算法之美_源代码发布（9）

本文辑录了《算法之美——隐匿在数据结构背后的语言》（电子工业出版社2016年出版）一书第10章前半部分之代码（P321~P357）。全文目录、“45个算法”目录、“22个经典问题目录”，以及有奖捉虫活动详情请见如下链接：http://blog.csdn.net/baimafujinji/article/details/50484348

附录中的经典笔试、面试问题参考答案请见：

http://blog.csdn.net/baimafujinji/article/details/50484683

In general， 我不太喜欢翻开一本书（技术书），里面密密麻麻的全部都是代码。所以我也希望能够在我的书中留下更多空间去讨论原理。当然，代码也很重要，所有的一切原理最终都要落实到代码上。为此我习惯于在博客中上传代码，而非是把他们全部罗列到书中去挤占篇幅。

如果你是该书的读者，强烈建议你加入算法学习群（495573865），内有更多资源等你，而你在读书中遇到的疑问也将得到我第一时间的解答。更多关注本博客，我将陆续发布该书全部源代码至本博客。

P327： 向量集合的声明部分

VecSet.h文件

#ifndef VECSET_H#define VECSET_H#include <iostream>#include <assert.h>using namespace std;const int DefaultSize = 100;class VecSet{int* contain;int size;public:VecSet(int MaxSize = DefaultSize);~VecSet();void Add(int add);void Del(int del);void MakeEmpty();int GetSize(){return size;}bool IsMember(const int x);VecSet& operator+(VecSet& another);VecSet& operator-(VecSet& another);VecSet& operator*(VecSet& another);VecSet& operator=(VecSet& another);bool operator==(VecSet& another);friend ostream& operator<<(ostream& stream,VecSet& set);};#endif

P329： 向量集合的实现部分

VecSet.cpp文件

#include "VecSet.h"VecSet::~VecSet(){if(contain != NULL)delete [] contain;}VecSet::VecSet(int MaxSize):size(MaxSize){assert(MaxSize>0);contain = new int[size];assert(contain != NULL);     MakeEmpty();}void VecSet::Add(int add){assert(add>=0 && add<size);contain[add]=1;}void VecSet::Del(int del){assert(del>=0 && del<size);contain[del]=0;}void VecSet::MakeEmpty(){for(int i=0;i<size;i++){contain[i]=0;}}bool VecSet::IsMember(const int x){assert(x >= 0 && x < size);return contain[x] != 0;}VecSet& VecSet::operator+(VecSet& another){assert(this->GetSize() == another.GetSize());VecSet* temp = new VecSet(this->GetSize()); for(int i=0;i<size;i++){(*temp).contain[i] = contain[i]||another.contain[i];}return *temp;}VecSet& VecSet::operator-(VecSet& another){assert(this->GetSize() == another.GetSize());VecSet* temp = new VecSet(this->GetSize()); for(int i=0;i<size;i++){(*temp).contain[i] = contain[i]&&(!another.contain[i]);}return *temp;}VecSet& VecSet::operator*(VecSet& another){assert(this->GetSize() == another.GetSize());VecSet* temp = new VecSet(this->GetSize()); for(int i=0;i<size;i++){(*temp).contain[i] = contain[i]&&another.contain[i];}return *temp;}VecSet& VecSet::operator=(VecSet& another){assert(this->GetSize() == another.GetSize());for(int i=0;i<size;i++){contain[i] = another.contain[i];}return *this;}bool VecSet::operator == (VecSet& another){assert(this->GetSize() == another.GetSize());for(int i=0;i<size;i++){if(contain[i] != another.contain[i]){return false;}}return true;}ostream& operator<<(ostream& stream,VecSet& set){for(int i=0;i<set.GetSize();i++){if(set.IsMember(i)) cout<<i<<" ";}cout<<endl;returnstream;}

向量集合测试程序

#include <iostream>#include "VecSet.h"using namespace std;int main(int argc, char** argv) {VecSet a(8);VecSet b(8);VecSet c(8);for(int i=1; i<=5; i++){a.Add(i);}b.Add(2);b.Add(3);b.Add(4);b.Add(5);b.Add(7);b.Del(4); cout<< a * b;cout<< a + b;cout<< a - b;c = b;cout<<c;cout<<(c==b);return 0;}

