1. 链表
数组是一种顺序表，index与value之间是一种顺序映射，以(O(1))的复杂度访问数据元素。但是，若要在表的中间部分插入（或删除）某一个元素时，需要将后续的数据元素进行移动，复杂度大概为(O(n))。链表（Linked List）是一种链式表，克服了上述的缺点，插入和删除操作均不会引起元素的移动；数据结构定义如下：
public class ListNode {
String val;
ListNode next;
// ...
}
常见的链表有单向链表（也称之为chain），只有next指针指向后继结点，而没有previous指针指向前驱结点。
链表的插入与删除操作只涉及到next指针的更新，而不会移动数据元素。比如，要在FAT与HAT插入结点GAT，如图所示：
Java实现：
ListNode fat, gat;
gat.next = fat.next;
fat.next = gat;
又比如，要删除结点GAT，如图所示：
Java实现：
fat.next = fat.next.next;
从上述代码中，可以看出：因为没有前驱指针，一般在做插入和删除操作时，我们需要通过操作前驱结点的next指针开始。
2. 题解
| LeetCode题目 | 归类 |
|---|---|
| 237. Delete Node in a Linked List | 删除 |
| 203. Remove Linked List Elements | |
| 19. Remove Nth Node From End of List | |
| 83. Remove Duplicates from Sorted List | |
| 82. Remove Duplicates from Sorted List II | |
| 24. Swap Nodes in Pairs | 移动 |
| 206. Reverse Linked List | |
| 92. Reverse Linked List II | |
| 61. Rotate List | |
| 86. Partition List | |
| 328. Odd Even Linked List | |
| 21. Merge Two Sorted Lists | 合并 |
| 23. Merge k Sorted Lists | |
| 141. Linked List Cycle | 有环 |
| 142. Linked List Cycle II | 有环 |
| 234. Palindrome Linked List | |
| 143. Reorder List | |
| 160. Intersection of Two Linked Lists | |
| 2. Add Two Numbers | |
| 445. Add Two Numbers II |
237. Delete Node in a Linked List
删除指定结点。由于是单向链表，因此只需更新待删除节点即可。
public void deleteNode(ListNode node) {
node.val = node.next.val;
node.next = node.next.next;
}
203. Remove Linked List Elements
删除指定值的结点。用两个指针实现，curr用于遍历，prev用于暂存前驱结点。
public ListNode removeElements(ListNode head, int val) {
ListNode fakeHead = new ListNode(Integer.MIN_VALUE);
fakeHead.next = head;
for (ListNode curr = head, prev = fakeHead; curr != null; curr = curr.next) {
if (curr.val == val) { // remove
prev.next = curr.next;
} else { // traverse
prev = prev.next;
}
}
return fakeHead.next;
}
19. Remove Nth Node From End of List
删除链表的倒数第n个结点。思路：因为单向链表是没有前驱指针的，所以应找到倒数第n+1个结点；n有可能等于链表的长度，故先new一个head的前驱结点fakeHead。用两个指针slow、fast从fakeHead开始，先移动fast n+1步，使得其距离slow为n+1；然后，两个指针同步移动，当fast走到null时，slow即处于倒数第n+1个结点，删除slow的next结点即可。
public ListNode removeNthFromEnd(ListNode head, int n) {
ListNode fakeHead = new ListNode(Integer.MIN_VALUE);
fakeHead.next = head;
ListNode slow = fakeHead, fast = fakeHead;
for (int i = 1; i <= n + 1; i++) {
fast = fast.next;
}
while(fast != null) {
fast = fast.next;
slow = slow.next;
}
slow.next = slow.next.next; // the n-th node from end is `slow.next`
return fakeHead.next;
}
83. Remove Duplicates from Sorted List
删除有序链表中的重复元素。处理思路有上一问题类似，不同的是判断删除的条件。
public ListNode deleteDuplicates(ListNode head) {
ListNode fakeHead = new ListNode(Integer.MIN_VALUE);
fakeHead.next = head;
for (ListNode curr = head, prev = fakeHead; curr != null && curr.next != null; curr = curr.next) {
if (curr.val == curr.next.val) { // remove
prev.next = curr.next;
} else {
prev = prev.next;
}
}
return fakeHead.next;
}
82. Remove Duplicates from Sorted List II
