/**
* 多項式-單連結串列實現
* 思路：
* 加法思路：P1(n~0) P2(i~0),假設n>i的(方便描述),P1(n)跟P2(n)比較關係,把大的或者相等的一方取出得到SumP(n~n-i)
* 並且指標下移，最後加上 P2(n-i~0)。
* 乘法思路一：P1(n~0)*P2(i~0) 然後合併同類項(排序) 複雜度為 O(N^4)
* 乘法思路二：P1(n~0) P2(i~0), 首先P1(n)*P2(i~0)得到MultP(i~0),然後P1(n-1~0)*P2(i~0)得到
* Tmp((n-1)*i~0)，把每次得到的記為Tmp(x),每次得到Tmp(x)就插入(合併)到MultP(i~0)中
* 最後得到 MultP(k~0)，k為合併同類項後得到的項數,跟次數不一樣;演算法複雜度為O(N^3)
*/
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <unistd.h>
typedef struct Node *PtrToNode;
struct Node {
int coefficient;
int exponent;
PtrToNode next;
};
typedef PtrToNode Polynomial;
/*typedef struct Node {
int coefficient;
int exponent;
stuct Node *next;
} *Polynomial;*/
void print_poly(Polynomial poly);
Polynomial create_poly();
void rand_poly(Polynomial poly);
void add_poly(const Polynomial poly1, const Polynomial poly2, Polynomial poly_sum);
void mult_poly( Polynomial poly1, Polynomial poly2, Polynomial poly_mult);
void attach(int coefficient, int exponent, Polynomial *pPoly);
void test();
int main(void)
{
test();
return 0;
}
Polynomial create_poly()
{
Polynomial P;
P = (Polynomial)malloc(sizeof(struct Node));
P->next = NULL;
return P;
}
void print_poly(Polynomial poly)
{
Polynomial P;
P = poly->next;
while(P != NULL) {
printf("%d*x^%d", P->coefficient, P->exponent);
if (P->next != NULL)
printf(" + ");
P = P->next;
}
printf("\n");
}
void rand_poly(Polynomial poly)
{
Polynomial tmpCell, P;
int hight, i;
P = poly;
srand((unsigned)time(NULL));
hight = rand() % 5 + 5; //5-9
for (i = hight; i >= 0; i--) {
tmpCell = (Polynomial)malloc(sizeof(struct Node));
tmpCell->coefficient = rand() % 100 + 1; //1-100
tmpCell->exponent = i;
P->next = tmpCell;
P = P->next;
}
P->next = NULL;
}
void attach(int coefficient, int exponent, Polynomial *pPoly)
{
Polynomial tmp;
tmp = (Polynomial)malloc(sizeof(struct Node));
tmp->coefficient = coefficient;
tmp->exponent =exponent;
tmp->next = NULL;
(*pPoly)->next = tmp; // 運算子的優先順序,必須有()
*pPoly = (*pPoly)->next;
}
void add_poly(const Polynomial poly1, const Polynomial poly2, Polynomial poly_sum)
{
Polynomial p1, p2, P;
P = poly_sum;
p1 = poly1->next;
p2 = poly2->next;
while (p1 && p2) {
if (p1->exponent > p2->exponent) {
attach(p1->coefficient, p1->exponent, &P);
p1 = p1->next;
} else if(p1->exponent == p2->exponent) {
attach(p1->coefficient + p2->coefficient, p2->exponent, &P);
p1 = p1->next;
p2 = p2->next;
} else {
attach(p2->coefficient, p2->exponent, &P);
p2 = p2->next;
}
}
// 加上沒有參與計算的多項式(長的的一條)
for (; p1; p1 = p1->next)
attach(p1->coefficient, p1->exponent, &P);
for (; p2; p2 = p2->next)
attach(p2->coefficient, p2->exponent, &P);
P->next = NULL;
}
void mult_poly( Polynomial poly1, Polynomial poly2, Polynomial poly_mult)
{
Polynomial p1, p2, P, tmp;
int coefficient, exponent;
P = poly_mult;
p1 = poly1->next;
p2 = poly2->next;
while (p2) {
attach(p1->coefficient * p2->coefficient, p1->exponent + p2->exponent, &P);
p2 = p2->next;
}
while (p1) {
p2 = poly2->next->next;
while(p2) {
coefficient = p1->coefficient * p2->coefficient;
exponent = p1->exponent + p2->exponent;
P = poly_mult->next;
while (P) {
if (P->exponent == exponent) {
P->coefficient += coefficient;
break;
} else if(P->next && P->exponent > exponent && P->next->exponent < exponent) {
tmp = (Polynomial)malloc(sizeof(struct Node));
tmp->exponent = exponent;
tmp->coefficient = coefficient;
tmp->next = P->next;
P->next = tmp;
break;
} else if(P->next == NULL) {
tmp = (Polynomial)malloc(sizeof(struct Node));
tmp->exponent = exponent;
tmp->coefficient = coefficient;
tmp->next = NULL;
P->next = tmp;
break;
}
P = P->next;
}
p2 = p2->next;
}
p1 = p1->next;
}
}
void test()
{
Polynomial poly1, poly2, poly_sum, poly_mult;
poly1 = create_poly();
poly2 = create_poly();
poly_sum = create_poly();
poly_mult = create_poly();
int act;
while(1) {
printf("\n\t\tplease input a intger and choose a option.\n");
printf("\t\t1.get tow random polynomial.\n");
printf("\t\t2.add tow polynomial.\n");
printf("\t\t3.multiplication tow polynomial.\n");
printf("\t\t4.print a polynomial.\n");
printf("\t\t0.exit.\n");
scanf("%d", &act);
if (act == 0)
break;
switch (act) {
case 1:
printf("get tow random polynomial.\n");
rand_poly(poly1);
printf("\t\tthe fist polynomial.\n");
print_poly(poly1);
sleep(1);
rand_poly(poly2);
printf("\t\tthe second polynomial.\n");
print_poly(poly2);
break;
case 2:
printf("add tow polynomial.\n");
add_poly(poly1, poly2, poly_sum);
print_poly(poly1);
printf("\t\t+\n");
print_poly(poly2);
printf("\t\t=\n");
print_poly(poly_sum);
break;
case 3:
printf("multiplication tow polynomial.\n");
mult_poly(poly1, poly2, poly_mult);
print_poly(poly1);
printf("\t\t\t*\n");
print_poly(poly2);
printf("\t\t\t=\n");
print_poly(poly_mult);
break;
case 4:
{
int temp; //c語言在 switch case 裡面要定義變數必須要有{}
printf("\t\t\tplease input a intger polynomial to print.\n");
scanf("%d", &temp);
switch (temp) {
case 1:
print_poly(poly1);
break;
case 2:
print_poly(poly2);
break;
case 3:
print_poly(poly_sum);
break;
case 4:
print_poly(poly_mult);
}
break;
}
}
}
}
執行結果截圖