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  • 数据结构-栈与队列

    1. 相比于数组这种存储数据的数据，栈(Stock)和队列(Queue)主要作用是在程序中作为构思算法的辅助工具，是一种程序员开发过程中的便利工具。Stock和Queue具有访问受限以及更加抽象的特征。

    一、栈

    栈只允许访问最后一个插入的元素，即栈是先进后出(FILO)的一种数据结构。栈主要提供的算法包括push，pop和peek。其中push是插入一个元素，pop是弹出最近添加的一个元素，peek是返回最近添加的一个元素。

    栈的底层实现可以是数组，也可以是链表，这里采用数组实现一个栈，代码如下：

     1 public class Stock1<T> {
 2     private static final int EMPTY_TOP = -1;
 3     private int maxSize;
 4     private Object[] stockArray;
 5     private int top;
 6 
 7     public Stock1() {
 8         this(16);
 9     }
10 
11     public Stock1(int initialCapacity) {
12         if (initialCapacity < 0) {
13             throw new IllegalArgumentException("The initialCapacity value must > 0, this value is:" + initialCapacity);
14         }
15 
16         this.maxSize = initialCapacity;
17         this.top = EMPTY_TOP;
18         this.stockArray = new Object[this.maxSize];
19     }
20 
21     public void push(T value) {
22         this.checkIndex(this.top + 1);
23         this.stockArray[++this.top] = value;
24     }
25 
26     @SuppressWarnings("unchecked")
27     public T pop() {
28         this.checkIndex(this.top);
29         return ((T) this.stockArray[this.top--]);
30     }
31 
32     @SuppressWarnings("unchecked")
33     public T peek() {
34         this.checkIndex(this.top);
35         return (T) this.stockArray[this.top];
36     }
37 
38     public boolean isEmpty() {
39         return this.top == EMPTY_TOP;
40     }
41 
42     public boolean isFull() {
43         return this.top == this.maxSize - 1;
44     }
45 
46     public int size() {
47         return this.top + 1;
48     }
49 
50     private void checkIndex(int index) {
51         if (index < 0 || index >= maxSize) {
52             throw new IllegalArgumentException("The index is error, index:=" + index + ", the max index is:" + (maxSize - 1));
53         }
54     }
55 
56     @Override
57     public String toString() {
58         StringBuffer sb = new StringBuffer(this.maxSize);
59         for (int i = this.top; i >= 0; i--) {
60             sb.append(this.stockArray[i]).append(",");
61         }
62         return "[" + sb.substring(0, Math.max(sb.length() - 1, 0)) + "]";
63     }
64 }
    View Code

    二、队列

    队列和栈一样，也只允许访问一个元素，但是这个元素是最早插入的，即队列是一个先进先出(FIFO)的数据结构。队列主要提供的算法包括insert，remove和peek。其中insert是在队列的尾部插入一个元素；remove是在队列的头部删除一个元素，并返回；peek是返回队列头部的元素的值。

    队列的底层实现和栈一样，可以是数组或者是链表，代码如下：

     1 public class Queue1<T extends Comparable<T>> {
 2     private static int EMPTY_INDEX = 0;
 3     protected final int maxSize;
 4     protected final Comparable<T>[] queueArray;
 5     protected int head;
 6     protected int tail;
 7     protected int size;
 8 
 9     @SuppressWarnings("unchecked")
10     public Queue1(int initialCapacity) {
11         if (initialCapacity < 0) {
12             throw new IllegalArgumentException("The initialCapacity value must > 0, this value is:" + initialCapacity);
13         }
14 
15         this.maxSize = initialCapacity;
16         this.queueArray = (Comparable<T>[]) Array.newInstance(Comparable.class, this.maxSize);
17         this.head = EMPTY_INDEX;
18         this.tail = EMPTY_INDEX;
19         this.size = 0;
20     }
21 
22     public void push(T value) {
23         if (isFull()) {
24             throw new IllegalArgumentException("The queue is full, can't push value to this queue.");
25         } else {
26             this.size++;
27             this.queueArray[(this.tail++) % this.maxSize] = value;
28         }
29     }
30 
31     @SuppressWarnings("unchecked")
32     public T pop() {
33         if (isEmpty()) {
34             throw new IllegalArgumentException("The queue is empty, can't pop value.");
35         } else {
36             this.size--;
37             return (T) this.queueArray[(this.head++) % this.maxSize];
38         }
39     }
40 
41     @SuppressWarnings("unchecked")
42     public T peek() {
43         if (isEmpty()) {
44             throw new IllegalArgumentException("The queue is empty, can't peek value.");
45         } else {
46             return (T) this.queueArray[this.head % this.maxSize];
47         }
48     }
49 
50     public boolean isEmpty() {
51         return this.size == 0;
52     }
53 
54     public boolean isFull() {
55         return this.size == this.maxSize;
56     }
57 
58     public int size() {
59         return this.size;
60     }
61 }
    View Code

