1 #ifndef VECTOR_H
2 #define VECTOR_H
3
4 #include <algorithm>
5
6 template<typename Object>
7 class Vector
8 {
9 private:
10 int theSize; //实际数据大小
11 int theCapacity; //实际容器容量大小
12 Object *objects; //基本数组
13 public:
14 enum { SPACE_CAPACITY = 16 }; //默认容量大小
15
16 explicit Vector(int initSize = 0) //单参数构造函数要用explicit()避免类型在后台转换
17 : theSize(initSize), theCapacity(initSize + SPACE_CAPACITY) {
18 objects = new Object[theCapacity];
19 }
20 Vector(const Vector& rhs) : objects(NULL) { //复制构造函数--调用operator=对已有的Vector进行复制
21 operator = (rhs);
22 }
23 ~Vector() {
24 delete[] objects;
25 }
26
27 const Vector& operator = (const Vector& rhs) //重载赋值运算符
28 {
29 if (this != &rhs) //避免复制自身--混淆检验
30 {
31 delete []objects; //删除旧的内存空间
32 theSize = rhs.size(); //生成同样的样本大小
33 theCapacity = rhs.theCapacity; //生成同样的容量大小
34
35 objects = new Object[capacity()]; //生成与所复制的Vector同样容量的新数组
36 for (int k = 0; k < size(); k++)
37 objects[k] = rhs.objects[k];
38 }
39 return *this;
40 }
41
42 void resize(int newSize)
43 {
44 if (newSize > theCapacity) //重置大小
45 reserve(newSize * 2 + 1); //新大小
46 theSize = newSize;
47 }
48
49 //扩容
50 void reserve(int newCapacity)
51 {
52 if (newCapacity < theSize) //至少和（样本大小）一样大
53 return;
54
55 Object *oldArray = objects; //oldArray--用于复制旧数组内容
56 objects = new Object[newCapacity];
57 for (int k = 0; k < theSize; k++)
58 objects[k] = oldArray[k];
59
60 theCapacity = newCapacity;
61 delete []oldArray;
62 }
63
64 Object& operator[] (int index)
65 {
66 return objects[index];
67 }
68 const Object& operator[] (int index) const
69 {
70 return objects[index];
71 }
72
73 bool empty() const {
74 return size() == 0;
75 }
76
77 int size() const {
78 return theSize;
79 }
80 int capacity() const {
81 return theCapacity;
82 }
83 //在数据尾端插入元素
84 void push_back(const Object& x) {
85 if (theSize == theCapacity)
86 reserve(2 * theCapacity + 1);
87 objects[theSize++] = x;
88 }
89
90 //在index位置前端插入数据data
91 void insert(int index, const Object& data) {
92 if (theSize == theCapacity)
93 reserve(2 * theCapacity + 1);
94 for (int i = theSize; i >= index; i--) {
95 objects[i] = objects[i - 1];
96 }
97 objects[index] = data;
98 theSize++;
99 }
100
101 void pop_back() {
102 theSize--;
103 }
104
105 //区间删除 [lo, hi) --- 左闭右开！！ --- 删除索引从 1,2..k
106 int remove(int lo, int hi) {
107 if (lo == hi) return 0;
108 while (hi < theSize) {
109 objects[lo++] = objects[hi++]; //[hi,theSize)顺次前移 hi-lo 位
110 }
111 theSize = lo;
112 return hi - lo; //返回被删除元素数目
113 }
114 //重载删除一个指定位置元素--删除r位置元素，[r,r+1). 如果先写删除单个元素函数，删除区间时会低效.
115 Object remove(int r) {
116 Object oldElem = objects[r];
117 remove(r, r + 1);
118 return oldElem; //返回删除的元素
119 }
120
121 //order the vector
122 //二分查找--有序向量
123 int Search(Object &elem, int lo, int hi) {
124 while (lo < hi) { //不变性: A[0,lo) <= e < A[hi,n)
125 int mid = (lo + hi) >> 1; // 以中点为轴
126 (elem < objects[mid]) ? hi = mid : lo = mid + 1; // [lo,mi) 或 (mi,hi)
127 } // 出口时,A[lo = hi]为大于elem的最小元素
128 return --lo; // lo-1即为不大于elem的元素的最大秩
129 }
130
131 /*mergesort()归并排序
132 /*无序向量的递归分解，两个有序的子序列合成大的子序列*/
133 void mergeSort(int lo, int hi) {
134 if (hi - lo < 2) return;
135 int mid = (lo + hi) >> 1;
136 mergeSort(lo, mid); //对前半段排序
137 mergeSort(mid, hi); //对后半段排序
138 merge(lo, mid, hi); //归并
139 }
140
141 //归并---O(nlogn), T(n) = 2T(n/2) + O(n)
142 void merge(int lo, int mid, int hi) {
143 //A用来存放合并后的向量，B，C进行比较(前后子向量比较)
144 Object *A = objects + lo; //合并后的向量A[0,hi-lo) = objects[lo,hi)
145 int lb = mid - lo;
146 Object *B = new Object[lb]; //前子向量 B[0,lb) = objects[lo,mi)
147 for (int i = 0; i < lb; B[i] = A[i++]); //复制前子向量
148 int lc = hi - mid;
149 Object *C = objects + mid; //后子向量
150 for (int i = 0, j = 0, k = 0; (j < lb || k < lc);) {
151 //B[i], C[k]中小者转至A的末尾.
