一、需求分析

1.本演示程序中，限定约定约瑟夫的节点数和密码均不超过100，每个节点的密码均不超过节点个数的两倍，且为方便起见所有密码均根据时间动态生成，程序需输入的有：①生成约瑟环的节点数，②程序的初始密码；若输入超出界，则起用默认值：10

2.程序执行的命令有：输入约瑟夫环的节点和初始密码，约瑟夫环的初始化及动态生成，约瑟夫环的运行演示

3.程序测试：正确输入测试，条件边界输入测试，超边界输入测试

二、概要设计

4.为实现题目要求功能，用单向循环链表来表示约瑟夫环

5.约瑟环中没释放掉一个环节点，则对应在循环链表中释放掉该节点

6.当剩下最后一个节点时，我们不再进行释放，而是输出，得到我们想要的结果！

三、详细设计

1.定义节点数据结构体：

typedef struct{

int num;        /*The num for Joseph struct*/

int password;    /*Password for Joseph struct*/

}SElemType;

2.定义节点结构体，用来创建循环链表：

typedef struct Joseph{ /*The Node for the ring of Joseph*/

SElemType elem;

struct Joseph *next;

}Joseph;

3.节点初始化函数的定义，用来初始化链表节点：

int InitList(Joseph *l){   /*Initial the the node*/

l=(Joseph *) malloc (sizeof(Joseph));

if(!l)

return OVERFLOW;

return OK;

}

4.约瑟夫链表节点的空间释放：

void FreeNode(Joseph *p){/*Free the node have been deleted*/

Joseph *temp=p;

while(temp->next!=p)

temp=temp->next;

temp->next=p->next;

printf("The node of num:%3d is free "n",p->elem.num);

free(p);

}

5.约瑟夫链表的创建以及随机初始化节点数据域数据：

void Creat_Joseph(Joseph *l,int length){/*creat the password of node by rand()*/

int i;

Joseph *p=l;

l->next=l;

l->elem.num=1;

srand( (unsigned)time(NULL));

l->elem.password=rand()%(length+3)+1;

printf("The flowing is the Joseph Ring created by rand():"n");

printf("The Node num: %3d      Password: %3d"n",l->elem.num,l->elem.password);/*print the first node of the ring of Joseph*/

for(i=1;i

Joseph* temp=(Joseph*)malloc (sizeof(Joseph));

p->next=temp;

temp->next=l;

temp->elem.num=i+1;

temp->elem.password=rand()%(2*length)+1;

printf("The Node num: %3d      Password: %3d"n",temp->elem.num,temp->elem.password);/*print all the node of the ring of Joseph expect the first one*/

p=p->next;

}

}

6.约瑟夫问题实际过程演示：

void Joseph_Run(Joseph *l, int m){/*do node free by password of node*/

int i,k;

Joseph *temp,*p;

if(l->next==l)

printf("The last Node num is: %d",l->elem.num);/*Print the last Node*/

else{

temp = l;

for(i=1; i

temp=temp->next;

p=temp->next;

k=temp->elem.password;

FreeNode(temp);/*Free The unusefull Node*/

Joseph_Run(p,k);/*Using The Recursive Functions*/

}

}

7.主函数的描述：

void main(){

int num=10;

int m=10;

Joseph *J_list;

printf("Please input the total num of Joseph Nodes( less than 100):");/*input the total num of Joseph Nodes*/

scanf("%d",&num);

if(num<=0||num>=100){

printf("What your input is not accepted,so using 10 instead!"n");/*Using the default to instead*/

num=10;

}

printf("Please input the first node num (less than 100):");/*input the first node num*/

scanf("%d",&m);

if(m<=0||m>=100){

printf("What your input is not accepted,so using 10 instead!"n");/*Using the default to instead*/

m=10;

}

InitList(J_list);

Creat_Joseph(J_list,num);

Joseph_Run(J_list,m);

}