資料結構線性表之約瑟夫環&&多項式求和&&差&&積&&導數&&給變數賦值小練習
阿新 • • 發佈：2019-02-17
問題描述
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約瑟夫環（約瑟夫問題）是一個數學的應用問題：已知n個人（以編號1，2，3…n分別表示）圍坐在一張圓桌周圍。從編號為k的人開始報數，數到m的那個人出列；他的下一個人又從1開始報數，數到m的那個人又出列；依此規律重複下去，直到圓桌周圍的人全部出列。通常解決這類問題時我們把編號從0~n-1，最後 [1] 結果+1即為原問題的解。
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數學上的一元多項式的表示是p(x) = p0 + p1 * x + p2 * x^2 + p3 * x^3 + … + pn * x^n;
用連結串列來表示就是p = (p0, p1, p2, … , pn);
所謂的多項式相加就是同類項的合併，也就是兩條連結串列的合併。
採用單鏈表儲存多項式，連結串列的每個結點表示多項式的每一非零項，連結串列應該按有序排列。
直接上原始碼
#include<stdio.h> #include<stdlib.h> typedef struct node{ int id ; int psd ; struct node * next ; }listnode,*linklist; void init_list(linklist * h); void input_data(int num ,linklist h); void out_queue(int s_key , linklist h); int main(){ int num , s_key ; linklist h ; init_list(&h); scanf("%d",&num); scanf("%d",&s_key); input_data(num , h); out_queue(s_key,h); return 0 ; } void out_queue(int s_key ,linklist h){ linklist q = h ; linklist p = q->next ; s_key -- ; while(p != p -> next){ if(p == h){ q = p ; p = p->next ; } if(s_key == 0){ s_key = p->psd ; printf("%d ",p->id); q->next = p->next ; free(p); p = q->next ; s_key -- ; } else{ q = p ; p = p->next ; s_key -- ; } } free(h); } void input_data(int num ,linklist h){ linklist q , p; p = h ; int i = 1 ; while(num){ q = (linklist)malloc(sizeof(listnode)); scanf("%d",&(q->psd)); q->id = i ; num -- ; i++ ; q ->next = p->next ; p->next = q ; p = q ; } } void init_list(linklist * h){ linklist q ; * h = NULL ; *h = (linklist)malloc(sizeof(listnode)); q = *h ; q ->next = * h ; }
求和差
#include<stdio.h> #include<stdlib.h> typedef struct node{ int zhishu ; int xishu ; struct node * next ; }nodelist ,* linklist; void init_list(linklist * h); void input_data(linklist h ,int i); void calcu(linklist h1 ,linklist h2); void prt(linklist h); void destroy(linklist h); int main(){ linklist h1,h2 ; init_list(&h1); init_list(&h2); input_data(h1,1); input_data(h2,1); calcu(h1 ,h2); } //通過傳i的值來判斷是"+"或"-" void calcu(linklist h1 ,linklist h2){ linklist h3=NULL , s ,t; init_list(&h3); t = h3 ; linklist p ,q ; p = h1 ->next ; q = h2 ->next ; while(p!=NULL && q!=NULL){ s= (nodelist*)malloc(sizeof(nodelist)); if(p->zhishu< q->zhishu){ s ->xishu = p->xishu ; s->zhishu = p->zhishu ; s-> next= t->next ; t->next = s ; t = s ; p = p->next ; } else if(p->zhishu > q->zhishu){ s->zhishu = q->zhishu ; s->xishu = q->xishu ; s->next = t->next ; t->next = s ; t = s ; q = q->next ; } else{ s->xishu = p->xishu + q->xishu ; s->zhishu = p->zhishu; if(s->xishu == 0){ free(s); p = p->next ; q = q->next ; continue ; } s->next = t->next; t->next = s ; t = s ; q = q->next ; p = p->next ; } } while(p != NULL){ s = (linklist)malloc(sizeof(nodelist)); s->xishu = p->xishu ; s->zhishu = p->zhishu ; s->next = t->next ; t ->next = s ; t = s ; p = p->next; } while(q != NULL){ s = (linklist)malloc(sizeof(nodelist)); s -> xishu= q->xishu ; s->zhishu = q->zhishu ; s->next = t->next ; t->next = s ; t = s ; q = q->next ; } prt(h3); destroy(h3); destroy(h2); destroy(h1); } void destroy(linklist h){ linklist p = h ; h = h->next ; while(h != NULL){ free(p); p = h ; h = h->next ; } free(h); return ; } void prt(linklist h){ if(h->next == NULL){ printf("0"); return ; } linklist p ; p = h->next ; while(p!