算法题解之链表
Copy List with Random Pointers
复制带随机指针的链表
思路1：使用哈希表，需要消耗O(N)的额外空间。
1 public class Solution { 2 /** 3 * @param head: The head of linked list with a random pointer. 4 * @return: A new head of a deep copy of the list. 5 */ 6 public RandomListNode copyRandomList(RandomListNode head) { 7 // write your code here 8 9 Map<RandomListNode, RandomListNode> map = new HashMap<RandomListNode, RandomListNode>(); 10 RandomListNode cur = head; 11 RandomListNode copyDummy = new RandomListNode(0); 12 RandomListNode copyCur = copyDummy; 13 14 while (cur != null) { 15 copyCur.next = new RandomListNode(cur.label); 16 copyCur = copyCur.next; 17 map.put(cur, copyCur); 18 cur = cur.next; 19 } 20 21 cur = head; 22 while (cur != null) { 23 copyCur = map.get(cur); 24 copyCur.random = map.get(cur.random); 25 cur = cur.next; 26 } 27 return copyDummy.next; 28 } 29 }
思路2：第一遍扫的时候巧妙运用next指针， 开始数组是1->2->3->4 。 然后扫描过程中 先建立copy节点 1->1`->2->2`->3->3`->4->4`, 然后第二遍copy的时候去建立边的copy， 拆分节点, 一边扫描一边拆成两个链表，这里用到两个dummy node。第一个链表变回 1->2->3 , 然后第二变成 1`->2`->3` 。消耗额外空间O(1)。
1 public class Solution { 2 /** 3 * @param head: The head of linked list with a random pointer. 4 * @return: A new head of a deep copy of the list. 5 */ 6 public RandomListNode copyRandomList(RandomListNode head) { 7 // write your code here 8 copyNext(head); 9 copyRandom(head); 10 return split(head); 11 12 } 13 14 public RandomListNode split(RandomListNode head) { 15 RandomListNode dummy = new RandomListNode(0); 16 RandomListNode cur = dummy; 17 18 while (head != null) { 19 cur.next = head.next; 20 cur = cur.next; 21 head.next = head.next.next; 22 head = head.next; 23 } 24 return dummy.next; 25 26 } 27 28 public void copyRandom(RandomListNode head) { 29 30 while (head != null) { 31 RandomListNode copy = head.next; 32 if (copy.random != null) { 33 copy.random = copy.random.next; 34 } 35 head = head.next.next; 36 } 37 38 } 39 40 public void copyNext(RandomListNode head) { 41 42 while (head != null) { 43 RandomListNode copy = new RandomListNode(head.label); 44 copy.next = head.next; 45 copy.random = head.random; 46 head.next = copy; 47 head = head.next.next; 48 } 49 50 } 51 }
Convert Binary Search Tree to Doubly Linked List
将二叉查找树转换成双链表
思路：用分治法做，分治函数要返回该子树对应的双链表的头节点和尾节点。
1 /** 2 * Definition of TreeNode: 3 * public class TreeNode { 4 * public int val; 5 * public TreeNode left, right; 6 * public TreeNode(int val) { 7 * this.val = val; 8 * this.left = this.right = null; 9 * } 10 * } 11 * Definition for Doubly-ListNode. 12 * public class DoublyListNode { 13 * int val; 14 * DoublyListNode next, prev; 15 * DoublyListNode(int val) { 16 * this.val = val; 17 * this.next = this.prev = null; 18 * } 19 * } 20 */ 21 public class Solution { 22 /** 23 * @param root: The root of tree 24 * @return: the head of doubly list node 25 */ 26 public DoublyListNode bstToDoublyList(TreeNode root) { 27 // Write your code here 28 return helper(root).head; 29 } 30 31 public Pair helper(TreeNode root) { 32 if (root == null) { 33 return new