P332：链表集合的实现

ListSet.h文件

#ifndef LISTSET_H#define LISTSET_H#include <iostream>using namespace std;template <class T> class ListSet;template <class T>class ListSetNode{friend class ListSet<T>;T data;ListSetNode<T>* link;public:ListSetNode() :link(NULL){}ListSetNode(T value) :link(NULL), data(value){}};template <class T>class ListSet{ListSetNode<T>* head;ListSetNode<T>* tail;public:ListSet();~ListSet();ListSet(ListSet & lset);void Add(T add);void Del(T del);bool IsEmpty();void MakeEmpty();ListSet<T>& operator+(ListSet<T>& another);ListSet<T>& operator-(ListSet<T>& another);ListSet<T>& operator*(ListSet<T>& another);ListSet<T>& operator=(ListSet<T>& another);bool operator==(ListSet<T>& another);void Output();ListSetNode<T>* GetHead(){ return head; }};template <class T>ListSet<T>::ListSet(){this->head = new ListSetNode<T>();this->tail = this->head;}template <class T>ListSet<T>::~ListSet(){MakeEmpty();delete head;}template <class T>void ListSet<T>::Add(T value){ListSetNode<T>* add = new ListSetNode<T>(value);ListSetNode<T>* preCurrent = head;//记录当前结点ListSetNode<T>* current = preCurrent->link;//记录当前结点的前驱结点while (current != NULL && current->data < value)//寻找插入位置{preCurrent = current;current = preCurrent->link;}if (head == tail && current == NULL)//向空链表中插入结点{head->link = add;tail = add;}if (head != tail && current == NULL)//向链表尾插入值add{preCurrent->link = add;add->link = NULL;tail = add;}if (current != NULL && current->data == value)//链表中已存在值add{return;}if (current != NULL && current->data > value){preCurrent->link = add;add->link = current;}}template <class T>void ListSet<T>::Del(T del){ListSetNode<T>* preCurrent = head;ListSetNode<T>* current = preCurrent->link;while (current != NULL && current->data != del)//寻找删除结点{preCurrent = current;current = preCurrent->link;}if (current != NULL){preCurrent->link = current->link;if (current->link == NULL){ tail = preCurrent; }//更新表尾指针delete current;}}template <class T>bool ListSet<T>::IsEmpty(){return head == tail;//判断集合是否为空}template <class T>void ListSet<T>::MakeEmpty(){ListSetNode<T>* current = head->link;ListSetNode<T>* del = NULL;while (head->link != NULL)//循环删除集合中的元素{head->link = current->link;del = current;current = current->link;delete del;//调用delete释放当前结点}tail = head;}template <class T>ListSet<T>& ListSet<T>::operator=(ListSet<T>& another){MakeEmpty();ListSetNode<T>* current = another.head->link;while (current != NULL){Add(current->data);current = current->link;}return *this;}template <class T>ListSet<T>::ListSet(ListSet<T>& lset){this->head = new ListSetNode<T>();this->tail = this->head;ListSetNode<T>* current = lset.head->link;while (current != NULL){Add(current->data);current = current->link;}}template <class T>ListSet<T>& ListSet<T>::operator+(ListSet<T>& another){ListSet<T>* tmpSet = new ListSet(another);ListSetNode<T>* current = this->head->link;while (current != NULL){tmpSet->Add(current->data);current = current->link;}return *tmpSet;//返回当前集合的引用}template <class T>ListSet<T>& ListSet<T>::operator-(ListSet<T>& another){ListSet<T>* tmpSet = new ListSet(*this);ListSetNode<T>* current = another.head->link;while (current != NULL){tmpSet->Del(current->data);current = current->link;}return *tmpSet;}template <class T>ListSet<T>& ListSet<T>::operator*(ListSet<T>& another){ListSet<T>* tmpSet = new ListSet(*this);*tmpSet = *this - another;*tmpSet = *this - *tmpSet;return *tmpSet;}template <class T>bool ListSet<T>::operator==(ListSet<T>& another){ListSetNode<T>* current1 = head->link;ListSetNode<T>* current2 = another.head->link;while (current1 != NULL){if (current2 == NULL){ return false; }if (current1->data != current2->data){ return false; }current1 = current1->link;current2 = current2->link;}if (current2 != NULL){ return false; }return true;}template <class T>void ListSet<T>::Output(){ListSetNode<T>* current = this->GetHead()->link;while(current != NULL){cout << current->data << " ";current = current->link;}cout << endl;}#endif

