左神算法课笔记（二）：链表、栈和队列、递归Master公式、哈希表、有序表

单向链表

双向链表

单链表、双链表最简单的面试题

1、单链表和双链表如何反转

package class02;import java.util.ArrayList;public class Code01_ReverseList {public static class Node {public int value;public Node next;public Node(int data) {value = data;}}public static class DoubleNode {public int value;public DoubleNode last;public DoubleNode next;public DoubleNode(int data) {value = data;}}public static Node reverseLinkedList(Node head) {Node pre = null;Node next = null;while (head != null) {next = head.next;head.next = pre;pre = head;head = next;}return pre;}public static DoubleNode reverseDoubleList(DoubleNode head) {DoubleNode pre = null;DoubleNode next = null;while (head != null) {next = head.next;head.next = pre;head.last = next;pre = head;head = next;}return pre;}public static Node testReverseLinkedList(Node head) {if (head == null) {return null;}ArrayList<Node> list = new ArrayList<>();while (head != null) {list.add(head);head = head.next;}list.get(0).next = null;int N = list.size();for (int i = 1; i < N; i++) {list.get(i).next = list.get(i - 1);}return list.get(N - 1);}public static DoubleNode testReverseDoubleList(DoubleNode head) {if (head == null) {return null;}ArrayList<DoubleNode> list = new ArrayList<>();while (head != null) {list.add(head);head = head.next;}list.get(0).next = null;DoubleNode pre = list.get(0);int N = list.size();for (int i = 1; i < N; i++) {DoubleNode cur = list.get(i);cur.last = null;cur.next = pre;pre.last = cur;pre = cur;}return list.get(N - 1);}public static Node generateRandomLinkedList(int len, int value) {int size = (int) (Math.random() * (len + 1));if (size == 0) {return null;}size--;Node head = new Node((int) (Math.random() * (value + 1)));Node pre = head;while (size != 0) {Node cur = new Node((int) (Math.random() * (value + 1)));pre.next = cur;pre = cur;size--;}return head;}public static DoubleNode generateRandomDoubleList(int len, int value) {int size = (int) (Math.random() * (len + 1));if (size == 0) {return null;}size--;DoubleNode head = new DoubleNode((int) (Math.random() * (value + 1)));DoubleNode pre = head;while (size != 0) {DoubleNode cur = new DoubleNode((int) (Math.random() * (value + 1)));pre.next = cur;cur.last = pre;pre = cur;size--;}return head;}// 要求无环，有环别用这个函数public static boolean checkLinkedListEqual(Node head1, Node head2) {while (head1 != null && head2 != null) {if (head1.value != head2.value) {return false;}head1 = head1.next;head2 = head2.next;}return head1 == null && head2 == null;}// 要求无环，有环别用这个函数public static boolean checkDoubleListEqual(DoubleNode head1, DoubleNode head2) {boolean null1 = head1 == null;boolean null2 = head2 == null;if (null1 && null2) {return true;}if (null1 ^ null2) {return false;}if (head1.last != null || head2.last != null) {return false;}DoubleNode end1 = null;DoubleNode end2 = null;while (head1 != null && head2 != null) {if (head1.value != head2.value) {return false;}end1 = head1;end2 = head2;head1 = head1.next;head2 = head2.next;}if (head1 != null || head2 != null) {return false;}while (end1 != null && end2 != null) {if (end1.value != end2.value) {return false;}end1 = end1.last;end2 = end2.last;}return end1 == null && end2 == null;}public static void main(String[] args) {int len = 50;int value = 100;int testTime = 100000;for (int i = 0; i < testTime; i++) {Node node1 = generateRandomLinkedList(len, value);Node reverse1 = reverseLinkedList(node1);Node back1 = testReverseLinkedList(reverse1);if (!checkLinkedListEqual(node1, back1)) {System.out.println("oops!");break;}DoubleNode node2 = generateRandomDoubleList(len, value);DoubleNode reverse2 = reverseDoubleList(node2);DoubleNode back2 = testReverseDoubleList(reverse2);if (!checkDoubleListEqual(node2, back2)) {System.out.println("oops!");break;}}System.out.println("finish!");}
}