Pair(null, null); 34 } 35 Pair leftPair = helper(root.left); 36 Pair rightPair = helper(root.right); 37 DoublyListNode rootNode = new DoublyListNode(root.val); 38 rootNode.next = rightPair.head; 39 rootNode.prev = leftPair.tail; 40 41 if (leftPair.head == null && rightPair.head == null) { 42 return new Pair(rootNode, rootNode); 43 } else if (leftPair.head == null) { 44 rightPair.head.prev = rootNode; 45 return new Pair(rootNode, rightPair.tail); 46 } else if (rightPair.head == null) { 47 leftPair.tail.next = rootNode; 48 return new Pair(leftPair.head, rootNode); 49 } else { 50 rightPair.head.prev = rootNode; 51 leftPair.tail.next = rootNode; 52 return new Pair(leftPair.head, rightPair.tail); 53 } 54 55 } 56 } 57 58 class Pair { 59 DoublyListNode head; 60 DoublyListNode tail; 61 Pair(DoublyListNode head, DoublyListNode tail) { 62 this.head = head; 63 this.tail = tail; 64 } 65 }
Convert Sorted List to Balanced BST
排序列表转换为二分查找树
思路：分治法。找到链表中点，中点作为根节点，左半段构造一个BST作为左子树，右半段构造一个BST作为右子树。
1 /** 2 * Definition for ListNode. 3 * public class ListNode { 4 * int val; 5 * ListNode next; 6 * ListNode(int val) { 7 * this.val = val; 8 * this.next = null; 9 * } 10 * } 11 * Definition of TreeNode: 12 * public class TreeNode { 13 * public int val; 14 * public TreeNode left, right; 15 * public TreeNode(int val) { 16 * this.val = val; 17 * this.left = this.right = null; 18 * } 19 * } 20 */ 21 public class Solution { 22 /** 23 * @param head: The first node of linked list. 24 * @return: a tree node 25 */ 26 public TreeNode sortedListToBST(ListNode head) { 27 // write your code here 28 if (head == null) { 29 return null; 30 } 31 32 if (head.next == null) { 33 return new TreeNode(head.val); 34 } 35 36 if (head.next.next == null) { 37 TreeNode root = new TreeNode(head.val); 38 root.right = new TreeNode(head.next.val); 39 return root; 40 } 41 42 ListNode befMid = beforeMid(head); 43 TreeNode root = new TreeNode(befMid.next.val); 44 root.right = sortedListToBST(befMid.next.next); 45 befMid.next = null; 46 root.left = sortedListToBST(head); 47 48 return root; 49 50 } 51 52 public ListNode beforeMid(ListNode head) { 53 ListNode cur = head; 54 int length = 0; 55 while (cur != null) { 56 cur = cur.next; 57 length++; 58 } 59 60 int mid = (length + 1) / 2; 61 for(int i = 2; i <= mid -1; i++){ 62 head = head.next; 63 } 64 65 return head; 66 } 67 }
Intersection of Two Linked Lists
两条链表的交点
思路：这道题还做了半天。。分别求出两条链表的长度，得出差值。再用两个指针分别指向两个链表头，将较长链表的指针移动差值个节点后，两个指针开始同时移动，并比较当前链表节点是否相等。
1 public class Solution { 2 public ListNode getIntersectionNode(ListNode headA, ListNode headB) { 3 if (headA == null || headB == null) { 4 return null; 5 } 6 int sizeA = 0; 7 ListNode curA = headA; 8 while (curA != null) { 9 curA = curA.next; 10 sizeA++; 11 } 12 13 int sizeB = 0; 14 ListNode curB = headB; 15 while (curB != null) { 16 curB = curB.next; 17 sizeB++; 18 } 19 20 int diff = Math.abs(sizeA - sizeB); 21 if (sizeA > sizeB) { 22 while (diff-- != 0) { 23 headA = headA.next; 24 } 25 } else { 26 while (diff-- != 0) { 27 headB = headB.next; 28 } 29 } 30 31 while (headA != null) { 32 if (headA == headB) { 33 return headA; 34 } else { 35 headA = headA.next; 36 headB = headB.next; 37 } 38 } 39 return null; 40 } 41 }