基于链表实现的集合之测试程序

#include "stdafx.h"#include "ListSet.h"using namespace std;int _tmain(int argc, _TCHAR* argv[]){ListSet<int> listSetA;ListSet<int> listSetB;ListSet<int> listSetC;for (int i = 1; i <= 5; i++){listSetA.Add(i);}//cout << listSetA.IsEmpty()<<endl;//listSetA.MakeEmpty();//cout << listSetA.IsEmpty()<<endl;//listSetC = listSetA;//listSetC.Output();ListSet<int> listSetD(listSetA);cout << (listSetA == listSetD) << endl;listSetB.Add(2);listSetB.Add(3);listSetB.Add(5);listSetB.Add(7);listSetB.Add(8);listSetB.Add(5);listSetB.Del(8);listSetC = listSetA + listSetB;listSetC.Output();listSetC = listSetA - listSetB;listSetC.Output();listSetC = listSetA * listSetB;listSetC.Output();system("PAUSE");return 0;}

P336：字典

Item.h文件

#ifndef _ITEM_H_#define _ITEM_H_#include <iostream>#include <string.h>using namespace std;class Item {string english;string chinese;Item*  link;public:Item() : link(NULL){}Item(string en, string ch) : link(NULL), english(en),chinese(ch) {}~Item(){};void SetLink(Item* next);Item*  GetLink();string GetIndex();string GetValue();};void Item::SetLink(Item* next){link = next;}Item* Item::GetLink(){return link;}string Item::GetIndex(){//返回结点中的数据return english;}string Item::GetValue(){//返回结点中的数据return chinese;}#endif

Dictionary.h文件

#ifndef _DICTIONARY_H_#define _DICTIONARY_H_#include "Item.h"class Dictionary{Item* head;Item* tail;public:Dictionary();virtual ~Dictionary();bool Add(string en, string ch);bool Del(string en);string Search(string en);int GetCount();void RemoveAll();};Dictionary::Dictionary(){head = new Item();tail = head;tail->SetLink(NULL);}Dictionary::~Dictionary(){RemoveAll();delete head;}bool Dictionary ::Add(string en, string ch){Item* add = new Item(en, ch);tail->SetLink(add);tail = tail->GetLink();tail->SetLink(NULL);if (tail != NULL)return true;elsereturn false;}bool Dictionary::Del(string en){Item* cur, *curPre;cur = head;curPre = cur->GetLink();while (cur != NULL){if (curPre->GetIndex() == en)break;cur = cur->GetLink();if (cur !=NULL)curPre = curPre->GetLink();}if (tail == curPre)tail = cur;cur->SetLink(curPre->GetLink());  //将被删除结点从链表中摘下delete curPre;if (curPre != NULL)return true;elsereturn false;}string  Dictionary::Search(string en) {Item* cur;cur = head->GetLink();while (cur != NULL){if (en == cur->GetIndex())break;cur = cur->GetLink();}if (cur != NULL)return cur->GetValue(); //返回结点中的 valueelsereturn "Cannot find";}int Dictionary::GetCount() {int count = 0;Item* current = head->GetLink();while (current != NULL) {++count;current = current->GetLink();  //顺序移动cur }return count;}void Dictionary::RemoveAll() { //删除所有结点Item* cur;while (head->GetLink() != NULL) {cur = head->GetLink();head->SetLink(cur->GetLink());delete cur;}tail = head; //置表尾为表头处}#endif