上一问题的升级版，删除所有重复元素结点。在里层增加一个while循环，跳过重复元素结点。
public ListNode deleteDuplicates(ListNode head) {
ListNode fakeHead = new ListNode(Integer.MIN_VALUE);
fakeHead.next = head;
for (ListNode curr = head, prev = fakeHead; curr != null; curr = curr.next) {
while (curr.next != null && curr.val == curr.next.val) { // find the last duplicate
curr = curr.next;
}
if (prev.next == curr) prev = prev.next;
else prev.next = curr.next;
}
return fakeHead.next;
}
24. Swap Nodes in Pairs
链表中两两交换。按step = 2 遍历链表并交换；值得注意的是在更新next指针是有次序的。
public ListNode swapPairs(ListNode head) {
ListNode fakeHead = new ListNode(Integer.MIN_VALUE);
fakeHead.next = head;
for (ListNode prev = fakeHead, p = head; p != null && p.next != null; ) {
ListNode temp = p.next.next;
prev.next = p.next; // update next pointer
p.next.next = p;
p.next = temp;
prev = p;
p = temp;
}
return fakeHead.next;
}
206. Reverse Linked List
逆序整个链表。逆序操作可以看作：依次遍历链表，将当前结点插入到链表头。
public ListNode reverseList(ListNode head) {
ListNode newHead = null;
for (ListNode curr = head; curr != null; ) {
ListNode temp = curr.next;
curr.next = newHead; // insert to the head of list
newHead = curr;
curr = temp;
}
return newHead;
}
92. Reverse Linked List II
上一问题的升级，指定区间[m, n]内做逆序；相当于把该区间的链表逆序后，再拼接到原链表中。
public ListNode reverseBetween(ListNode head, int m, int n) {
ListNode newHead = null, curr = head, firstHead = null, firstHeadPrev = null;
for (int i = 1; curr != null && i <= n; i++) {
if (i < m - 1) {
curr = curr.next;
continue;
}
if (i == m - 1) {
firstHeadPrev = curr; // mark first head previous node
curr = curr.next;
} else {
if (i == m) firstHead = curr; // mark first head node
ListNode temp = curr.next;
curr.next = newHead;
newHead = curr;
curr = temp;
}
}
firstHead.next = curr;
if (firstHeadPrev != null) firstHeadPrev.next = newHead;
if (m == 1) return newHead;
return head;
}
61. Rotate List
指定分隔位置，将链表的左右部分互换。只需修改左右部分的最后节点的next指针即可，有一些special case需要注意，诸如：链表为空，k为链表长度的倍数等。为了得到链表的长度，需要做一次pass。故总共需要遍历链表两次。
public ListNode rotateRight(ListNode head, int k) {
if (head == null || k == 0) return head;
int n = 0, i;
ListNode curr, leftLast = head, rightFist, rightLast = head;
for (curr = head; curr != null; curr = curr.next) { // get the length of list
n++;
}
k %= n; // k maybe larger than n
if (k == 0) return head;
for (i = 1, curr = head; i <= n; i++, curr = curr.next) { // mark the split node
if (i == n - k) leftLast = curr;
if (i == n) rightLast = curr;
}
rightFist = leftLast.next;
leftLast.next = null;
rightLast.next = head;
return rightFist;
}
86. Partition List
类似于quick sort的partition，不同的是要保持链表的原顺序。思路：用两个链表，一个保留小于指定数x，一个保留不大于指定数x；最后拼接到一起即可。
public ListNode partition(ListNode head, int x) {
if (head == null) return null;
ListNode lt = new ListNode(-1), gte = new ListNode(-2); // less than, greater than and equal
ListNode p, p1, p2;
for (p = head, p1 = lt, p2 = gte; p != null; p = p.next) {
if (p.val < x) {
