链表结构、栈、队列、递归行为、哈希表和有序表
链表节点结构
单向链表节点结构
public class Node{
public int value;
public Node next;
public Node(int data){
value=data;
}
}
双向链表节点结构
public class DoubleNode{
public int value;
public DoubleNode last;
public DoubleNode next;
public DoubleNode(int data){
value=data;
}
}
单向链表和双向链表最简单的练习题（链表的相关问题几乎都是coding问题）
1、反转单向链表和双向链表
package com.harrison.two;
import java.util.ArrayList;
import java.util.List;
//反转单向链表和双向链表
public class Code01_ReverseList {
public static class Node {
public int value;
public Node next;
public Node(int data) {
// 构造方法
this.value = data;
}
}
public static class DoubleNode {
public int value;
public DoubleNode last;
public DoubleNode next;
public DoubleNode(int data) {
this.value = data;
}
}
// 反转单链表
// 1->2->3->4
public static Node reverseLinkedList(Node head) {
Node pre = null;
Node next = null;
while (head != null) {
next = head.next;// next指向2，意味着next就是2->3->4
head.next = pre;// head.next为null，意味着1和2断开，此时head就是1
pre = head;// pre为1，这是反转后的链表
head = next;// head重新赋值为next，也就是2->3->4
}
return pre;
}
// 反转双向链表
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;
}
public static List<Integer> getLinkedListOriginOrder(Node head) {
List<Integer> ans = new ArrayList<>();
while (head != null) {
ans.add(head.value);
head = head.next;
}
return ans;
}
public static boolean checkLinkedListReverse(List<Integer> origin, Node head) {
for (int i = origin.size() - 1; i >= 0; i--) {
if (!origin.get(i).equals(head.value)) {
return false;
}
head = head.next;
}
return true;
}
public static List<Integer> getDoubleListOriginOrder(DoubleNode head) {
List<Integer> ans = new ArrayList<>();
while (head != null) {
ans.add(head.value);
head = head.next;
}
return ans;
}
public static boolean checkDoubleListReverse(List<Integer> origin, DoubleNode head) {
DoubleNode end = null;
for (int i = origin.size() - 1; i >= 0; i--) {
if (!origin.get(i).equals(head.value)) {
return false;
}
end = head;
head = head.next;
}
for (int i = 0; i < origin.size(); i++) {
if (!origin.get(i).equals(end.value)) {
return false;
}
end = end.last;
}
return true;
}
public static void main(String[] args) {
int len = 50;
int value = 100;
int testTime = 100000;
System.out.println("test begin!");
for (int i = 0; i < testTime; i++) {
Node node1 = generateRandomLinkedList(len, value);
List<Integer> list1 = getLinkedListOriginOrder(node1);
node1 = reverseLinkedList(node1);
if (!checkLinkedListReverse(list1, node1)) {
System.out.println("Oops1!");
}
Node node2 = generateRandomLinkedList(len, value);
List<Integer> list2 = getLinkedListOriginOrder(node2);
node2 = testReverseLinkedList(node2);
if (!checkLinkedListReverse(list2, node2)) {
System.out.println("Oops2!");
}
DoubleNode node3 = generateRandomDoubleList(len, value);
List<Integer> list3 = getDoubleListOriginOrder(node3);
node3 = reverseDoubleList(node3);
if (!checkDoubleListReverse(list3, node3)) {
System.out.println("Oops3!");
}
DoubleNode node4 = generateRandomDoubleList(len, value);
List<Integer> list4 = getDoubleListOriginOrder(node4);
node4 = reverseDoubleList(node4);
if (!checkDoubleListReverse(list4, node4)) {
System.out.println("Oops4!");
}
}
System.out.println("test finish!");
}
}
2、把给定值都删除
package com.harrison.two;
//删除给定值
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) {