2、把给定值都删除

package class02;public class Code02_DeleteGivenValue {public static class Node {public int value;public Node next;public Node(int data) {this.value = data;}}public static Node removeValue(Node head, int num) {while (head != null) {if (head.value != num) {break;}head = head.next;}// head来到 第一个不需要删的位置Node pre = head;Node cur = head;// while (cur != null) {if (cur.value == num) {pre.next = cur.next;} else {pre = cur;}cur = cur.next;}return head;}
}

栈和队列

栈
队列
栈和队列的实际实现：

双向链表实现（头指针、尾指针）提供四种方法：从头部进、从头部出、从尾部进、从尾部出
数组实现

1、双向链表实现

package class02;import java.util.LinkedList;
import java.util.Queue;
import java.util.Stack;public class Code03_DoubleEndsQueueToStackAndQueue {public static class Node<T> {public T value;public Node<T> last;public Node<T> next;public Node(T data) {value = data;}}public static class DoubleEndsQueue<T> {public Node<T> head;public Node<T> tail;public void addFromHead(T value) {Node<T> cur = new Node<T>(value);if (head == null) {head = cur;tail = cur;} else {cur.next = head;head.last = cur;head = cur;}}public void addFromBottom(T value) {Node<T> cur = new Node<T>(value);if (head == null) {head = cur;tail = cur;} else {cur.last = tail;tail.next = cur;tail = cur;}}public T popFromHead() {if (head == null) {return null;}Node<T> cur = head;if (head == tail) {head = null;tail = null;} else {head = head.next;cur.next = null;head.last = null;}return cur.value;}public T popFromBottom() {if (head == null) {return null;}Node<T> cur = tail;if (head == tail) {head = null;tail = null;} else {tail = tail.last;tail.next = null;cur.last = null;}return cur.value;}public boolean isEmpty() {return head == null;}}public static class MyStack<T> {private DoubleEndsQueue<T> queue;public MyStack() {queue = new DoubleEndsQueue<T>();}public void push(T value) {queue.addFromHead(value);}public T pop() {return queue.popFromHead();}public boolean isEmpty() {return queue.isEmpty();}}public static class MyQueue<T> {private DoubleEndsQueue<T> queue;public MyQueue() {queue = new DoubleEndsQueue<T>();}public void push(T value) {queue.addFromHead(value);}public T poll() {return queue.popFromBottom();}public boolean isEmpty() {return queue.isEmpty();}}public static boolean isEqual(Integer o1, Integer o2) {if (o1 == null && o2 != null) {return false;}if (o1 != null && o2 == null) {return false;}if (o1 == null && o2 == null) {return true;}return o1.equals(o2);}public static void main(String[] args) {int oneTestDataNum = 100;int value = 10000;int testTimes = 100000;for (int i = 0; i < testTimes; i++) {MyStack<Integer> myStack = new MyStack<>();MyQueue<Integer> myQueue = new MyQueue<>();Stack<Integer> stack = new Stack<>();Queue<Integer> queue = new LinkedList<>();for (int j = 0; j < oneTestDataNum; j++) {int nums = (int) (Math.random() * value);if (stack.isEmpty()) {myStack.push(nums);stack.push(nums);} else {if (Math.random() < 0.5) {myStack.push(nums);stack.push(nums);} else {if (!isEqual(myStack.pop(), stack.pop())) {System.out.println("oops!");}}}int numq = (int) (Math.random() * value);if (stack.isEmpty()) {myQueue.push(numq);queue.offer(numq);} else {if (Math.random() < 0.5) {myQueue.push(numq);queue.offer(numq);} else {if (!isEqual(myQueue.poll(), queue.poll())) {System.out.println("oops!");}}}}}System.out.println("finish!");}
}