p1.next = p;
p1 = p1.next;
} else {
p2.next = p;
p2 = p2.next;
}
}
p2.next = null;
p1.next = gte.next;
return lt.next;
}
328. Odd Even Linked List
链表分成两部分：偶数编号与奇数编号，将偶数链表拼接到奇数链表的后面。
public ListNode oddEvenList(ListNode head) {
if (head == null || head.next == null) return head;
ListNode odd = head, even = head.next, evenHead = head.next;
while (odd.next != null && odd.next.next != null) {
odd.next = odd.next.next;
odd = odd.next;
if (even != null && even.next != null) {
even.next = even.next.next;
even = even.next;
}
}
odd.next = evenHead; // splice even next to odd
return head;
}
21. Merge Two Sorted Lists
合并两个有序链表。比较简单，分情况比较。
public ListNode mergeTwoLists(ListNode l1, ListNode l2) {
ListNode head = new ListNode(-1), p, p1, p2;
for (p = head, p1 = l1, p2 = l2; p1 != null || p2 != null; p = p.next) {
if (p1 != null) {
if (p2 != null && p1.val > p2.val) {
p.next = p2;
p2 = p2.next;
} else {
p.next = p1;
p1 = p1.next;
}
} else {
p.next = p2;
p2 = p2.next;
}
}
return head.next;
}
23. Merge k Sorted Lists
合并k个有序链表。思路：借助于堆，堆的大小为k，先将每个链表的首结点入堆，堆顶元素即为最小值，堆顶出堆后将next入堆；依此往复，即可得到整个有序链表。
public ListNode mergeKLists(ListNode[] lists) {
if (lists.length == 0) return null;
PriorityQueue<ListNode> minHeap = new PriorityQueue<>(lists.length, new Comparator<ListNode>() {
@Override
public int compare(ListNode o1, ListNode o2) {
return o1.val - o2.val;
}
});
// initialization
for (ListNode node : lists) {
if (node != null)
minHeap.offer(node);
}
ListNode head = new ListNode(-1);
for (ListNode p = head; !minHeap.isEmpty(); ) {
ListNode top = minHeap.poll();
p.next = top;
p = p.next;
if (top.next != null)
minHeap.offer(top.next);
}
return head.next;
}
141. Linked List Cycle
判断链表是否有环。用两个指针，一个快指针一个慢指针，一个每次移动两步，一个每次移动一步；最后两者相遇，即说明有环。
public boolean hasCycle(ListNode head) {
if (head == null) return false;
for (ListNode slow = head, fast = head; fast.next != null && fast.next.next != null; ) {
slow = slow.next;
fast = fast.next.next;
if (slow == fast) return true;
}
return false;
}
142. Linked List Cycle II
找出链表中环的起始节点(s)。解决思路：用两个指针——fast、slow，先判断是否环；两者第一次相遇的节点与(s)的距离 == 链表起始节点与(s)的距离（有兴趣可以证明一下）。
public ListNode detectCycle(ListNode head) {
if (head == null || head.next == null) return null;
ListNode slow = head, fast = head;
boolean isCycled = false;
while (slow != null && fast != null && fast.next != null) { // first meeting
slow = slow.next;
fast = fast.next.next;
if (slow == fast) {
isCycled = true;
break;
}
}
if (!isCycled) return null;
for (fast = head; slow != fast; ) { // find the cycle start node
slow = slow.next;
fast = fast.next;
}
return slow;
}
234. Palindrome Linked List
判断链表(L)是否中心对称。中心对称的充分必要条件：对于任意的 i <= n/2 其中n为链表长度，有L[i] = L[n+1-i]成立。因此先找出middle结点（在距离首结点n/2处），然后逆序右半部分链表，与左半部分链表的结点一一比较，即可得到结果。在找出middle结点时也用到了小技巧——快慢两个指针遍历链表，当fast遍历完成时，slow即为middle结点（证明分n为奇偶情况）；当n为偶数时，middle结点有两个，此时slow为左middle结点。换句话说，无论n为奇数或偶数，此时的slow为右半部分子链表的第一个结点的前驱结点。
