
            ListNode *fast = head,*slow = head;
            while(fast->next != NULL && fast->next->next != NULL)
            {
                fast = fast->next->next;
                slow = slow->next;
            }
            fast = slow;
            slow = slow->next;
            fast->next = NULL;
            fast = sortList(head);//前半段排序
            slow = sortList(slow);//后半段排序
            return merge(fast,slow);
        }
         
    }
    // merge two sorted list to one
    ListNode *merge(ListNode *head1, ListNode *head2)
    {
        if(head1 == NULL)return head2;
        if(head2 == NULL)return head1;
        ListNode *res , *p ;
        if(head1->val < head2->val)
            {res = head1; head1 = head1->next;}
        else{res = head2; head2 = head2->next;}
        p = res;
         
        while(head1 != NULL && head2 != NULL)
        {
            if(head1->val < head2->val)
            {
                p->next = head1;
                head1 = head1->next;
            }
            else
            {
                p->next = head2;
                head2 = head2->next;
            }
            p = p->next;
        }
        if(head1 != NULL)p->next = head1;
        else if(head2 != NULL)p->next = head2;
        return res;
    }
http://www.dontforgettothink.com/2011/11/23/merge-sort-of-linked-list/
    public Node merge_sort(Node head) {
        if(head == null || head.next == null) { return head; }
        Node middle = getMiddle(head);      //get the middle of the list
        Node sHalf = middle.next; middle.next = null;   //split the list into two halfs

        return merge(merge_sort(head),merge_sort(sHalf));  /recurse on that 
    }

    public Node merge(Node a, Node b) {
        Node dummyHead, curr; dummyHead = new Node(); curr = dummyHead;
        while(a !=null && b!= null) {
            if(a.info <= b.info) { curr.next = a; a = a.next; }
            else { curr.next = b; b = b.next; }
            curr = curr.next;
        }
        curr.next = (a == null) ? b : a;
        return dummyHead.next;
    }