    这段代码中我将insert方法换成了push方法，remove方法换成了pop方法。

    三、优先级队列

    优先级队列和普通队列类似，区别在于在remove元素的时候，返回的元素值是按照某种顺序来定义的。实现优先级队列有两种方式：

    第一种，在插入元素的时候，按顺排列。即每次插入的时候，都会将要插入的元素插入到对应位置，并移动其他元素。此时插入的时间复杂度是O(n2)，但是这样删除的代码和普通队列一样。

    第二中，在插入元素的时候，直接将元素填充到队列尾部，但是在删除的时候，search全部数据，选择出要删除的数据出来。此时插入时间复杂度O(1)，删除复杂度为O(n2)。

    我们采用第一种方式来实现一个队列，针对插入数据慢的问题，我们可以采用堆来解决这个问题，以后再说。代码如下：

    第一种代码是继承普通队列，只修改push方法:

     1 public class PriorityQueue1<T extends Comparable<T>> extends Queue1<T> {
 2     public PriorityQueue1(int initialCapacity) {
 3         super(initialCapacity);
 4     }
 5 
 6     public void push(T value) {
 7         if (isFull()) {
 8             throw new IllegalArgumentException("This queue is full");
 9         } else {
10             int index = super.head;
11             for (int i = 0; i < super.size; i++) {
12                 int compareResult = super.queueArray[index++ % super.maxSize].compareTo(value);
13                 if (compareResult >= 0) {
14                     index--;
15                     break;
16                 }
17             }
18 
19             for (int i = super.tail; i > index; i--) {
20                 super.queueArray[i % super.maxSize] = super.queueArray[(i - 1) % super.maxSize];
21             }
22 
23             super.queueArray[index] = value;
24             super.tail++;
25             super.size++;
26         }
27     }
28 }
    View Code

    第二种是不继承普通队列，自己实现：

     1 public class PriorityQueue2<T extends Comparable<T>> {
 2     protected final int maxSize;
 3     protected int nItems;
 4     protected Comparable<T>[] basicArray;
 5 
 6     @SuppressWarnings("unchecked")
 7     public PriorityQueue2(int initialCapacity) {
 8         if (initialCapacity < 0) {
 9             throw new IllegalArgumentException("The initialCapacity value must > 0, this value is:" + initialCapacity);
10         }
11 
12         this.maxSize = initialCapacity;
13         this.basicArray = (Comparable<T>[]) Array.newInstance(Comparable.class, this.maxSize);
14         this.nItems = 0;
15     }
16 
17     public boolean isEmpty() {
18         return this.nItems == 0;
19     }
20 
21     public boolean isFull() {
22         return this.nItems == this.maxSize;
23     }
24 
25     public int size() {
26         return this.nItems;
27     }
28 
29     public void push(T value) {
30         if (this.isFull()) {
31             throw new IllegalArgumentException("This queue is full, can't push value.");
32         } else {
33             int index = 0;
34             for (; index < this.nItems; index++) {
35                 if (this.basicArray[index].compareTo(value) <= 0) {
36                     break;
37                 }
38             }
39 
40             for (int j = this.nItems; j > index; j--) {
41                 this.basicArray[j] = this.basicArray[j - 1];
42             }
43 
44             this.basicArray[index] = value;
45             this.nItems++;
46         }
47     }
48 
49     @SuppressWarnings("unchecked")
50     public T pop() {
51         if (this.isEmpty()) {
52             throw new IllegalArgumentException("This queue is empty, can't pop value.");
53         } else {
54             return (T) this.basicArray[--nItems];
55         }
56     }
57 
58     @SuppressWarnings("unchecked")
59     public T peek() {
60         if (this.isEmpty()) {
61             throw new IllegalArgumentException("This queue is empty, can't peek value.");
62         } else {
63             return (T) this.basicArray[this.nItems - 1];
64         }
65     }
66 }
    View Code