public boolean isPalindrome(ListNode head) {
if (head == null) return true;
ListNode slow = head, fast = head, p;
while (fast.next != null && fast.next.next != null) {
slow = slow.next;
fast = fast.next.next;
}
ListNode q = reverseList(slow.next); // the first node of the right half is `slow.next`
for (p = head; q != null; p = p.next, q = q.next) {
if (p.val != q.val) return false;
}
return true;
}
143. Reorder List
对于除去首结点外的链表，将右半部分子链表从后往前依次插入进左半部分链表。解决思路与上类似，找出middle结点，然后依次插入。值得注意：Java的对象传参是引用类型，需要更新左半部份子链表的最后一个结点的next指针，不然则链表的结点的无限循环导致OOM。
public void reorderList(ListNode head) {
if (head == null || head.next == null) return;
ListNode slow = head.next, fast = head.next;
while (fast.next != null && fast.next.next != null) {
slow = slow.next;
fast = fast.next.next;
}
ListNode p, q = reverseList(slow.next);
slow.next = null; // update the next pointer of the left half's last node
for (p = head; q != null; ) {
ListNode pNext = p.next, qNext = q.next;
p.next = q; // insert qNode into the next of p node
q.next = pNext;
p = pNext;
q = qNext;
}
}
160. Intersection of Two Linked Lists
求两个链表相交的第一个结点(P)。假定两个链表的长度分别为m、n，相交的第一个结点(P)分别距离两个链表的首结点为a、b，则根据链表相交的特性：两个链表的尾节点都是同一个，即m-a = n-b；移项后有m+b = n+a。根据上述性质，在遍历完第一个链表后，再往右b个结点，即到达了结点(P)。
public ListNode getIntersectionNode(ListNode headA, ListNode headB) {
if (headA == null || headB == null) return null;
ListNode ptrA = headA, ptrB = headB;
while (ptrA != ptrB) { // in case ptrA == ptrB == null
ptrA = (ptrA != null) ? ptrA.next : headB;
ptrB = (ptrB != null) ? ptrB.next : headA;
}
return ptrA;
}
2. Add Two Numbers
模拟两个链表的加法。开始的时候没理解清楚题意，被坑了多次WA。链表的head表示整数的个位，则应从首端对齐开始做加法。
public ListNode addTwoNumbers(ListNode l1, ListNode l2) {
ListNode head = new ListNode(-1);
boolean carry = false; // mark whether has carry
for (ListNode p = l1, q = l2, r = head; p != null || q != null || carry; r = r.next) {
int pVal = (p == null) ? 0 : p.val;
int qVal = (q == null) ? 0 : q.val;
int sum = carry ? pVal + qVal + 1 : pVal + qVal;
carry = sum >= 10;
r.next = new ListNode(sum % 10);
if (p != null) p = p.next;
if (q != null) q = q.next;
}
return head.next;
}
445. Add Two Numbers II
与上一题不同的是，链表的head表示整数的最高位，则应是尾端对齐相加。为了尾端对齐，将采用stack来逆序链表，之后相加步骤与上类似；但创建新链表应使用头插法。
public ListNode addTwoNumbers(ListNode l1, ListNode l2) {
ListNode p;
Stack<Integer> s1 = new Stack<>();
Stack<Integer> s2 = new Stack<>();
for (p = l1; p != null; p = p.next) {
s1.push(p.val);
}
for (p = l2; p != null; p = p.next) {
s2.push(p.val);
}
ListNode head = new ListNode(-1);
boolean carry = false; // mark whether has carry
for (ListNode r = null; !s1.isEmpty() || !s2.isEmpty() || carry; ) {
int pVal = (s1.isEmpty()) ? 0 : s1.pop();
int qVal = (s2.isEmpty()) ? 0 : s2.pop();
int sum = carry ? pVal + qVal + 1 : pVal + qVal;
carry = sum >= 10;
ListNode node = new ListNode(sum % 10);
node.next = r;
head.next = node;
r = node;
}
return head.next;
}