    public Node getMiddle(Node head) {
        if(head == null) { return head; }
        Node slow, fast; slow = fast = head;
        while(fast.next != null && fast.next.next != null) {
            slow = slow.next; fast = fast.next.next;
        }
        return slow;
    }
http://www.dontforgettothink.com/2011/11/23/merge-sort-of-linked-list/
http://bookshadow.com/weblog/2014/11/21/java-merge-sort-of-linked-list/
public Node merge_sort(Node head) { if (head == null || head.next == null) { return head; } Node middle = getMiddle(head); // get the middle of the list Node sHalf = middle.next; middle.next = null; // split the list into two halfs return merge(merge_sort(head), merge_sort(sHalf)); // recurse on that } // Merge subroutine to merge two sorted lists public Node merge(Node a, Node b) { Node dummyHead, curr; dummyHead = new Node(); curr = dummyHead; while (a != null && b != null) { if (a.val <= b.val) { curr.next = a; a = a.next; } else { curr.next = b; b = b.next; } curr = curr.next; } curr.next = (a == null) ? b : a; return dummyHead.next; } // Finding the middle element of the list for splitting public Node getMiddle(Node head) { if (head == null) { return head; } Node slow, fast; //“快慢指针” slow = fast = head; while (fast.next != null && fast.next.next != null) { slow = slow.next; fast = fast.next.next; } return slow; }
快速排序1(算法只交换节点的val值,平均时间复杂度O(nlogn),不考虑递归栈空间的话空间复杂度是O(1))
这里的partition我们参考数组快排partition的第二种写法(选取第一个元素作为枢纽元的版本,因为链表选择最后一元素需要遍历一遍),具体可以参考here
这里我们还需要注意的一点是数组的partition两个参数分别代表数组的起始位置,两边都是闭区间,这样在排序的主函数中:
void quicksort(vector<int>&arr, int low, int high)
{
  if(low < high)
  {
   int middle = mypartition(arr, low, high);
   quicksort(arr, low, middle-1);
   quicksort(arr, middle+1, high);
  }
}
对左边子数组排序时,子数组右边界是middle-1,如果链表也按这种两边都是闭区间的话,找到分割后枢纽元middle,找到middle-1还得再次遍历数组,因此链表的partition采用前闭后开的区间(这样排序主函数也需要前闭后开区间),这样就可以避免上述问题
    ListNode *quickSortList(ListNode *head) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        //链表快速排序
        if(head == NULL || head->next == NULL)return head;
        qsortList(head, NULL);
        return head;
    }
    void qsortList(ListNode*head, ListNode*tail)
    {
        //链表范围是[low, high)
        if(head != tail && head->next != tail)
        {
            ListNode* mid = partitionList(head, tail);
            qsortList(head, mid);
            qsortList(mid->next, tail);
        }
    }
    ListNode* partitionList(ListNode*low, ListNode*high)
    {
        //链表范围是[low, high)
        int key = low->val;
        ListNode* loc = low;
        for(ListNode*i = low->next; i != high; i = i->next)
            if(i->val < key)
            {
                loc = loc->next;
                swap(i->val, loc->val);
            }
        swap(loc->val, low->val);
        return loc;
    }
快速排序2(算法交换链表节点,平均时间复杂度O(nlogn),不考虑递归栈空间的话空间复杂度是O(1))
这里的partition,我们选取第一个节点作为枢纽元,然后把小于枢纽的节点放到一个链中,把不小于枢纽的及节点放到另一个链中,最后把两条链以及枢纽连接成一条链。
这里我们需要注意的是,1.在对一条子链进行partition时,由于节点的顺序都打乱了,所以得保正重新组合成一条新链表时,要和该子链表的前后部分连接起来,因此我们的partition传入三个参数,除了子链表的范围(也是前闭后开区间),还要传入子链表头结点的前驱;2.partition后链表的头结点可能已经改变
    ListNode *quickSortList(ListNode *head) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        //链表快速排序
        if(head == NULL || head->next == NULL)return head;
        ListNode tmpHead(0); tmpHead.next = head;
        qsortList(&tmpHead, head, NULL);
        return tmpHead.next;
    }
    void qsortList(ListNode *headPre, ListNode*head, ListNode*tail)
    {
        //链表范围是[low, high)
        if(head != tail && head->next != tail)
        {
            ListNode* mid = partitionList(headPre, head, tail);//注意这里head可能不再指向链表头了
            qsortList(headPre, headPre->next, mid);
            qsortList(mid, mid->next, tail);
        }
    }
    ListNode* partitionList(ListNode* lowPre, ListNode* low, ListNode* high)
    {
        //链表范围是[low, high)
        int key = low->val;
        ListNode node1(0), node2(0);//比key小的链的头结点,比key大的链的头结点
        ListNode* little = &node1, *big = &node2;
        for(ListNode*i = low->next; i != high; i = i->next)
            if(i->val < key)
            {
                little->next = i;
                little = i;
            }
            else
            {
                big->next = i;
                big = i;
            }
        big->next = high;//保证子链表[low,high)和后面的部分连接
        little->next = low;
        low->next = node2.next;
        lowPre->next = node1.next;//为了保证子链表[low,high)和前面的部分连接
        return low;
    }