Linked List Cycle
带环链表
思路：先起一个快指针和一个慢指针，如果快慢指针能相遇，说明带环。
1 /** 2 * Definition for ListNode. 3 * public class ListNode { 4 * int val; 5 * ListNode next; 6 * ListNode(int val) { 7 * this.val = val; 8 * this.next = null; 9 * } 10 * } 11 */ 12 public class Solution { 13 /** 14 * @param head: The first node of linked list. 15 * @return: True if it has a cycle, or false 16 */ 17 public boolean hasCycle(ListNode head) { 18 // write your code here 19 if (head == null || head.next == null) { 20 return false; 21 } 22 ListNode slow = head; 23 ListNode fast = head.next; 24 while (fast != null && fast.next != null) { 25 if (slow == fast) { 26 return true; 27 } 28 slow = slow.next; 29 fast = fast.next.next; 30 } 31 return false; 32 } 33 }
Linked List Cycle II
带环链表II
思路：先起一个快指针和一个慢指针，快指针和慢指针重合时，从表头再起一个慢指针，两个慢指针继续走，相遇的地方就是环的入口。
1 /** 2 * Definition for ListNode. 3 * public class ListNode { 4 * int val; 5 * ListNode next; 6 * ListNode(int val) { 7 * this.val = val; 8 * this.next = null; 9 * } 10 * } 11 */ 12 public class Solution { 13 /** 14 * @param head: The first node of linked list. 15 * @return: The node where the cycle begins. 16 * if there is no cycle, return null 17 */ 18 public ListNode detectCycle(ListNode head) { 19 // write your code here 20 if (head == null || head.next == null) { 21 return null; 22 } 23 ListNode slow = head; 24 ListNode fast = head.next; 25 26 while (slow != fast) { 27 if (fast == null || fast.next == null) { 28 return null; 29 } 30 slow = slow.next; 31 fast = fast.next.next; 32 } 33 34 while (head != slow.next) { 35 head = head.next; 36 slow = slow.next; 37 } 38 return head; 39 40 } 41 }
merge k sorted lists
合并k个排序链表
思路1：分治法。
时间复杂度分析：
1 T(N,k) = T(N1, k/2) + T(N2, k/2) + N1 + N2 2 3 = T(N1, k/2) + T(N2, k/2) + N 4 5 = T(N11, k/4) + T(N12, k/4) + N11 + N12 + T(N21, k/4) + T(N22, k/4) + N21 + N22 + N 6 7 = T(N11, k/4) + T(N12, k/4) + N1 + T(N21, k/4) + T(N22, k/4) + N2 + N 8 9 = T(N11, k/4) + T(N12, k/4) + T(N21, k/4) + T(N22, k/4) + 2N 10 11 ...... 12 13 = T(n1, 1) + T(n2, 1) +...+ T(nk, 1) + Nlgk = O(Nlgk) 14
1 public class Solution { 2 /** 3 * @param lists: a list of ListNode 4 * @return: The head of one sorted list. 5 */ 6 public ListNode mergeKLists(List<ListNode> lists) { 7 if (lists.size() == 0) { 8 return null; 9 } 10 return mergeHelper(lists, 0, lists.size() - 1); 11 } 12 13 private ListNode mergeHelper(List<ListNode> lists, int start, int end) { 14 if (start == end) { 15 return lists.get(start); 16 } 17 18 int mid = start + (end - start) / 2; 19 ListNode left = mergeHelper(lists, start, mid); 20 ListNode right = mergeHelper(lists, mid + 1, end); 21 return mergeTwoLists(left, right); 22 } 23 24 private ListNode mergeTwoLists(ListNode list1, ListNode list2) { 25 ListNode dummy = new ListNode(0); 26 ListNode tail = dummy; 27 while (list1 != null && list2 != null) { 28 if (list1.val < list2.val) { 29 tail.next = list1; 30 tail = list1; 31 list1 = list1.next; 32 } else { 33 tail.next = list2; 34 tail = list2; 35 list2 = list2.next; 36 } 37 } 38 if (list1 != null) { 39 tail.next = list1; 40 } else { 41 tail.next = list2; 42 } 43 44 return dummy.next; 45 } 46 }