= NULL){ if(p->xishu < 0){ printf("-"); p->xishu = -p->xishu ; } printf("%d",p->xishu); if(p->zhishu != 0){ printf("X"); if(p->zhishu != 1) printf("^%d",p->zhishu); } p = p->next ; if(p == NULL)break ; if(p->xishu > 0){ printf("+"); } } } void input_data(linklist h ,int i){ linklist p ,q ; p = h ; int num ; scanf("%d",&num); getchar(); if(num){ q = (linklist)malloc(sizeof(nodelist)); while((scanf("(%d,%d)",&(q->xishu) ,&(q->zhishu)))!=EOF&& num){ q->xishu*= i ; q->next = p->next; p->next = q ; p = q ; num -- ; if(num == 0)break ; q = (linklist)malloc(sizeof(nodelist)); } } else{ return ; } } void init_list(linklist * h){ *h = NULL ; *h = (linklist)malloc(sizeof(nodelist)); (*h)->next =NULL ; }
求積
#include<stdio.h>
#include<stdlib.h>
#include<string.h>
typedef struct node{
int zhishu ;
int xishu ;
struct node * next ;
}nodelist ,* linklist;
void init_list(linklist * h);
void input_data(linklist h ,int i);
void calcu(linklist h1 ,linklist h2);
void prt(linklist h);
void destroy(linklist h);
int main(){
linklist h1,h2 ;
init_list(&h1);
init_list(&h2);
input_data(h1,1);
input_data(h2,1);
calcu(h1 ,h2);
return 0;
}
void calcu(linklist h1 ,linklist h2){
linklist h3,s,t ;
init_list(&h3);
memset(h3 ,0 ,sizeof(h3));
linklist p , q ;
p = h1->next ;
t = h3 ;
while(p){
q = h2->next ;
while(q){
s = (linklist)malloc(sizeof(nodelist));
s->xishu = p->xishu*q->xishu ;
s->zhishu = p->zhishu+q->zhishu ;
if(s->xishu == 0){
free(s) ;
q = q->next ;
continue ;
}
if(s->zhishu == t->zhishu){
t->xishu = t->xishu + s->xishu ;
free(s);
q= q->next ;
continue ;
}
else{
if(t->zhishu < s->zhishu){
s->next = t->next ;
t->next = s ;
t = s ;
}
else{
t->zhishu = s->zhishu+t->zhishu ;
s->zhishu = t->zhishu -s->zhishu ;
t->zhishu = t->zhishu -s->zhishu ;
t->xishu = s->xishu+t->xishu ;
s->xishu = t->xishu - s->xishu ;
t->xishu = t->xishu - s->xishu ;
s->next = t->next ;
t->next = s ;
t = s ;
}
q= q->next ;
}
}
p = p->next ;
}
prt(h3);
destroy(h1);
destroy(h2);
destroy(h3);
}
void destroy(linklist h){
linklist p = h ;
h = h->next ;
while(h != NULL){
free(p);
p = h ;
h = h->next ;
}
free(h);
return ;
}
void prt(linklist h){
if(h->next == NULL){
printf("0");
return ;
}
linklist p ;
p = h->next ;
while(p!= NULL){
if(p->xishu < 0){
printf("-");
p->xishu = -p->xishu ;
}
printf("%d",p->xishu);
if(p->zhishu != 0){
printf("X");
if(p->zhishu != 1)
printf("^%d",p->zhishu);
}
p = p->next ;
if(p == NULL)break ;
if(p->xishu > 0){
printf("+");
}
}
}
void input_data(linklist h ,int i){
linklist p ,q ;
p = h ;
int num ;
scanf("%d",&num);
getchar();
if(num){