字典测试程序

#include "stdafx.h"#include <iostream>#include "Dictionary.h"using namespace std;int _tmain(int argc, _TCHAR* argv[]){Dictionary dic;dic.Add("box", "盒子");dic.Add("apple", "苹果");dic.Add("tree", "树");dic.Add("good", "好的");dic.Add("swim", "游泳");dic.Add("interesting", "有趣的");cout << dic.Search("good").c_str() << endl;cout << dic.Search("interesting").c_str() << endl;dic.Del("box");dic.Del("interesting");cout << dic.Search("box").c_str() << endl;cout << dic.Search("interesting").c_str() << endl;cout << dic.Search("apple").c_str() << endl;system("PAUSE");return 0;}

P343

template <class T>class Item{int key;T data;public:Item():key(-1){}Item(int keyInput,T value):key(keyInput),data(value){assert(key>=0);}int GetKey(){return key;}T GetData(){return data;}friend ostream& operator<<(ostream& stream,Item<T>& item);};template <class T>class OrderSearch{Item<T>* contain;int size;public:OrderSearch():contain(NULL),size(0){}OrderSearch(int maxSize);void Add(Item<T> add);int GetSize(){return size;}Item<T>* GetContain(){return contain;}Item<T>& Search(int k);friend ostream& operator<<(ostream& stream,OrderSearch<T>& set);};

P344

template <class T>ostream& operator<<(ostream& stream,Item<T>& item){cout<<"key:"<<item.GetKey()<<"\t"<<"data:"<<item.GetData()<<endl;return stream;}

P345

template <class T>OrderSearch<T>::OrderSearch(int maxSize){contain = new Item<T>[maxSize];//建立数组，存放二元组size = maxSize;//记录数组大小for(int i=0;i<maxSize;i++)//初始化字典{Item<T> ini;contain[i] = ini;}}template <class T>void OrderSearch<T>::Add(Item<T> add){assert(add.GetKey()>=0 && add.GetKey()<size);//判断key的合法性contain[add.GetKey()] = add;//添加二元组}template <class T>Item<T>& OrderSearch<T>::Search(int k){assert(k>=0 && k<size);//判断key的合法性return contain[k];//返回二元组}template <class T>ostream& operator<<(ostream& stream,OrderSearch<T>& set){for(int i=0;i<set.GetSize();i++){if(set.GetContain()[i].GetKey() != -1){cout<<"key:"<<set.GetContain()[i].GetKey()<<"\t";cout<<"data:"<<set.GetContain()[i].GetData()<<endl;}}return stream;}

P346

template <class T>int BinarySearch(List<T>& dic, T& item) {int lowKey = 0;int highKey = dic.GetCount() - 1;int midKey;while (lowKey <= highKey){midKey = (lowKey + highKey) / 2;//寻找中间结点if (dic.GetAt(midKey) < item){lowKey = midKey + 1;//在右半集合中搜索       }else if (dic.GetAt(midKey) > item){highKey = midKey - 1;//在左半集合中搜索}else return midKey;}return -1;}

P351-1：  BKDR散列

连同测试程序一并给出。你会发现这个算法在处理C语言关键字时可以获得非常小的冲突率。例如当我们去HASHSIZE为101时，就可以做到完全没有冲突。

#include <iostream>#include <string>#include <iomanip>#include <stdint.h>using namespace std;#define HASHSIZE 101string keywords[] = {  "auto",   "break",  "case",     "char",   "const",    "continue", "default",  "do",  "double", "else",   "enum",     "extern", "float",    "for",      "goto",     "if",  "int",    "long",   "register", "return", "short",    "signed",   "sizeof",   "static",  "struct", "switch", "typedef",  "union",  "unsigned", "void",     "volatile", "while"};unsigned long BKDRHash(const string& str)  {unsigned long seed = 31;unsigned long hashval = 0;     for(int i = 0; i < str.length(); i++)hashval = hashval * seed + str[i];return hashval % HASHSIZE;  }int main(int argc, char** argv) {  int size, pos;  int count[HASHSIZE];    for(int i = 0; i < HASHSIZE; i++)     count[i] = 0;  size = sizeof(keywords) / sizeof(keywords[0]);  for(int i = 0;i < size; i++)    count[BKDRHash(keywords[i])]++;  for(int i = 0; i < size; i++) {    pos = BKDRHash(keywords[i]);    cout<<setw(8)<<keywords[i]<<setw(5)<<pos<<setw(5)<<count[pos]<<endl;  }return 0;}