插入排序(算法中是直接交换节点,时间复杂度O(n^2),空间复杂度O(1))
    ListNode *insertionSortList(ListNode *head) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        if(head == NULL || head->next == NULL)return head;
        ListNode *p = head->next, *pstart = new ListNode(0), *pend = head;
        pstart->next = head; //为了操作方便,添加一个头结点
        while(p != NULL)
        {
            ListNode *tmp = pstart->next, *pre = pstart;
            while(tmp != p && p->val >= tmp->val) //找到插入位置
                {tmp = tmp->next; pre = pre->next;}
            if(tmp == p)pend = p;
            else
            {
                pend->next = p->next;
                p->next = tmp;
                pre->next = p;
            }
            p = pend->next;
        }
        head = pstart->next;
        delete pstart;
        return head;
    }
http://geeksquiz.com/insertion-sort-for-singly-linked-list/
void insertionSort(struct node **head_ref)
{
    // Initialize sorted linked list
    struct node *sorted = NULL;
    // Traverse the given linked list and insert every
    // node to sorted
    struct node *current = *head_ref;
    while (current != NULL)
    {
        // Store next for next iteration
        struct node *next = current->next;
        // insert current in sorted linked list
        sortedInsert(&sorted, current);
        // Update current
        current = next;
    }
    // Update head_ref to point to sorted linked list
    *head_ref = sorted;
}
/* function to insert a new_node in a list. Note that this
  function expects a pointer to head_ref as this can modify the
  head of the input linked list (similar to push())*/
void sortedInsert(struct node** head_ref, struct node* new_node)
{
    struct node* current;
    /* Special case for the head end */
    if (*head_ref == NULL || (*head_ref)->data >= new_node->data)
    {
        new_node->next = *head_ref;
        *head_ref = new_node;
    }
    else
    {
        /* Locate the node before the point of insertion */
        current = *head_ref;
        while (current->next!=NULL &&
               current->next->data < new_node->data)
        {
            current = current->next;
        }
        new_node->next = current->next;
        current->next = new_node;
    }
}
选择排序(算法中只是交换节点的val值,时间复杂度O(n^2),空间复杂度O(1))
    ListNode *selectSortList(ListNode *head) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        //选择排序
        if(head == NULL || head->next == NULL)return head;
        ListNode *pstart = new ListNode(0);
        pstart->next = head; //为了操作方便,添加一个头结点
        ListNode*sortedTail = pstart;//指向已排好序的部分的尾部
        
        while(sortedTail->next != NULL)
        {
            ListNode*minNode = sortedTail->next, *p = sortedTail->next->next;
            //寻找未排序部分的最小节点
            while(p != NULL)
            {
                if(p->val < minNode->val)
                    minNode = p;
                p = p->next;
            }
            swap(minNode->val, sortedTail->next->val);
            sortedTail = sortedTail->next;
        }
        
        head = pstart->next;
        delete pstart;
        return head;
    }
冒泡排序(算法交换链表节点val值,时间复杂度O(n^2),空间复杂度O(1))
    ListNode *bubbleSortList(ListNode *head) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        //链表快速排序
        if(head == NULL || head->next == NULL)return head;
        ListNode *p = NULL;
        bool isChange = true;
        while(p != head->next && isChange)
        {
            ListNode *q = head;
            isChange = false;//标志当前这一轮中又没有发生元素交换,如果没有则表示数组已经有序
            for(; q->next && q->next != p; q = q->next)
            {
                if(q->val > q->next->val)
                {
                    swap(q->val, q->next->val);
                    isChange = true;
                }
            }
            p = q;
        }
        return head;
    }
对于希尔排序,因为排序过程中经常涉及到arr[i+gap]操作,其中gap为希尔排序的当前步长,这种操作不适合链表。
对于堆排序,一般是用数组来实现二叉堆,当然可以用二叉树来实现,但是这么做太麻烦,还得花费额外的空间构建二叉树



