数据结构课程设计--polynomial

最新推荐文章于 2023-04-10 21:57:16 发布

George_Fal

最新推荐文章于 2023-04-10 21:57:16 发布

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文章标签：数据结构与算法

原文链接：http://www.cnblogs.com/anderson0/archive/2009/09/05/1560710.html

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本文介绍了一种使用链表实现一元多项式的加法和减法的方法。通过定义链表节点结构并实现初始化、复制、输出、加法及减法等关键函数，实现了用户输入多项式并进行运算的功能。

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Code
  1 #include <iostream.h>
  2 typedef struct lnode
  3 {
  4     float coef, exp;
  5     struct lnode *next;
  6 }Lnode, *Linklist;
  7 //初始化，使多项式按升幂排列
  8 void Initialization(Linklist &L)
  9 {
10     int flag;
11     L = (Linklist)malloc(sizeof(Lnode));
12     L->next = NULL;
13     Linklist p, r;
14     cout << "请依次输入各项的系数和指数" << endl;
15     p = (Linklist)malloc(sizeof(Lnode));
16     while (cin >> p->coef >> p->exp && (p->coef != 0 || p->exp != 0))
17     {
18         if (p->coef == 0)
19             continue;
20         if (L->next == NULL)                //第一项
21         {
22             flag = 1;
23             L->next = p;
24             p->next = NULL;
25         }
26         else
27         {
28             for (r = L,flag = 0; r->next != NULL;r = r->next)        //查找
29             {
30                 if (r->next->exp == p->exp)                            //如果插入的数据与前面的数据的指数项相同
31                 {
32                     flag = 1;
33                     r->next->coef += p->coef;
34                     free(p);
35                     break;
36                 }
37                 else if (r->next->exp < p->exp)                        //插入的元素大于多项式中的指数项
38                     continue;
39                 else                                                //小于时插入
40                 {
41                     flag = 1;
42                     p->next = r->next;
43                     r->next = p;
44                     break;
45                 }
46
47             }
48         }
49         if (flag == 0)                                                //如果它比多项式中任何数据的指数项都大，则插到最后
50         {
51             p->next = r->next;
52             r->next = p;
53         }
54         p = (Linklist)malloc(sizeof(Lnode));
55     }
56 }
57 Linklist copy(Linklist a)                                            //复制数据，保护原数据
58 {
59     Linklist p = (Linklist)malloc(sizeof(Lnode));
60     Linklist r, q = a->next, t;
61     p->coef = a->coef;
62     p->exp = a->exp;
63     p->next = NULL;
64     t = p;
65     while(q != NULL)
66     {
67         r = (Linklist)malloc(sizeof(Lnode));
68         r->coef = q->coef;
69         r->exp = q->exp;
70         r->next = t->next;
71         t->next = r;
72         t = r;
73         q = q->next;
74     }
75     return p;
76 }
77 void output(Linklist L)
78 {
79     if (L->next == NULL)
80         cout << "空";
81     else
82     {
83         L = L->next;
84         cout << L->coef << "*" << "x^" << L->exp;
85         while(L->next != NULL)
86         {
87             L = L->next;
88             if (L->coef >= 0)
89                 cout << "+" << L->coef << "*" << "x^" << L->exp;
90             else
91                 cout << L->coef << "*" << "x^" <<L->exp;
92         }
93     }
94 }
95
96 Linklist add(Linklist a, Linklist b)
97 {
98     Linklist p, q, r, t;
99     p = a->next;
100     q = b->next;
101     r = a;
102     if(a->next == NULL)
103         return b;
104     if(b->next == NULL)
105         return a;
106     while (q != NULL && p != NULL)
107     {
108         if (p->exp < q->exp)                    //小于时
109         {
110             r = r->next;
111             p = p->next;
112         }
113         else if (p->exp > q->exp)                //大于时插入
114         {
115             t = (Linklist)malloc(sizeof(Lnode));
116             t->coef = q->coef;
117             t->exp = q->exp;
118             r->next = t;
119             t->next = p;
120             r = t;
121             q = q->next;
122         }
123         else                                    //相同时相加
124         {
125             p->coef += q->coef;
126             if (p->coef == 0)
127             {
128                 r->next = p->next;
129             }
130             q = q->next;
131             r = p;
132             p = p->next;
133         }
134     }
135     if (q)                                        //把第二个多项式没有插入的部分，插入到第一个多项式的最后
136         r->next = q;
137     return a;
138 }
139
140 Linklist sub(Linklist a, Linklist b)
141 {
142     Linklist c = b->next;
143     while (c != NULL)
144     {
145         c->coef = 0 - c->coef;
146         c = c->next;
147     }
148     return add(a, b);
149 }
150

