线性表应用多项式加法

我们这个世界的一个问题是，蠢人信誓旦旦，智人满腹狐疑。
——Bertrand Russell

文章目录

单链表定义
- 重载pair的输出运算符
- 求和函数
总体代码

多项式求和，即输入两个多项式，然后将它们合并为一个多项式，解决多项式求和问题是链表的应用之一。
用链表的原因是，多项式的指数可能不是连续的，当指数最大值很高而离散度很高时，用线性表存储会导致空间利用率很低。于是可以使用动态开辟结点的链表来进行优化。

首先呈上老师的代码

#include <stdio.h>
#include <malloc.h>/*** Linked list of integers. The key is data. The key is sorted in non-descending order.*/
typedef struct LinkNode{int coefficient;int exponent;struct LinkNode *next;
} *LinkList, *NodePtr;/*** Initialize the list with a header.* @return The pointer to the header.*/
LinkList initLinkList(){LinkList tempHeader = (LinkList)malloc(sizeof(struct LinkNode));tempHeader->coefficient = 0;tempHeader->exponent = 0;tempHeader->next = NULL;return tempHeader;
}// Of initLinkList/*** Print the list.* @param paraHeader The header of the list.*/
void printList(LinkList paraHeader){NodePtr p = paraHeader->next;while (p != NULL) {printf("%d * 10^%d + ", p->coefficient, p->exponent);p = p->next;}// Of whileprintf("\r\n");
}// Of printList/*** Print one node for testing.* @param paraPtr The pointer to the node.* @param paraChar The name of the node.*/
void printNode(NodePtr paraPtr, char paraChar){if (paraPtr == NULL) {printf("NULL\r\n");} else {printf("The element of %c is (%d * 10^%d)\r\n", paraChar, paraPtr->coefficient, paraPtr->exponent);}// Of while
}// Of printNode/*** Add an element to the tail.* @param paraCoefficient The coefficient of the new element.* @param paraExponent The exponent of the new element.*/
void appendElement(LinkList paraHeader, int paraCoefficient, int paraExponent){NodePtr p, q;// Step 1. Construct a new node.q = (NodePtr)malloc(sizeof(struct LinkNode));q->coefficient = paraCoefficient;q->exponent = paraExponent;q->next = NULL;// Step 2. Search to the tail.p = paraHeader;while (p->next != NULL) {p = p->next;}// Of while// Step 3. Now add/link.p->next = q;
}// Of appendElement/*** Polynomial addition.* @param paraList1 The first list.* @param paraList2 The second list.*/
void add(NodePtr paraList1, NodePtr paraList2){NodePtr p, q, r, s;// Step 1. Search to the position.p = paraList1->next;printNode(p, 'p');q = paraList2->next;printNode(q, 'q');r = paraList1; // Previous pointer for inserting.printNode(r, 'r');free(paraList2); // The second list is destroyed. while ((p != NULL) && (q != NULL)) {if (p->exponent < q->exponent) {//Link the current node of the first list.printf("case 1\r\n");r->next = p;r = p;printNode(r, 'r');p = p->next;printNode(p, 'p');} else if ((p->exponent > q->exponent)) {//Link the current node of the second list.printf("case 2\r\n");r->next = q;r = q;printNode(r, 'r');q = q->next;printNode(q, 'q');} else {printf("case 3\r\n");//Change the current node of the first list.p->coefficient = p->coefficient + q->coefficient;printf("The coefficient is: %d.\r\n", p->coefficient);if (p->coefficient == 0) {printf("case 3.1\r\n");s = p;p = p->next;printNode(p, 'p');// free(s);} else {printf("case 3.2\r\n");r = p;printNode(r, 'r');p = p->next;printNode(p, 'p');}// Of ifs = q;q = q->next;//printf("q is pointing to (%d, %d)\r\n", q->coefficient, q->exponent);free(s);}// Of ifprintf("p = %ld, q = %ld \r\n", p, q);} // Of whileprintf("End of while.\r\n");if (p == NULL) {r->next = q;} else {r->next = p;} // Of ifprintf("Addition ends.\r\n");
}// Of add/*** Unit test 1.*/
void additionTest1(){// Step 1. Initialize the first polynomial.LinkList tempList1 = initLinkList();appendElement(tempList1, 7, 0);appendElement(tempList1, 3, 1);appendElement(tempList1, 9, 8);appendElement(tempList1, 5, 17);printList(tempList1);// Step 2. Initialize the second polynomial.LinkList tempList2 = initLinkList();appendElement(tempList2, 8, 1);appendElement(tempList2, 22, 7);appendElement(tempList2, -9, 8);printList(tempList2);// Step 3. Add them to the first.add(tempList1, tempList2);printf("The result is: ");printList(tempList1);printf("\r\n");
}// Of additionTest1/*** Unit test 2.*/
void additionTest2(){// Step 1. Initialize the first polynomial.LinkList tempList1 = initLinkList();appendElement(tempList1, 7, 0);appendElement(tempList1, 3, 1);appendElement(tempList1, 9, 8);appendElement(tempList1, 5, 17);printList(tempList1);// Step 2. Initialize the second polynomial.LinkList tempList2 = initLinkList();appendElement(tempList2, 8, 1);appendElement(tempList2, 22, 7);appendElement(tempList2, -9, 10);printList(tempList2);// Step 3. Add them to the first.add(tempList1, tempList2);printf("The result is: ");printList(tempList1);printf("\r\n");
}// Of additionTest2/*** The entrance.*/
int main(){additionTest1();additionTest2();printf("Finish.\r\n");return 0;
}// Of main