q = (linklist)malloc(sizeof(nodelist));
while((scanf("(%d,%d)",&(q->xishu) ,&(q->zhishu)))!=EOF&& num){
q->xishu*= i ;
q->next = p->next;
p->next = q ;
p = q ;
num -- ;
if(num == 0)break ;
q = (linklist)malloc(sizeof(nodelist));
}
}
else{
return ;
}
}
void init_list(linklist * h){
*h = NULL ;
*h = (linklist)malloc(sizeof(nodelist));
(*h)->next =NULL ;
}
取值
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
typedef struct node{
int zhishu ;
int xishu ;
struct node * next ;
}nodelist ,* linklist;
void init_list(linklist * h);
void input_data(linklist h);
void calcu(linklist h);
void destroy(linklist h);
int main(){
linklist h ;
init_list(&h);
input_data(h);
calcu(h);
}
void calcu(linklist h){
double sum = 0;
int n ;
scanf("%d",&n);
linklist p ;
p = h->next ;
while(p){
sum += (p->xishu)*pow(n,(p->zhishu));
p = p->next ;
}
printf("%.0lf",sum);
destroy(h);
}
void destroy(linklist h){
linklist p = h ;
h = h->next ;
while(h != NULL){
free(p);
p = h ;
h = h->next ;
}
free(h);
return ;
}
void input_data(linklist h){
linklist p ,q ;
p = h ;
int num ;
scanf("%d",&num);
getchar();
if(num){
q = (linklist)malloc(sizeof(nodelist));
while((scanf("(%d,%d)",&(q->xishu) ,&(q->zhishu)))!=EOF&& num){
q->next = p->next;
p->next = q ;
p = q ;
num -- ;
if(num == 0)break ;
q = (linklist)malloc(sizeof(nodelist));
}
}
else{
return ;
}
}
void init_list(linklist * h){
*h = NULL ;
*h = (linklist)malloc(sizeof(nodelist));
(*h)->next =NULL ;
}
導數
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
typedef struct node{
int zhishu ;
int xishu ;
struct node * next ;
}nodelist ,* linklist;
void init_list(linklist * h);
void input_data(linklist h);
void calcu(linklist h);
void prt(linklist h);
void destroy(linklist h);
int main(){
linklist h ;
init_list(&h);
input_data(h);
calcu(h);
}
void calcu(linklist h){
linklist p ,tmp ;
tmp = h ;
p = tmp->next ;
while(p){
p->xishu = p->xishu * p->zhishu ;
p->zhishu = p->zhishu -1 ;
if(p->xishu == 0){
tmp->next = p->next ;
free(p);
p = tmp->next ;
continue ;
}
tmp = p ;
p = p->next ;
}
prt(h);
destroy(h);
}
void prt(linklist h){
linklist p;
p = h->next;
while(p!= NULL){
if(p->xishu < 0){
printf("-");
p->xishu = -p->xishu ;
}
printf("%d",p->xishu);
if(p->zhishu != 0){
printf("X");
if(p->zhishu != 1)
printf("^%d",p->zhishu);
}
p = p->next ;
if(p == NULL)break ;
if(p->xishu > 0){
printf("+");
}
}
}
void destroy(linklist h){
linklist p = h ;
h = h->next ;
while(h != NULL){
free(p);
p = h ;
h = h->next ;
}
free(h);
return ;
}
void input_data(linklist h){
linklist p ,q ;
p = h ;
int num ;
scanf("%d",&num);
getchar();
if(num){
q = (linklist)malloc(sizeof(nodelist));
while((scanf("(%d,%d)",&(q->xishu) ,&(q->zhishu)))!=EOF&& num){
q->next = p->next;
p->next = q ;
p = q ;
num -- ;
if(num == 0)break ;
q = (linklist)malloc(sizeof(nodelist));
}
}
else{
return ;
}
}
void init_list(linklist * h){
*h = NULL ;
*h = (linklist)malloc(sizeof(nodelist));
(*h)->next =NULL ;
}