Code
1

#include<iostream.h>
2

#include<stdlib.h>
3

#include "polynomial.h"
5

int main()
7

{
8

Linklist pa, pb;
9

char y = 'y';
10

while (y == 'Y' || y == 'y')
11

{
12

cout << "*****一元多项式加减法*****" << endl;
13

cout << "建立一元多项式A(x)[以0 0 为结束符]" << endl;
14

Initialization(pa);
15

cout << "A(x) = ";
16

output(pa);
17

cout << endl;
18

cout << "建立一元多项式B(x)[以0 0 为结束符]" << endl;
19

Initialization(pb);
20

cout << "B(x) = ";
21

output(pb);
22

cout << endl;
23

cout << "两式相加 = " << endl;
24

output(add(copy(pa), copy(pb)));
25

cout<< endl;
26

cout << "两式相减 = " << endl;
27

output(sub(copy(pa), copy(pb)));
28

cout<< endl;
29

cout << "are you continue? y or n?" << endl;
30

cin >> y;
31

if (y != 'y' && y != 'Y')
32

break;
33

}
34

return 0;
35

}

Code
#include <iostream.h>
typedef struct lnode
{
    float coef, exp;
    struct lnode *next;
}Lnode, *Linklist;
//初始化，使多项式按升幂排列
void Initialization(Linklist &L)
{
    int flag;
    L = (Linklist)malloc(sizeof(Lnode));
    L->next = NULL;
    Linklist p, r;
    cout << "请依次输入各项的系数和指数" << endl;
    p = (Linklist)malloc(sizeof(Lnode));
    while (cin >> p->coef >> p->exp && (p->coef != 0 || p->exp != 0))
    {
        if (p->coef == 0)
            continue;
        if (L->next == NULL)                //第一项
        {
            flag = 1;
            L->next = p;
            p->next = NULL;
        }
        else
        {
            for (r = L,flag = 0; r->next != NULL;r = r->next)        //查找
            {
                if (r->next->exp == p->exp)                            //如果插入的数据与前面的数据的指数项相同
                {
                    flag = 1;
                    r->next->coef += p->coef;
                    free(p);
                    break;
                }
                else if (r->next->exp < p->exp)                        //插入的元素大于多项式中的指数项
                    continue;
                else                                                //小于时插入
                {
                    flag = 1;
                    p->next = r->next;
                    r->next = p;
                    break;
                }

            }
        }
        if (flag == 0)                                                //如果它比多项式中任何数据的指数项都大，则插到最后
        {
            p->next = r->next;
            r->next = p;
        }
        p = (Linklist)malloc(sizeof(Lnode));
    }
}
Linklist copy(Linklist a)                                            //复制数据，保护原数据
{
    Linklist p = (Linklist)malloc(sizeof(Lnode));
    Linklist r, q = a->next, t;
    p->coef = a->coef;
    p->exp = a->exp;
    p->next = NULL;
    t = p;
    while(q != NULL)
    {
        r = (Linklist)malloc(sizeof(Lnode));
        r->coef = q->coef;
        r->exp = q->exp;
        r->next = t->next;
        t->next = r;
        t = r;
        q = q->next;
    }
    return p;
}
void output(Linklist L)
{
    if (L->next == NULL)
        cout << "空";
    else
    {
        L = L->next;
        cout << L->coef << "*" << "x^" << L->exp;
        while(L->next != NULL)
        {
            L = L->next;
            if (L->coef >= 0)
                cout << "+" << L->coef << "*" << "x^" << L->exp;
            else
                cout << L->coef << "*" << "x^" <<L->exp;
        }
    }
}

Linklist add(Linklist a, Linklist b)
{
    Linklist p, q, r, t;
    p = a->next;
    q = b->next;
    r = a;
    if(a->next == NULL)
        return b;
    if(b->next == NULL)
        return a;
    while (q != NULL && p != NULL)
    {
        if (p->exp < q->exp)                    //小于时
        {
            r = r->next;
            p = p->next;
        }
        else if (p->exp > q->exp)                //大于时插入
        {
            t = (Linklist)malloc(sizeof(Lnode));
            t->coef = q->coef;
            t->exp = q->exp;
            r->next = t;
            t->next = p;
            r = t;
            q = q->next;
        }
        else                                    //相同时相加
        {
            p->coef += q->coef;
            if (p->coef == 0)
            {
                r->next = p->next;
            }
            q = q->next;
            r = p;
            p = p->next;
        }
    }
    if (q)                                        //把第二个多项式没有插入的部分，插入到第一个多项式的最后
        r->next = q;
    return a;
}

Linklist sub(Linklist a, Linklist b)
{
    Linklist c = b->next;
    while (c != NULL)
    {
        c->coef = 0 - c->coef;
        c = c->next;
    }
    return add(a, b);
}

Code
#include<iostream.h>
#include<stdlib.h>

#include "polynomial.h"

int main()
{
    Linklist pa, pb;
    char y = 'y';
    while (y == 'Y' || y == 'y')
    {
        cout << "*****一元多项式加减法*****" << endl;
        cout << "建立一元多项式A(x)[以0 0 为结束符]" << endl;
        Initialization(pa);
        cout << "A(x) = ";
        output(pa);
        cout << endl;
        cout << "建立一元多项式B(x)[以0 0 为结束符]" << endl;
        Initialization(pb);
        cout << "B(x) = ";
        output(pb);
        cout << endl;
        cout << "两式相加 = " << endl;
        output(add(copy(pa), copy(pb)));
        cout<< endl;
        cout << "两式相减 = " << endl;
        output(sub(copy(pa), copy(pb)));
        cout<< endl;
        cout << "are you continue? y or n?" << endl;
        cin >> y;
        if (y != 'y' && y != 'Y')
            break;
    }
    return 0;
}

转载于:https://www.cnblogs.com/anderson0/archive/2009/09/05/1560710.html