单链表定义

#include <iostream>
#include <vector>
#define remilia int
#define isMyWife mainusing namespace std;template<class ElemType>
class LinkedList {private:class Node {private:ElemType data;Node* next;public:virtual ~Node() {}Node();Node(ElemType data, Node* next) {this -> data = data;this -> next = next;    }ElemType getData() {return this -> data;}void setData(ElemType elem) {this -> data = elem;}Node* getNext() {return this -> next;}void setNext(Node* node) {this -> next = node;}};int length;Node* head;Node* tail;// 引入迭代器 Node* iterator;public:virtual ~LinkedList();LinkedList();LinkedList(vector<ElemType> v);Node* initIterator() {return (this -> iterator = this -> head);}// get the length of linkedlistint getLength();// print all of the linkedlistvoid outputList();/*** @brief  append a node to the tail* @return the result of appending  1 -> success* @param elem * the appending is always successful**/bool pushBack(ElemType elem);/*** @brief append a node to the head* @param elem * @return the result of appending  1 -> success* the appending is always successful**/bool pushHead(ElemType elem);/*** @brief delete a node from head* @return the result of deleting 1 -> success, 0 -> failute* the reason of failure is that the head node isn't existed**/bool popHead();/*** @brief delete a node from tail* @return the result of deleting 1 -> success, 0 -> failute* the reason of failure is that the tail node isn't existed* @return **/bool popBack();// insert an element to the given positionbool insertElement(int paraPosition, ElemType elem);/*** @brief delete a node by the paraPosition* @param the position of the node needed deleted* @return 1 -> success, 0 -> fail* the reason of failure is the position out of range**/bool deleteElementByParaPosition(int paraPosition); /*** @brief clear the list* **/void clear();/*** @brief get a element by paraPosition* * * @return the element**/ElemType getElement(int paraPosition);
}; template<class ElemType>
LinkedList<ElemType>::~LinkedList() {}template<class ElemType>
LinkedList<ElemType>::LinkedList() {this -> length = 0;this -> head = this -> tail = nullptr;
}template<class ElemType>
LinkedList<ElemType>::LinkedList(vector<ElemType> v) {for (auto e : v) {this -> pushBack(e);}
}template<class ElemType>
bool LinkedList<ElemType>::pushBack(ElemType elem) {// if the tail equals null, the head equals null tooif (this -> tail == nullptr) {this -> head = this -> tail = new Node(elem, nullptr);} else {Node* newTail = new Node(elem, nullptr);this -> tail -> setNext(newTail);this -> tail = newTail; }this -> length++;return 1;
}template<class ElemType>
bool LinkedList<ElemType>::pushHead(ElemType elem) {if (this -> head == nullptr) {this -> head = this -> tail = new Node(elem, nullptr);} else {Node* newTail = new Node(elem, head);this -> head = newTail;}this -> length++;return 1;
}template<class ElemType>
bool LinkedList<ElemType>::popHead() {if (this -> length == 1) {this -> head = this -> tail = nullptr;}if (this -> head == nullptr) {return 0;} else {Node* temp = this -> head;this -> head = this -> head -> getNext();delete temp;return 1;}
}template<class ElemType>