思路2：最小堆
时间复杂度分析：T(N, k) = N * lgk = O(Nlgk)
1 public class Solution { 2 /** 3 * @param lists: a list of ListNode 4 * @return: The head of one sorted list. 5 */ 6 public ListNode mergeKLists(List<ListNode> lists) { 7 // write your code here 8 if (lists == null || lists.size()==0) { 9 return null; 10 } 11 Comparator<ListNode> listNodeComparator = new Comparator<ListNode>() { 12 public int compare(ListNode l1, ListNode l2) { 13 if (l1 == null && l2 == null) { 14 return 1; 15 } else if (l1 == null) { 16 return 1; 17 } else if (l2 == null) { 18 return -1; 19 } else { 20 return l1.val - l2.val; 21 } 22 } 23 }; 24 25 ListNode dummy = new ListNode(0); 26 ListNode cur = dummy; 27 28 PriorityQueue<ListNode> minHeap = new PriorityQueue<ListNode>(lists.size(), listNodeComparator); 29 for (ListNode l : lists) { 30 if (l != null) { 31 minHeap.offer(l); 32 } 33 } 34 35 while (minHeap.peek() != null) { 36 cur.next = minHeap.poll(); 37 cur = cur.next; 38 if (cur.next != null) { 39 minHeap.offer(cur.next); 40 } 41 } 42 cur.next = null; 43 return dummy.next; 44 } 45 }
思路3：两两合并。
时间复杂度分析：
1 T(N, k) = N + T(N, k/2) 2 3 = 2N + T(N, k/4) 4 5 = 3N + T(N, k/8) 6 7 ...... 8 9 = Nlgk + T(N, 1) = O(Nlgk)
1 public class Solution { 2 /** 3 * @param lists: a list of ListNode 4 * @return: The head of one sorted list. 5 */ 6 public ListNode mergeKLists(List<ListNode> lists) { 7 // write your code here 8 if (lists.size() == 0) { 9 return null; 10 } 11 if (lists.size() == 1) { 12 return lists.get(0); 13 } 14 int size = lists.size(); 15 List<ListNode> nextLists = new ArrayList<ListNode>(); 16 for (int i = 0; i<=size-1; i+=2) { 17 if (i == size-1) { 18 nextLists.add(lists.get(i)); 19 break; 20 } 21 ListNode afterMerge = mergeTwoLists(lists.get(i), lists.get(i+1)); 22 nextLists.add(afterMerge); 23 } 24 return mergeKLists(nextLists); 25 } 26 27 public ListNode mergeTwoLists(ListNode l1, ListNode l2) { 28 ListNode dummy = new ListNode(0); 29 ListNode cur = dummy; 30 31 while (l1 != null && l2 != null) { 32 if (l1.val <= l2.val) { 33 cur.next = l1; 34 cur = cur.next; 35 l1 = l1.next; 36 } else { 37 cur.next = l2; 38 cur = cur.next; 39 l2 = l2.next; 40 } 41 } 42 43 if (l1 != null) { 44 cur.next = l1; 45 } 46 47 if (l2 != null) { 48 cur.next = l2; 49 } 50 51 return dummy.next; 52 } 53 }
Partition List
链表划分
思路：用两个dummy接，最后再把两段合起来。