    四、其他代码

    1.解析表达式，将中缀表达式转换成后缀表达式

      1 public class InToPost {
  2     private Stock1<Character> stock;
  3     private Queue1<String> queue;
  4     private String input;
  5     private StringBuffer sb;
  6 
  7     public InToPost(String input) {
  8         if (input != null && input.length() != 0) {
  9             this.input = input.trim();
 10         } else {
 11             this.input = "";
 12         }
 13 
 14         this.stock = new Stock1<>(this.input.length());
 15         this.sb = new StringBuffer(this.input.length());
 16         this.queue = new Queue1<>(this.input.length());
 17     }
 18 
 19     public String getInput() {
 20         return input;
 21     }
 22 
 23     public String getOutput() {
 24         return this.sb.toString();
 25     }
 26 
 27     public String doTranshi() {
 28         StringBuffer tmp = new StringBuffer();
 29 
 30         for (int j = 0; j < this.input.length(); j++) {
 31             char ch = this.input.charAt(j);
 32             switch (ch) {
 33             case '+':
 34             case '-':
 35                 pushValueToQueue(tmp.toString());
 36                 sb.append(tmp.toString());
 37                 tmp = new StringBuffer();
 38                 gotPot(ch, 1);
 39                 break;
 40 
 41             case '*':
 42             case '/':
 43                 pushValueToQueue(tmp.toString());
 44                 sb.append(tmp.toString());
 45                 tmp = new StringBuffer();
 46                 gotPot(ch, 2);
 47                 break;
 48 
 49             case '(':
 50                 this.stock.push(ch);
 51                 break;
 52 
 53             case ')':
 54                 pushValueToQueue(tmp.toString());
 55                 sb.append(tmp.toString());
 56                 tmp = new StringBuffer();
 57                 while (!this.stock.isEmpty()) {
 58                     char chx = this.stock.pop();
 59                     if (chx == '(') {
 60                         break;
 61                     } else {
 62                         sb.append(chx);
 63                         pushValueToQueue(String.valueOf(chx));
 64                     }
 65                 }
 66                 break;
 67 
 68             default:
 69                 tmp.append(ch);
 70                 break;
 71             }
 72         }
 73 
 74         pushValueToQueue(tmp.toString());
 75         sb.append(tmp.toString());
 76 
 77         while (!this.stock.isEmpty()) {
 78             char ch = this.stock.pop();
 79             this.sb.append(ch);
 80             pushValueToQueue(String.valueOf(ch));
 81         }
 82 
 83         return this.getOutput();
 84     }
 85 
 86     private void gotPot(char ch, int prec) {
 87         while (!this.stock.isEmpty()) {
 88             char chx = this.stock.pop();
 89             if (chx == '(') {
 90                 this.stock.push(chx);
 91                 break;
 92             } else {
 93                 int prec2 = 2;
 94                 if (chx == '+' || chx == '-') {
 95                     prec2 = 1;
 96                 }
 97                 if (prec2 >= prec) {
 98                     sb.append(chx);
 99                     pushValueToQueue(String.valueOf(chx));
100                 } else {
101                     this.stock.push(chx);
102                     break;
103                 }
104             }
105         }
106         this.stock.push(ch);
107     }
108 
109     private void pushValueToQueue(String value) {
110         if (value == null || value.trim().length() == 0) {
111             return;
112         }
113         this.queue.push(value.trim());
114     }
115 
116     public Queue1<String> getQueue() {
117         return this.queue;
118     }
119 }
120 
121 class InToPostUtil {
122     public static String doTranshi(String line) {
123         return new InToPost(line).doTranshi();
124     }
125 }
126 
127 class InToPostApp {
128     public static void main(String[] args) {
129         System.out.println(InToPostUtil.doTranshi(null));
130         System.out.println(InToPostUtil.doTranshi(""));
131         System.out.println(InToPostUtil.doTranshi("     "));
132         System.out.println(InToPostUtil.doTranshi("a*b+c"));
133         System.out.println(InToPostUtil.doTranshi("a*(b+c)"));
134         System.out.println(InToPostUtil.doTranshi("a*(b+c*d)"));
135         System.out.println(InToPostUtil.doTranshi("a*(b+c*d/(e-f*g))"));
136     }
137 }
    View Code