bool LinkedList<ElemType>::popBack() {if (this -> length == 1) {this -> head = this -> tail = nullptr;}if (this -> tail == nullptr) {return 0;} else {Node* temp = this -> head;while (temp -> getNext() != this -> tail) {temp = temp -> getNext();}delete temp -> getNext();this -> tail = temp;return 1;}
}template<class ElemType>
void LinkedList<ElemType>::outputList() {Node* temp = this -> head;while (temp != nullptr) {cout << temp -> getData() << " ";temp = temp -> getNext();} putchar('\n');
}template<class ElemType>
int LinkedList<ElemType>::getLength() {return this -> length;
}template<class ElemType>
void LinkedList<ElemType>::clear() {Node* temp = this -> head;Node* storge = temp;while (temp != nullptr) {temp = temp -> getNext();delete storge;storge = temp;}  delete storge;this -> head = this -> tail = nullptr;this -> length = 0;
}template<class ElemType>
bool LinkedList<ElemType>::deleteElementByParaPosition(int paraPosition) {if (paraPosition > this -> getLength()) {return 0;}if (paraPosition == 1) {return popHead();}int recordIndex = 1;Node* temp = this -> head;while (recordIndex < paraPosition - 1) {temp = temp -> getNext();    recordIndex++;}Node* recorder = temp -> getNext();temp -> setNext(recorder -> getNext());delete recorder;return 1;
}template<class ElemType>
bool LinkedList<ElemType>::insertElement(int paraPosition, ElemType elem) {if (paraPosition > this -> getLength() + 1) {return 0;  }if (paraPosition == 1) {return this -> pushHead(elem);}Node* temp = this -> head;int recordIndex = 1;while (recordIndex < paraPosition - 1) {temp = temp -> getNext();recordIndex++;    }Node* newNode = new Node(elem, temp -> getNext());temp -> setNext(newNode);this -> length++;return 1;
}template<class ElemType>
ElemType LinkedList<ElemType>::getElement(int paraPosition) {if (paraPosition > this -> length) {throw "out of range...";}int recordIndex = 1;Node* temp = this -> head;while (recordIndex < paraPosition) {temp = temp -> getNext();recordIndex++;}return temp -> getData();
}remilia isMyWife() {return 0;
}

重载pair的输出运算符

// 重载pair的输出运算符
template<class T, class U>
std::ostream& operator<<(std::ostream& os, const std::pair<T, U>& p) {os << p.first << "x^" << p.second << " ";return os;
}

求和函数

// 参数使用pair
// pair<系数， 指数>
LinkedList<pair<int, int>> add(LinkedList<pair<int, int>>& a, LinkedList<pair<int, int>>& b) {// Node是内部私有类， 因此这里使用自动类型进行推断 LinkedList<pair<int, int>> ans;auto iteratorA = a.initIterator();auto iteratorB = b.initIterator();while (iteratorA && iteratorB) {if (iteratorA -> getData().second < iteratorB -> getData().second) {ans.pushBack({iteratorA -> getData().first, iteratorA -> getData().second});iteratorA = iteratorA -> getNext();} else if (iteratorA -> getData().second > iteratorB -> getData().second) {ans.pushBack({iteratorB -> getData().first, iteratorB -> getData().second});iteratorB = iteratorB -> getNext();} else {int sum = iteratorA -> getData().second + iteratorB -> getData().second;if (sum) {ans.pushBack({sum, iteratorA -> getData().second});}iteratorA = iteratorA -> getNext();iteratorB = iteratorB -> getNext();}}while (iteratorA) {ans.pushBack({iteratorA -> getData().first, iteratorA -> getData().second});iteratorA = iteratorA -> getNext();}while (iteratorB) {ans.pushBack({iteratorB -> getData().first, iteratorB -> getData().second});iteratorB = iteratorB -> getNext();}a.clear();b.clear();return ans;
}