// head来到第一个不需要删的位置
while (head != null) {
if (head.value != num) {
break;
}
head = head.next;
}
// 1 ) head == null
// 2 ) head != null
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;
}
}
栈和队列的实际实现
其底层实现原理双向链表的调整，而且时间复杂度都是O(1)，跟数据量没有关系，因为总是在操作一个头和一个尾。实现方式有两种：双向链表实现和数组实现
栈和队列常见面试题：怎么用数组实现不超过固定大小的队列和栈？栈——正常使用 队列——环形数组
1、双向链表实现
package com.harrison.two;
import java.util.Stack;
import java.util.LinkedList;
import java.util.Queue;
//栈和队列的实际实现：1、双向链表实现
//使用双向链表节点类型实现一个队列
public class Code03_DoubleEndsQueueToStackAndQueue {
// 双向链表节点类型
public static class Node<T> {
public T value;
public Node<T> last;
public Node<T> next;
public Node(T data) {
this.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
package com.harrison.two;
//栈和队列的实际实现：2、数组实现
public class Code04_RingArray {
public static class MyQueue {
private int[] arr;
private int pushi;// end
private int polli;// begin
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("队列满了，不能再加了");
}
size++;
arr[pushi] = value;
pushi = nextIndex(pushi);
}
public int pop() {
if (size == 0) {
throw new RuntimeException("队列空了，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、实现一个特殊的栈，在基本功能（pop()和push()）的基础上，再实现返回栈中最小元素的功能
- pop()、push()、getMin()操作的时间都是O(1)
- 设计的栈类型可以使用现成的栈结构
分析1）：设计两个栈，data栈和min栈，data栈是普通的栈，正常加数据，第一个数两个栈都加，从第二个数开始，min栈加数据的原则为：当前的数和目前最小栈的栈顶谁小加谁。所以说，data栈和min栈同步上升，弹出数据的时候两个栈一起弹，弹出数据没有规则。这种方法费一点空间，省一点时间，因为弹出时不要判断。
分析2）：前面相同，从第二个数开始，如果当前数比最小栈的栈顶大，不压入min栈；如果当前数小于等于最小栈的栈顶，压入min栈。弹出规则：当前要弹出的数与最小栈的栈顶相等的时候弹出。这种方法省一点空间，费一点时间
package com.harrison.two;
import java.util.Stack;
//实现一个特殊的栈，在基本功能（pop()和push()）的基础上，再实现返回栈中最小元素的功能
public class Code05_GetMinStack {
public static class MyStack1 {
private Stack<Integer> stackData;
private Stack<Integer> stackMin;
public MyStack1() {
this.stackData = new Stack<Integer>();
this.stackMin = new Stack<Integer>();
}
public void push(int newNum) {
if (this.stackMin.isEmpty()) {
this.stackMin.push(newNum);
} else if (newNum <= this.getmin()) {
this.stackMin.push(newNum);
}
this.stackData.push(newNum);
}
public int pop() {
if (this.stackData.isEmpty()) {
throw new RuntimeException("Your stack is empty.");
}
int value = this.stackData.pop();
if (value == this.getmin()) {
this.stackMin.pop();
}
return value;
}
public int getmin() {
if (this.stackMin.isEmpty()) {
throw new RuntimeException("Your stack is empty.");
}
return this.stackMin.peek();
}
}
public static class MyStack2 {
private Stack<Integer> stackData;
private Stack<Integer> stackMin;
public MyStack2() {
this.stackData = new Stack<Integer>();
this.stackMin = new Stack<Integer>();
}
public void push(int newNum) {
if (this.stackMin.isEmpty()) {
this.stackMin.push(newNum);
} else if (newNum < this.getmin()) {
this.stackMin.push(newNum);
} else {
int newMin = this.stackMin.peek();
this.stackMin.push(newMin);
}
this.stackData.push(newNum);
}
public int pop() {
if (this.stackData.isEmpty()) {
throw new RuntimeException("Your stack is empty.");
}
this.stackMin.pop();
return this.stackData.pop();
}
public int getmin() {
if (this.stackMin.isEmpty()) {
throw new RuntimeException("Your stack is empty.");
}
return this.stackMin.peek();
}
}
public static void main(String[] args) {
MyStack1 stack1 = new MyStack1();
stack1.push(3);
System.out.println(stack1.getmin());
stack1.push(4);