152 //因为C本来就占据A中，不需要考虑提前耗尽情况
153 if ((j < lb) && (k >= lc || C[k] >= B[j])) //C[k]已无或不小
154 A[i++] = B[j++];
155 if ((k < lc) && (j >= lb || B[j] >= C[k])) //B[k]已无或不小
156 A[i++] = C[k++];
157 }
158 delete []B;
159 }
160
161 //有序向量的去重, 重复的元素必定紧邻,每个区间只保留单个---每次常数，累计O(n)
162 int uniquify() {
163 int i = 0, j = 0; //各对互异,"相邻"元素的秩,逐一扫描,直至末元素
164 while (++j < theSize) {
165 //跳过雷同者,发现不同元素时，向前移至紧邻元素
166 if (objects[i] != objects[j]) objects[++i] = objects[j];
167 }
168 theSize = ++i;
169 return j - i; //返回被删除元素总数
170 }
171
172
173 //得到尾元素
174 const Object& back() const {
175 return objects[theSize - 1];
176 }
177
178 typedef Object * iterator;
179 typedef const Object * const_iterator;
180
181 iterator begin() {
182 return &objects[0];
183 }
184 const_iterator begin() const {
185 return &objects[0];
186 }
187 iterator end() { //尾后的不存在的指针
188 return &objects[size()];
189 }
190 const_iterator end() const {
191 return &objects[size()];
192 }
193
194 };
195
196
197
198 #endif // VECTOR_H
1 /************************************************************************/
2 /* Vs2013, c++11标准编写 测试vector.h */
3 /************************************************************************/
4 #include <iostream>
5 #include <cstring>
6 #include "Vector.h"
7 using namespace std;
8
9 int test[100] = { 0 };
10
11 void Merge(int *test, int lo, int mid, int hi);
12 void MergeSort(int *test, int lo, int hi) {
13 if (hi - lo < 2) return;
14 int mid = (lo + hi) >> 1;
15 MergeSort(test, lo, mid); //对前半段排序
16 MergeSort(test, mid, hi); //对后半段排序
17 Merge(test, lo, mid, hi); //归并
18 }
19
20 //归并---O(nlogn), T(n) = 2T(n/2) + O(n)
21 void Merge(int *test, int lo, int mid, int hi) {
22 //A用来存放合并后的向量，B，C进行比较(前后子向量比较)
23 int *A = test + lo; //合并后的向量A[0,hi-lo) = int s[lo,hi)
24 int lb = mid - lo;
25 int *B = new int [lb]; //前子向量 B[0,lb) = int s[lo,mi)
26 for (int i = 0; i < lb; B[i] = A[i++]); //复制前子向量
27 int lc = hi - mid;
28 int *C = test + mid; //后子向量
29 for (int i = 0, j = 0, k = 0; (j < lb || k < lc);) {
30 //B[i], C[k]中小者转至A的末尾.
31 //因为C本来就占据A中，不需要考虑提前耗尽情况
32 if ((j < lb) && (k >= lc || C[k] >= B[j])) //C[k]已无或不小
33 A[i++] = B[j++];
34 if ((k < lc) && (j >= lb || B[j] >= C[k])) //B[k]已无或不小
35 A[i++] = C[k++];
36 }
37 delete[]B;
38 }
39
40
41 int main()
42 {
43 //用来测试 非模板写的 归并排序 算法
44 /*int Test[13] = { 1, 5, 2, 3, 6, 8, 9, 10, 13, 12, 4, 7, 11 };
45 MergeSort(Test, 0, 13);
46 for (int i = 0; i < 13; i++)
47 cout << Test[i] << " ";
48 cout << endl;*/
49
50 Vector<int> testOne;
51 int testData, cnt, index;
52 cout << "输入数字数目: ";
53 cin >> cnt;
54 cout << "输入 " << cnt << "个数: ";
55 while (cnt-- && cin >> testData)
56 {
57 testOne.push_back(testData);
58 }
59
60 cout << "显示所有元素: ";
61 for (int i = 0; i < testOne.size(); i++) {
62 cout << testOne[i] << " ";
63 }
64 cout << endl;
65
66 cout << "\n输入插入元素位置(0...k)和插入的数值: ";
67 cin >> index >> testData;
68 testOne.insert(index, testData);
69 cout << "显示所有元素: ";
70 for (int i = 0; i < testOne.size(); i++) {
71 cout << testOne[i] << " ";
72 }
73 cout << endl;
74
75 cout << "\n输入删除元素位置(0...k): ";
76 cin >> index;
77 testOne.remove(index);
78 cout << "显示所有元素: ";
79 for (int i = 0; i < testOne.size(); i++) {
80 cout << testOne[i] << " ";
81 }
82 cout << endl;
83
84 cout << "\n归并排序向量元素: \n"; testOne.mergeSort(0, testOne.size());
85 cout << "显示所有元素: ";
86 for (int i = 0; i < testOne.size(); i++) {
87 cout << testOne[i] << " ";
88 }
89 cout << endl;
90
91 cout << "\n(有序向量)(二分查找:)输入查找元素: ";
92 cin >> testData;
93 cout << "查找位置返回(不大于查找元素的最大的秩): "
94 << testOne.Search(testData, 0, testOne.size()) << endl;
95
96 cout << "\n(有序向量)去除重复元素: \n"; testOne.uniquify();
97 cout << "显示所有元素: ";
98 for (int i = 0; i < testOne.size(); i++) {
99 cout << testOne[i] << " ";
100 }
101 cout << endl;
102
103 return 0;
104
105 }
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