2、数组实现

动态数组 / 固定大小的静态数组

package class02;public class Code04_RingArray {public static class MyQueue {private int[] arr;private int pushi;private int polli;private int size;private final int limit;public MyQueue(int limit) {arr = new int[limit];pushi = 0;polli = 0;size = 0;this.limit = limit;}public void push(int value) {if (size == limit) {throw new RuntimeException("栈满了，不能再加了");}size++;arr[pushi] = value;pushi = nextIndex(pushi);}public int pop() {if (size == 0) {throw new RuntimeException("栈空了，不能再拿了");}size--;int ans = arr[polli];polli = nextIndex(polli);return ans;}public boolean isEmpty() {return size == 0;}// 如果现在的下标是i，返回下一个位置private int nextIndex(int i) {return i < limit - 1 ? i + 1 : 0;}}
}

3、实现一个特殊额栈

维护一个最小栈。

普通栈正常使用，最小栈存放的是每一个状态下当前数的最小值

普通栈和最小栈同步push、pop，只不过给用户返回的是普通栈里的内容

4、如何用队列实现一个栈

两个队列，都是从头进、从尾出
data队列
help队列

例如，现在要push进1,2,3,4,5

现在要 pop 1,2,3,4,5
（除了最后一个数5以外，剩余的移动到help队列中，留下5用来给用户返回，更改data队列和help队列的属性，这样以此类推）

package class02;import java.util.Stack;public class Code06_TwoStacksImplementQueue {public static class TwoStacksQueue {public Stack<Integer> stackPush;public Stack<Integer> stackPop;public TwoStacksQueue() {stackPush = new Stack<Integer>();stackPop = new Stack<Integer>();}// push栈向pop栈倒入数据private void pushToPop() {if (stackPop.empty()) {while (!stackPush.empty()) {stackPop.push(stackPush.pop());}}}public void add(int pushInt) {stackPush.push(pushInt);pushToPop();}public int poll() {if (stackPop.empty() && stackPush.empty()) {throw new RuntimeException("Queue is empty!");}pushToPop();return stackPop.pop();}public int peek() {if (stackPop.empty() && stackPush.empty()) {throw new RuntimeException("Queue is empty!");}pushToPop();return stackPop.peek();}}public static void main(String[] args) {TwoStacksQueue test = new TwoStacksQueue();test.add(1);test.add(2);test.add(3);System.out.println(test.peek());System.out.println(test.poll());System.out.println(test.peek());System.out.println(test.poll());System.out.println(test.peek());System.out.println(test.poll());}}

5、如何用栈实现一个队列

维护两个栈：
push栈，pop栈
现用户给我1,2,3,4,5

现在我要pop

（1）pop栈为空的时候才能往外导数据
（2）如果决定导数据，push栈在导的过程中要一次性的导完

只要满足上面两个原则，不管什么时候导数据，都是对的

package class02;import java.util.LinkedList;
import java.util.Queue;
import java.util.Stack;public class Code07_TwoQueueImplementStack {public static class TwoQueueStack<T> {public Queue<T> queue;public Queue<T> help;public TwoQueueStack() {queue = new LinkedList<>();help = new LinkedList<>();}public void push(T value) {queue.offer(value);}public T poll() {while (queue.size() > 1) {help.offer(queue.poll());}T ans = queue.poll();Queue<T> tmp = queue;queue = help;help = tmp;return ans;}public T peek() {while (queue.size() > 1) {help.offer(queue.poll());}T ans = queue.poll();help.offer(ans);Queue<T> tmp = queue;queue = help;help = tmp;return ans;}public boolean isEmpty() {return queue.isEmpty();}}public static void main(String[] args) {System.out.println("test begin");TwoQueueStack<Integer> myStack = new TwoQueueStack<>();Stack<Integer> test = new Stack<>();int testTime = 1000000;int max = 1000000;for (int i = 0; i < testTime; i++) {if (myStack.isEmpty()) {if (!test.isEmpty()) {System.out.println("Oops");}int num = (int) (Math.random() * max);myStack.push(num);test.push(num);} else {if (Math.random() < 0.25) {int num = (int) (Math.random() * max);myStack.push(num);test.push(num);} else if (Math.random() < 0.5) {if (!myStack.peek().equals(test.peek())) {System.out.println("Oops");}} else if (Math.random() < 0.75) {if (!myStack.poll().equals(test.pop())) {System.out.println("Oops");}} else {if (myStack.isEmpty() != test.isEmpty()) {System.out.println("Oops");}}}}System.out.println("test finish!");}
}