P351-2：  RS散列（连同测试程序一并给出）

#include <iostream>#include <string>#include <iomanip>#include <stdint.h>using namespace std;#define HASHSIZE 41string keywords[] = {  "auto",   "break",  "case",     "char",   "const",    "continue", "default",  "do",  "double", "else",   "enum",     "extern", "float",    "for",      "goto",     "if",  "int",    "long",   "register", "return", "short",    "signed",   "sizeof",   "static",  "struct", "switch", "typedef",  "union",  "unsigned", "void",     "volatile", "while"};unsigned long RSHash(const string& str)  {unsigned long a = 31415, b = 27183;  unsigned long hashval = 0;  for(int i = 0; i < str.length(); i++)  {  hashval = (hashval * a + str[i])%HASHSIZE;  a = a * b % (HASHSIZE-1);  }  return hashval;  }int main(int argc, char** argv) {int size, pos;int count[HASHSIZE];  for(int i = 0; i < HASHSIZE; i++)count[i] = 0;size = sizeof(keywords) / sizeof(keywords[0]);size = 32;for(int i = 0;i < size; i++)count[RSHash(keywords[i])]++;for(int i = 0; i < size; i++) {pos = RSHash(keywords[i]);cout<<setw(8)<<keywords[i]<<setw(5)<<pos<<setw(5)<<count[pos]<<endl;}return 0;}

P352：  FNV散列（连同测试程序一并给出）

#include <iostream>#include <string>#include <iomanip>#include <stdint.h>using namespace std;//const long offsetbasis32 = 2166136261;#define FNV_32_INIT ((uint32_t)0x811c9dc5)//const long FNVprime32 = 16777619;#define FNV_32_PRIME ((uint32_t)0x01000193)unsigned long FNV1a_32_Hash(const string& str)  {  unsigned long hashval = FNV_32_INIT;  for(int i = 0; i < str.length(); i++)  {  hashval = hashval ^ str[i];  //hashval = hashval * FNV_32_PRIME;//  上面一句代码等价于下面之位操作 hashval += (hashval <<1) + (hashval <<4) + (hashval <<7) + (hashval <<8) + (hashval <<24);}return hashval;  }//const long offsetbasis64 = 14695981039346656037;//#define FNV_64_INIT ((uint64_t)0x14650FB0739D0383);#define FNV_64_INIT ((uint64_t)0xcbf29ce484222325ULL);//const long FNVprime64 = 1099511628211;#define FNV_64_PRIME ((uint64_t)0x100000001b3ULL)uint64_t FNV1a_64_Hash(const char* bp, size_t len)  {  uint64_t hval = FNV_64_INIT;  const char *be = bp + len;  while (bp < be) {  hval ^= (uint64_t) *bp++;  hval += (hval << 1) + (hval << 4) + (hval << 5) + (hval << 7) + (hval << 8) + (hval << 40);  }  return hval;  }int main(int argc, char** argv) {string str = "interesting";cout<<hex<<FNV1a_32_Hash(str)<<endl;cout<<hex<<FNV1a_64_Hash(str.c_str(), str.length())<<endl;return 0;}

内容简介：探秘算法世界，求索数据结构之道；汇集经典问题，畅享编程技法之趣；点拨求职热点，敲开业界名企之门。本书围绕算法与数据结构这个话题，循序渐进、深入浅出地介绍了现代计算机技术中常用的四十余个经典算法，以及回溯法、分治法、贪婪法和动态规划等算法设计思想。在此过程中，本书也系统地讲解了链表（包括单向链表、单向循环链表和双向循环链表）、栈、队列（包括普通队列和优先级队列）、树（包括二叉树、哈夫曼树、堆、红黑树、AVL树和字典树）、图、集合（包括不相交集）与字典等常用数据结构。同时，通过对二十二个经典问题（包括约瑟夫环问题、汉诺塔问题、八皇后问题和骑士周游问题等）的讲解，逐步揭开隐匿在数据结构背后的算法原理，力图帮助读者夯实知识储备，激活思维技巧，并最终冲破阻碍编程能力提升的重重藩篱。辅有完整的C++源代码，并穿插介绍了STL中的各种容器。

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