总体代码

#include <bits/stdc++.h>
#define remilia int
#define isMyWife mainusing namespace std;// 重载pair的输出运算符
template<class T, class U>
std::ostream& operator<<(std::ostream& os, const std::pair<T, U>& p) {os << p.first << "x^" << p.second << " ";return os;
}template<class ElemType>
class LinkedList {private:class Node {private:ElemType data;Node* next;public:virtual ~Node() {}Node();Node(ElemType data, Node* next) {this -> data = data;this -> next = next;    }ElemType getData() {return this -> data;}void setData(ElemType elem) {this -> data = elem;}Node* getNext() {return this -> next;}void setNext(Node* node) {this -> next = node;}};   int length;Node* head;Node* tail;public:virtual ~LinkedList();LinkedList();LinkedList(vector<ElemType> v);// 引入迭代器 Node* iterator;Node* initIterator() {return (this -> iterator = this -> head);}// get the length of linkedlistint getLength();// print all of the linkedlistvoid outputList();/*** @brief  append a node to the tail* @return the result of appending  1 -> success* @param elem * the appending is always successful**/bool pushBack(ElemType elem);/*** @brief append a node to the head* @param elem * @return the result of appending  1 -> success* the appending is always successful**/bool pushHead(ElemType elem);/*** @brief delete a node from head* @return the result of deleting 1 -> success, 0 -> failute* the reason of failure is that the head node isn't existed**/bool popHead();/*** @brief delete a node from tail* @return the result of deleting 1 -> success, 0 -> failute* the reason of failure is that the tail node isn't existed* @return **/bool popBack();// insert an element to the given positionbool insertElement(int paraPosition, ElemType elem);/*** @brief delete a node by the paraPosition* @param the position of the node needed deleted* @return 1 -> success, 0 -> fail* the reason of failure is the position out of range**/bool deleteElementByParaPosition(int paraPosition); /*** @brief clear the list* **/void clear();/*** @brief get a element by paraPosition* * * @return the element**/ElemType getElement(int paraPosition);
}; template<class ElemType>
LinkedList<ElemType>::~LinkedList() {}template<class ElemType>
LinkedList<ElemType>::LinkedList() {this -> length = 0;this -> head = this -> tail = nullptr;
}template<class ElemType>
LinkedList<ElemType>::LinkedList(vector<ElemType> v) {for (auto e : v) {this -> pushBack(e);}
}template<class ElemType>
bool LinkedList<ElemType>::pushBack(ElemType elem) {// if the tail equals null, the head equals null tooif (this -> tail == nullptr) {this -> head = this -> tail = new Node(elem, nullptr);} else {Node* newTail = new Node(elem, nullptr);this -> tail -> setNext(newTail);this -> tail = newTail; }this -> length++;return 1;
}template<class ElemType>
bool LinkedList<ElemType>::pushHead(ElemType elem) {if (this -> head == nullptr) {this -> head = this -> tail = new Node(elem, nullptr);} else {Node* newTail = new Node(elem, head);this -> head = newTail;}this -> length++;return 1;
}template<class ElemType>
bool LinkedList<ElemType>::popHead() {if (this -> length == 1) {this -> head = this -> tail = nullptr;}if (this -> head == nullptr) {return 0;} else {Node* temp = this -> head;this -> head = this -> head -> getNext();delete temp;return 1;}
}template<class ElemType>
bool LinkedList<ElemType>::popBack() {if (this -> length == 1) {this -> head = this -> tail = nullptr;}if (this -> tail == nullptr) {return 0;} else {Node* temp = this -> head;while (temp -> getNext() != this -> tail) {temp = temp -> getNext();}delete temp -> getNext();this -> tail = temp;return 1;}