    2.计算后缀表达式的值

     1 package com.augmentum.gby.ds;
 2 
 3 public class ParsePost {
 4     private String line;
 5     private InToPost inToPost;
 6 
 7     public ParsePost(String line) {
 8         this.line = line;
 9         this.inToPost = new InToPost(this.line);
10     }
11 
12     public double doParse() {
13         String reline = this.inToPost.doTranshi();
14         if (reline == null || reline.length() == 0) {
15             throw new IllegalArgumentException("The input line value is empty. can't calc those value.");
16         } else {
17             Stock1<Double> stock = new Stock1<>(reline.length());
18             Queue1<String> queue = this.inToPost.getQueue();
19             while (!queue.isEmpty()) {
20                 String value = queue.pop();
21                 if ("+".equals(value) || "-".equals(value) || "*".equals(value) || "/".equals(value)) {
22                     double num1 = stock.pop();
23                     double num2 = stock.pop();
24                     switch (value.charAt(0)) {
25                     case '+':
26                         stock.push(num1 + num2);
27                         break;
28                     case '-':
29                         stock.push(num2 - num1);
30                         break;
31                     case '*':
32                         stock.push(num2 * num1);
33                         break;
34                     case '/':
35                         stock.push(num2 / num1);
36                         break;
37                     }
38                 } else {
39                     stock.push(Double.valueOf(value));
40                 }
41             }
42             return stock.pop();
43         }
44     }
45 }
46 
47 class ParsePostUtil {
48     public static double doParse(String line) {
49         return new ParsePost(line).doParse();
50     }
51 }
52 
53 class ParsePostApp {
54     public static void main(String[] args) {
55         System.out.println(InToPostUtil.doTranshi("2*((3+4)*5+5)"));
56         System.out.println(InToPostUtil.doTranshi("2*3+4") + "; The result is:" + ParsePostUtil.doParse("2*3+4"));
57         System.out.println(InToPostUtil.doTranshi("2*(3+4)") + "; The result is:" + ParsePostUtil.doParse("2*(3+4)"));
58         System.out.println(InToPostUtil.doTranshi("2*(3+4*5)") + "; The result is:" + ParsePostUtil.doParse("2*(3+4*5)"));
59         System.out.println(InToPostUtil.doTranshi("2*3+4*5") + "; The result is:" + ParsePostUtil.doParse("2*3+4*5"));
60         System.out.println(InToPostUtil.doTranshi("2*((3+4)*5+5)") + "; The result is:" + ParsePostUtil.doParse("2*((3+4)*5+5)"));
61         System.out.println(InToPostUtil.doTranshi("2*((3+4)*5+9)") + "; The result is:" + ParsePostUtil.doParse("2*((3+4)*5+9)"));
62         System.out.println(InToPostUtil.doTranshi("20*3+4") + "; The result is:" + ParsePostUtil.doParse("20*3+4"));
63         System.out.println(InToPostUtil.doTranshi("20.5*4+4") + "; The result is:" + ParsePostUtil.doParse("20.5*4+4"));
64     }
65 }
    View Code
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  • 原文地址：https://www.cnblogs.com/liuming1992/p/4205303.html
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