1 /** 2 * Definition for ListNode. 3 * public class ListNode { 4 * int val; 5 * ListNode next; 6 * ListNode(int val) { 7 * this.val = val; 8 * this.next = null; 9 * } 10 * } 11 */ 12 public class Solution { 13 /** 14 * @param head: The first node of linked list. 15 * @param x: an integer 16 * @return: a ListNode 17 */ 18 public ListNode partition(ListNode head, int x) { 19 // write your code here 20 ListNode leftDummy = new ListNode(0); 21 ListNode rightDummy = new ListNode(0); 22 ListNode left = leftDummy; 23 ListNode right = rightDummy; 24 ListNode cur = head; 25 26 while (cur != null) { 27 if (cur.val >= x) { 28 right.next = cur; 29 right = cur; 30 } else { 31 left.next = cur; 32 left = cur; 33 } 34 cur = cur.next; 35 } 36 37 right.next = null; 38 left.next = rightDummy.next; 39 return leftDummy.next; 40 } 41 }
Palindrome Linked List
回文链表
思路：从链表中间切开，对第二段链表做反转，然后看两段链表是否一 一对应。
1 /** 2 * Definition for singly-linked list. 3 * public class ListNode { 4 * int val; 5 * ListNode next; 6 * ListNode(int x) { val = x; } 7 * } 8 */ 9 public class Solution { 10 /** 11 * @param head a ListNode 12 * @return a boolean 13 */ 14 public boolean isPalindrome(ListNode head) { 15 // Write your code here 16 if (head == null || head.next == null) { 17 return true; 18 } 19 ListNode mid = findMid(head); 20 ListNode aftermid = reverse(mid.next); 21 while (aftermid != null) { 22 if (aftermid.val != head.val) { 23 return false; 24 } 25 aftermid = aftermid.next; 26 head = head.next; 27 } 28 return true; 29 30 } 31 32 public ListNode findMid(ListNode head) { 33 if (head == null || head.next == null) { 34 return head; 35 } 36 ListNode slow = head; 37 ListNode fast = head.next; 38 while (fast != null && fast.next != null) { 39 slow = slow.next; 40 fast = fast.next.next; 41 } 42 return slow; 43 } 44 45 public ListNode reverse(ListNode head) { 46 if (head == null || head.next == null) { 47 return head; 48 } 49 ListNode pre = head; 50 ListNode cur = head.next; 51 while (cur != null) { 52 ListNode tmp = cur; 53 cur = cur.next; 54 tmp.next = pre; 55 pre = tmp; 56 } 57 head.next = null; 58 return pre; 59 } 60 }
Reverse Nodes in k-Group
k组翻转链表
思路：先判断能否翻转，如果能，先翻转第一段，后面的递归地进行翻转。
1 /** 2 * Definition for singly-linked list. 3 * public class ListNode { 4 * int val; 5 * ListNode next; 6 * ListNode(int x) { val = x; } 7 * } 8 */ 9 public class Solution { 10 /** 11 * @param head a ListNode 12 * @param k an integer 13 * @return a ListNode 14 */ 15 public ListNode reverseKGroup(ListNode head, int k) { 16 if (head == null || head.next == null) { 17 return head; 18 } 19 20 ListNode cur = head; 21 int count = 0; 22 while (cur != null && count < k) { 23 cur = cur.next; 24 count++; 25 } 26 if (count < k) { 27 return head; 28 } 29 ListNode pre = head; 30 cur = head.next; 31 count = 1; 32 while (count < k) { 33 ListNode tmp = cur; 34 cur = cur.next; 35 tmp.next = pre; 36 pre = tmp; 37 count++; 38 } 39 head.next = reverseKGroup(cur, k); 40 return pre; 41 } 42 }
Swap Two Nodes in Linked List
交换链表中两个节点
思路：先查找这两个节点，如果存在就有两种情况：两个节点相邻，两个节点不相邻。要分开讨论。