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How To (1) Algorithm - New (1) Algorithm Series (1) Algorithms Part I (1) Analysis of Algorithm (1) Array-Element Index Negative (1) Array-Rearrange (1) Auxiliary Array (1) Auxiliary Array: Inc&Dec (1) BACK (1) BK-Tree (1) BZOJ (1) Basic (1) Bayes (1) Beauty of Math (1) Big Integer (1) Big Number (1) Binary (1) Binary Tree Variant (1) Bipartite (1) Bit-Missing Number (1) BitMap (1) BitMap index (1) BitSet (1) Bug Free Code (1) BuildIt (1) C/C++ (1) CC Interview (1) Cache (1) Calculate Height at Same Recusrion (1) Cartesian tree (1) Check Tree Property (1) Chinese (1) Circular Buffer (1) Code Quality (1) Codesolutiony (1) Company - Alibaba (1) Company - Palantir (1) Company - WalmartLabs (1) Company-Apple (1) Company-Epic (1) Company-Salesforce (1) Company-Snapchat (1) Company-Yelp (1) Compression Algorithm (1) Concurrency (1) Convert BST to DLL (1) Convert DLL to BST (1) Custom Sort (1) Cyclic Replacement (1) DFS-Matrix (1) DP - Probability (1) DP Fill Diagonal First (1) DP-Difficult (1) DP-End with 0 or 1 (1) DP-Fill Diagonal First (1) DP-Graph (1) DP-Left and Right Array (1) DP-MaxMin (1) DP-Memoization (1) DP-Node All Possibilities (1) DP-Optimization (1) DP-Preserve Previous Value (1) DP-Print All Solution (1) Database (1) Detect Negative Cycle (1) Directed Graph (1) Do Two Things at Same Recusrion (1) Domino (1) Dr Dobb's (1) Duplicate (1) Equal probability (1) External Sort (1) FST (1) Failure Function (1) Fraction (1) Front End Pointers (1) Funny (1) Fuzzy String Search (1) Game (1) Generating Function (1) Generation (1) Genetic algorithm (1) GeoHash (1) Geometry - Orientation (1) Google APAC (1) Graph But No Graph (1) Graph Transpose (1) Graph Traversal (1) Graph-Coloring (1) Graph-Longest Path (1) Gray Code (1) HOJ (1) Hanoi (1) Hard Algorithm (1) How Hash (1) How to Test (1) Improve It (1) In Place (1) Inorder-Reverse Inorder Traverse Simultaneously (1) Interpolation search (1) Interview (1) Interview - Easy (1) Interview - Facebook (1) Isomorphic (1) JDK8 (1) K Dimensional Tree (1) Knapsack - Fractional (1) Knapsack - ZeroOnePack (1) Knight (1) Kosaraju’s algorithm (1) Kruskal (1) Kruskal MST (1) Kth Element (1) Least Common Ancestor (1) LeetCode - Binary Tree (1) LeetCode - Coding (1) LeetCode - Detail (1) LeetCode - Related (1) LeetCode Diffcult (1) Linked List Reverse (1) Linkedin (1) Linkedin Interview (1) Local MinMax (1) Logic Pattern (1) Longest Common Subsequence (1) Longest Common Substring (1) Longest Prefix Suffix(LPS) (1) Manhattan Distance (1) Map && Reverse Map (1) Math - Induction (1) Math-Multiply (1) Math-Sum Of Digits (1) Matrix - O(N+M) (1) Matrix BFS (1) Matrix Graph (1) Matrix Search (1) Matrix+DP (1) Matrix-Rotate (1) Max Min So Far (1) Median (1) Memory-Efficient (1) MinHash (1) MinMax Heap (1) Monotone Queue (1) Monto Carlo (1) Multi-Reverse (1) Multiple DFS (1) Multiple Tasks (1) Next Successor (1) Offline Algorithm (1) PAT (1) Parent-Only Tree (1) Partition (1) Path Finding (1) Patience Sort (1) Persistent (1) Pigeon Hole Principle (1) Power Set (1) Pratical Algorithm (1) Probabilistic Data Structure (1) Proof (1) Python (1) Queue & Stack (1) RSA (1) Ranking (1) Rddles (1) ReHash (1) Realtime (1) Recurrence Relation (1) Recursive DFS (1) Recursive to Iterative (1) Red-Black Tree (1) Region (1) Regular Expression (1) Resources (1) Reverse Inorder Traversal (1) Robin (1) Selection (1) Self Balancing BST (1) Similarity (1) Sort && Binary Search (1) String Algorithm. Symbol Table (1) String DP (1) String Distance (1) SubMatrix (1) Subsequence (1) System of Difference Constraints(差分约束系统) (1) TSP (1) Ternary Search Tree (1) Test (1) Thread (1) TimSort (1) Top-Down (1) Tournament (1) Tournament Tree (1) Transform Tree in Place (1) Tree Diameter (1) Tree Rotate (1) Trie + DFS (1) Trie and Heap (1) Trie vs Hash (1) Trie vs HashMap (1) Triplet (1) Two Data Structures (1) Two Stacks (1) USACO - Classical (1) USACO - Problems (1) UyHiP (1) Valid Tree (1) Vector (1) Wiggle Sort (1) Wikipedia (1) Yahoo Interview (1) ZOJ (1) baozitraining (1) codevs (1) cos126 (1) javabeat (1) jum (1) namic Programming (1) sqrt(N) (1) 两次dijkstra (1) 九度 (1) 二进制枚举 (1) 夹逼法 (1) 归一化 (1) 折半枚举 (1) 枚举 (1) 状态压缩DP (1) 男人八题 (1) 英雄会 (1) 逆向思维 (1)

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