System.out.println(stack1.getmin());
stack1.push(1);
System.out.println(stack1.getmin());
System.out.println(stack1.pop());
System.out.println(stack1.getmin());
System.out.println("=============");
MyStack1 stack2 = new MyStack1();
stack2.push(3);
System.out.println(stack2.getmin());
stack2.push(4);
System.out.println(stack2.getmin());
stack2.push(1);
System.out.println(stack2.getmin());
System.out.println(stack2.pop());
System.out.println(stack2.getmin());
}
}
如何用栈结构实现队列结构（用两个栈）
如何用两个栈拼队列结构：设计两个栈，push栈和pop栈，压入pop栈的时候，pop必须为空。push栈倒出数据的时候，一定要一次全都倒空
package com.harrison.two;
import java.util.Stack;
//如何用栈结构实现队列结构：用两个栈拼队列结构
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());
}
}
如何用队列结构实现栈结构（用两个队列）
package com.harrison.two;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Stack;
//如何用队列结构实现栈结构（用两个队列）
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
- 怎么从思想上理解递归
- 怎么从实际实现的角度出发理解递归
递归是有实际结构支持其运行的，任何递归行为都能改成非递归行为，方法就是不让系统帮忙压栈，而是自己去压栈模拟这个行为。因为递归实际上运用的是系统栈。
例：求数组arr[L…R]中的最大值，怎么用递归方法实现：
- 将arr[L…R]范围分成左右两半，左边[L…Mid]，右边[Mid+1…R]
- 左部分求最大值，右部分求最大值
- [L…R]范围上的最大值就是max{左部分最大值，右部分最大值}
注意：2是个递归过程，当范围上只有一个数，就可以不用再递归了
package com.harrison.two;
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 N
public static int process(int[] arr, int L, int R) {
// arr[L..R]范围上只有一个数，直接返回，base case
if (L == R) {
return arr[L];
}
// L...R 不只一个数
// mid = (L + R) / 2
int mid = L + ((R - L) >> 1); // 中点 1
int leftMax = process(arr, L, mid);
int rightMax = process(arr, mid + 1, R);
return Math.max(leftMax, rightMax);
}
}
哈希表和有序表
哈希表
Java中int、double、float等基本类型是按值传递；Integer、Double、Float等包裹出来的大类型，使用的时候是按引用传递，但是如果值在-128~127范围时，又变成按值传递。超过此范围才按引用传递。但是这些大类型在哈希表里一律按值传递！！！但是哈希表并不总是按值传递，非系统规定的类型，如自己定义的类型就会按引用传递。
哈希表在使用层面可以理解为一种集合结构，如果只有key，没有伴随数据value，可以使用HashSet结构；如果都有，可以使用HashMap结构。有无伴随数据是二者唯一的区别，实际结构是一回事。
使用哈希表增删改查的操作，可以认为时间复杂度为O(1)，但是常数时间比较大。
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有序表
哈希表所有的增删改查有序表都支持，次外，可以把记录乱序存入有序表，但在有序表内部是按顺序组织好的，从小到大的顺序。但是以上操作的时间复杂度为O(logn)。
package com.harrison.two;
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) {
// key value
HashMap<Integer, String>map=new HashMap<>();
map.put(1,"我是1");
map.put(2,"我是2");
map.put(3,"我是3");
map.put(4,"我是4");
System.out.println(map.containsKey(1));
System.out.println(map.containsKey(10));
System.out.println(map.get(4));
System.out.println(map.get(10));
System.out.println(map.get(10)==null);
map.put(4,"他是4");
System.out.println(map.get(4));
map.remove(4);
System.out.println(map.get(4));
// key
HashSet<String> set=new HashSet<>();
set.add("abc");
set.contains("abc");
set.remove("abc");
//哈希表 增、删、改、查，在使用时，时间复杂度都是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==d);
Integer e=127;
Integer f=127;
System.out.println(e==f);
Integer g=128;
Integer h=128;
System.out.println(g==h);
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(10,"我是10");
treeMap.put(2,"我是2");
treeMap.put(40,"我是40");
treeMap.put(7,"我是7");
System.out.println(treeMap.containsKey(1));
System.out.println(treeMap.containsKey(10));
System.out.println(treeMap.get(4));
System.out.println(treeMap.get(10));
System.out.println(treeMap.get(10)==null);
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());
//<=8
System.out.println(treeMap.floorKey(8));
//>=8
System.out.println(treeMap.ceilingKey(8));
}
}