1 /** 2 * Definition for singly-linked list. 3 * public class ListNode { 4 * int val; 5 * ListNode next; 6 * ListNode(int x) { val = x; } 7 * } 8 */ 9 public class Solution { 10 /** 11 * @param head a ListNode 12 * @oaram v1 an integer 13 * @param v2 an integer 14 * @return a new head of singly-linked list 15 */ 16 public ListNode swapNodes(ListNode head, int v1, int v2) { 17 // Write your code here 18 ListNode dummy = new ListNode(0); 19 dummy.next = head; 20 ListNode pre1 = null; 21 ListNode pre2 = null; 22 ListNode cur = dummy; 23 while (cur.next != null) { 24 if (cur.next.val == v1) { 25 pre1 = cur; 26 } 27 if (cur.next.val == v2) { 28 pre2 = cur; 29 } 30 cur = cur.next; 31 } 32 33 if (pre1 == null || pre2 == null) { 34 return dummy.next; 35 } 36 if (pre1.val == v2) { 37 ListNode tmp = pre1.next; 38 pre2.next = tmp; 39 pre1.next = tmp.next; 40 tmp.next = pre1; 41 } else if (pre2.val == v1) { 42 ListNode tmp = pre2.next; 43 pre1.next = tmp; 44 pre2.next = tmp.next; 45 tmp.next = pre2; 46 } else { 47 ListNode n1 = pre1.next; 48 ListNode n2 = pre2.next; 49 pre1.next = n2; 50 pre2.next = n1; 51 ListNode tmp = n1.next; 52 n1.next = n2.next; 53 n2.next = tmp; 54 } 55 56 return dummy.next; 57 } 58 }
Sort List
链表排序
思路1：快速排序。
1 /** 2 * Definition for ListNode. 3 * public class ListNode { 4 * int val; 5 * ListNode next; 6 * ListNode(int val) { 7 * this.val = val; 8 * this.next = null; 9 * } 10 * } 11 */ 12 public class Solution { 13 /** 14 * @param head: The head of linked list. 15 * @return: You should return the head of the sorted linked list, 16 using constant space complexity. 17 */ 18 public ListNode sortList(ListNode head) { 19 // write your code here 20 if (head == null || head.next == null) { 21 return head; 22 } 23 resultType pair = partition(head, head.val); 24 ListNode left = sortList(pair.l1); 25 ListNode right = sortList(pair.l2); 26 ListNode equal = pair.l3; 27 28 ListNode dummy = new ListNode(0); 29 dummy.next = left; 30 ListNode leftTail = dummy; 31 32 33 while (leftTail.next != null) { 34 leftTail = leftTail.next; 35 } 36 37 if (equal != null) { 38 leftTail.next = equal; 39 while (equal.next != null) { 40 equal = equal.next; 41 } 42 43 equal.next = right; 44 } else { 45 leftTail.next = right; 46 } 47 return dummy.next; 48 } 49 50 public resultType partition(ListNode head, int x) { 51 ListNode leftDummy = new ListNode(0); 52 ListNode rightDummy = new ListNode(0); 53 ListNode equalDummy = new ListNode(0); 54 ListNode leftTail = leftDummy; 55 ListNode rightTail = rightDummy; 56 ListNode equalTail = equalDummy; 57 58 while (head != null) { 59 if (head.val < x) { 60 leftTail.next = head; 61 head = head.next; 62 leftTail = leftTail.next; 63 } else if (head.val > x) { 64 rightTail.next = head; 65 head = head.next; 66 rightTail = rightTail.next; 67 } else { 68 equalTail.next = head; 69 head = head.next; 70 equalTail = equalTail.next; 71 } 72 } 73 leftTail.next = null; 74 rightTail.next = null; 75 equalTail.next = null; 76 77 return new resultType(leftDummy.next, rightDummy.next, equalDummy.next); 78 79 } 80 81 } 82 83 class resultType { 84 ListNode l1; 85 ListNode l2; 86 ListNode l3; 87 resultType(ListNode l1, ListNode l2, ListNode l3) { 88 this.l1 = l1; 89 this.l2 = l2; 90 this.l3 = l3; 91 } 92 }
思路2：归并排序也是可以的，因为链表的merge操作不需要额外的空间。