递归

例子

递归函数的思维导图

下面这个解法的复杂度是O(n)

package class02;public class Code08_GetMax {// 求arr中的最大值public static int getMax(int[] arr) {return process(arr, 0, arr.length - 1);}// arr[L..R]范围上求最大值  L ... R   Npublic static int process(int[] arr, int L, int R) {if (L == R) { // arr[L..R]范围上只有一个数，直接返回，base casereturn arr[L];}int mid = L + ((R - L) >> 1); // 中点     1int leftMax = process(arr, L, mid);int rightMax = process(arr, mid + 1, R);return Math.max(leftMax, rightMax);}
}

递归在语言上是怎么实现的？
递归实际上是运用的系统栈
任何递归都可以改成非递归。
“尾递归”是一些语言对递归行为进行的优化，在底层执行的过程中已经是迭代了。

对于某一类递归，它的时间复杂度是可以直接确定的：
子问题的规模是N/b，子问题被调用a次，除去递归调用过程之外剩下所有行为的时间复杂度是O(n^d)

则时间复杂度可以直接确定如下（Master公式）：

比如说我们上面这个问题就是

哈希表 HashMap

有序表 TreeMap

有序表的特点在于，你可以乱序插入元素，但他自己内部是有序的。
但是它的时间复杂度是O(logn)
有序表的底层实现可以是AVL树/SB树/红黑树，或跳表
非基础类型在有序表中，怎么比较大小？以后会在堆的章节讲。

package class02;import java.util.HashMap;
import java.util.HashSet;
import java.util.TreeMap;public class HashMapAndSortedMap {public static class Node{public int value;public Node(int v) {value = v;}}public static void main(String[] args) {// UnSortedMapHashMap<Integer, String> map = new HashMap<>();map.put(1000000, "我是1000000");map.put(2, "我是2");map.put(3, "我是3");map.put(4, "我是4");map.put(5, "我是5");map.put(6, "我是6");map.put(1000000, "我是1000001");System.out.println(map.containsKey(1));System.out.println(map.containsKey(10));System.out.println(map.get(4));System.out.println(map.get(10));map.put(4, "他是4");System.out.println(map.get(4));map.remove(4);System.out.println(map.get(4));//       keyHashSet<String>  set = new HashSet<>();set.add("abc");set.contains("abc");set.remove("abc");// 哈希表，增、删、改、查，在使用时，O（1）System.out.println("=====================");int a = 100000;int b = 100000;System.out.println(a == b);Integer c = 100000;Integer d = 100000;System.out.println(c.equals(d));Integer e = 127;  //  - 128  ~  127Integer f = 127;System.out.println(e == f);HashMap<Node, String> map2 = new HashMap<>();Node node1 = new Node(1);Node node2 = node1;map2.put(node1, "我是node1");map2.put(node2, "我是node1");System.out.println(map2.size());System.out.println("======================");TreeMap<Integer, String> treeMap = new TreeMap<>();treeMap.put(3, "我是3");treeMap.put(4, "我是4");treeMap.put(8, "我是8");treeMap.put(5, "我是5");treeMap.put(7, "我是7");treeMap.put(1, "我是1");treeMap.put(2, "我是2");System.out.println(treeMap.containsKey(1));System.out.println(treeMap.containsKey(10));System.out.println(treeMap.get(4));System.out.println(treeMap.get(10));treeMap.put(4, "他是4");System.out.println(treeMap.get(4));treeMap.remove(4);System.out.println(treeMap.get(4));System.out.println(treeMap.firstKey());System.out.println(treeMap.lastKey());// <= 4System.out.println(treeMap.floorKey(4));// >= 4System.out.println(treeMap.ceilingKey(4));// O(logN)  }
}