}template<class ElemType>
void LinkedList<ElemType>::outputList() {Node* temp = this -> head;while (temp != nullptr) {cout << temp -> getData() << " ";temp = temp -> getNext();} putchar('\n');
}template<class ElemType>
int LinkedList<ElemType>::getLength() {return this -> length;
}template<class ElemType>
void LinkedList<ElemType>::clear() {Node* temp = this -> head;Node* storge = temp;while (temp != nullptr) {temp = temp -> getNext();delete storge;storge = temp;}  delete storge;this -> head = this -> tail = nullptr;this -> length = 0;
}template<class ElemType>
bool LinkedList<ElemType>::deleteElementByParaPosition(int paraPosition) {if (paraPosition > this -> getLength()) {return 0;}if (paraPosition == 1) {return popHead();}int recordIndex = 1;Node* temp = this -> head;while (recordIndex < paraPosition - 1) {temp = temp -> getNext();    recordIndex++;}Node* recorder = temp -> getNext();temp -> setNext(recorder -> getNext());delete recorder;return 1;
}template<class ElemType>
bool LinkedList<ElemType>::insertElement(int paraPosition, ElemType elem) {if (paraPosition > this -> getLength() + 1) {return 0;  }if (paraPosition == 1) {return this -> pushHead(elem);}Node* temp = this -> head;int recordIndex = 1;while (recordIndex < paraPosition - 1) {temp = temp -> getNext();recordIndex++;    }Node* newNode = new Node(elem, temp -> getNext());temp -> setNext(newNode);this -> length++;return 1;
}template<class ElemType>
ElemType LinkedList<ElemType>::getElement(int paraPosition) {if (paraPosition > this -> length) {throw "out of range...";}int recordIndex = 1;Node* temp = this -> head;while (recordIndex < paraPosition) {temp = temp -> getNext();recordIndex++;}return temp -> getData();
}// 参数使用pair
// pair<系数， 指数>
LinkedList<pair<int, int>> add(LinkedList<pair<int, int>>& a, LinkedList<pair<int, int>>& b) {// Node是内部私有类， 因此这里使用自动类型进行推断 LinkedList<pair<int, int>> ans;auto iteratorA = a.initIterator();auto iteratorB = b.initIterator();while (iteratorA && iteratorB) {if (iteratorA -> getData().second < iteratorB -> getData().second) {ans.pushBack({iteratorA -> getData().first, iteratorA -> getData().second});iteratorA = iteratorA -> getNext();} else if (iteratorA -> getData().second > iteratorB -> getData().second) {ans.pushBack({iteratorB -> getData().first, iteratorB -> getData().second});iteratorB = iteratorB -> getNext();} else {int sum = iteratorA -> getData().second + iteratorB -> getData().second;if (sum) {ans.pushBack({sum, iteratorA -> getData().second});}iteratorA = iteratorA -> getNext();iteratorB = iteratorB -> getNext();}}while (iteratorA) {ans.pushBack({iteratorA -> getData().first, iteratorA -> getData().second});iteratorA = iteratorA -> getNext();}while (iteratorB) {ans.pushBack({iteratorB -> getData().first, iteratorB -> getData().second});iteratorB = iteratorB -> getNext();}a.clear();b.clear();return ans;
}remilia isMyWife() {srand(time(NULL));LinkedList<pair<int, int>> a, b, c;for (int i = 1; i <= 10; i++) {a.pushBack({i, i});}for (int j = 10; j <= 20; j++) {b.pushBack({j, j});}c = add(a, b);c.outputList();return 0;
}

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线性表应用多项式加法

文章目录

单链表定义

重载pair的输出运算符

求和函数

总体代码

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线性表应用 多项式加法

文章目录

单链表定义

重载pair的输出运算符

求和函数

总体代码

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最新文章

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线性表应用多项式加法

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