chapter4 队列

,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,单击此处编辑母版标题样式,LOGO,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,单击此处编辑母版标题样式,第四章：队列（,queue,）,4.1,概念,4.2,队列的顺序存储结构,4.3,循环队列,4.4,链队列,4.5,队列应用,1,定义和特点,定义,：队列是限定只能在表的一端进行插入，在表的另一端进行删除的线性表。,队尾,(rear),允许插入的一端。,队头,(front),允许删除的一端。,队列特点,：先进先出,(FIFO),a,1,a,2,a,3,.a,n,入队,出队,front,rear,队列,Q=(a,1,a,2,a,n,),4.1,概念,2,front=-1,rear=-1,1,2,3,4,5,0,队空,1,2,3,4,5,0,front,a,b,c,入队,a,b,c,rear,rear,1,2,3,4,5,0,d,e,f,入队,d,e,f,front,设两个指针,front,rear,约定：,rear,指示队尾元素；,front,指示队头元素前一位置,初值,front=rear=-1,空队列条件：,front=rear,入队列：,Q+rear=x;,出队列：,x=Q+front;,rear,rear,front,rear,1,2,3,4,5,0,a,b,c,出队,a,b,c,front,front,front,实现：,用一维数组实现,QM,4.2,队列的顺序存储结构,3,rear,1,2,3,4,5,0,d,e,f,Front=-1,a,b,c,真溢出,存在问题,设数组维数为,M,，,则：,当,front=-1,rear=M-1,时，再有元素入队发生溢出,真溢出,当,front,-1,rear=M-1,时，再有元素入队发生溢出,假溢出,rear,1,2,3,4,5,0,d,e,f,front,假溢出,4,解决方案,方案,1,：队首固定，每次出队剩余元素向下移动,浪费时间。,方案,2,：循环队列,基本思想：把队列设想成环形，让,Q0,接在,QM-1,之后，若,rear+1=M,则令,rear=0,。,5,front,rear,d,e,f,0,1,2,3,4,M-1,rear,1,2,3,4,0,d,e,f,front,M-1,4.3,循环队列,实现,：,利用“模”运算,入队,：,rear=(rear+1)%M; Qrear=x;,出队,：,front=(front+1)%M; x=Qfront;,6,rear,front,0,1,2,3,4,5,a4,a5,a6,0,1,2,3,4,5,rear,front,a9,a8,a7,a4,a5,a6,0,1,2,3,4,5,rear,front,初始状态,a4,a5,a6,出队,a7,a8,a9,入队,队空：,front= =rear,队满：,front= =rear,队满、队空判定条件,7,解决方案,：,1.,另外,设一个标志,以区别队空、队满：,int flag;,if(,front=rear&,“,出现在入队操作之后 ”,),flag=1; /,队满,else if(,front=rear&,“,出现在出队操作之后 ”,),flag=0,；,/,队空,2.,少用一个元素空间：,队空：,front=rear,队满：(,rear+1)%M= =front,a4,a5,a6,0,1,2,3,4,5,rear,front,a8,a7,队满,8,typedef struct,DataType* Q; /*,数据的存储区首地址*,/,int front,rear; /*,队头，队尾指针*,/,CycQue;,/*,循环队*,/,void InitCycQue(CycQue* sp) /,构造一个空队列,sp-Q=(DataType*)malloc(MAXLEN*sizeof(DataType); /MAXLEN,表示 队列最大元素个数,if (sp-Q=NULL),printf(,内存分配错误,);,sp-front=sp-rear=0;,printf(,内存分配成功,);,初始化队列,循环队列类型定义,9,int InsertCycQue(CycQue* sp,DataType x),if (,(sp-rear+1)%MAXLEN=sp-front,),printf (,队满,! );,return 0; /*,队满不能入队*,/,else,sp-rear=(sp-rear+1) % MAXLEN;,sp-Qsp-rear=x;,return 1; /*,入队完成*,/,入队,10,int ExitCycQue(CycQue* sp, DataType* x),/*,将循环队列的队首元素出队,值送入,x*/,if (,sp-rear=sp-front,),printf (,“,队空,! );,return 0; /*,队空不能出队*,/,else,sp-front=(sp- front,+1) % MAXLEN;,*x=sp-Qsp- front; /*,返回队头元素*,/,return 1; /*,出队完成*,/,出队,11,int LenCycQue(CycQue* sp),/*,求循环队列的长度*,/,return (sp-rear- sp- front,+ MAXLEN) % MAXLEN;,rearfront,求循环队列的长度,12,头结点,.,lp-front,队头,队尾,lp-rear,设队首、队尾指针,front,和,rear,front,指向头结点，,rear,指向队尾,结点定义,:,typedef struct node,DataType data; /*,存储数据元素*,/,struct node* next; /*,指向直接后继元素的指针*,/, QueNode;,链队列定义,：,typedef struct, QueNode *front,*rear; /*,定义队列的头指针和尾指针*,/,LinkQue;,LinkQue* lp,；,data,next,4.4,链队列,13,front,rear,x,入,队,x,front,rear,y,入,队,x,y,front,rear,x,出,队,x,y,front,rear,空队,front,rear,y,出,队,基本操作,14,void InitLQue(LinkQue* Lp),QueNode* p;,p=(QueNode*) malloc(sizeof(QueNode) ; /*,申请链队头结点*,/,if (p=NULL),printf(,内存分配不成功,!);,else,printf(,内存分配成功,!);,p-next=NULL; /*,置头结点指针域为空*,/,Lp-front=p; /*,头指针指向头结点*,/,Lp-rear =Lp-front; /*,尾指针指向头结点*,/,队列初始化，创建带头结点的空队,Lp-,front,Lp-,rear,空队,p,算法实现,15,void InsertLQue(LinkQue *Lp, DataType x),QueNode *p;,p=(QueNode *)malloc(sizeof(QueNode); /,申请新结点,p-data=x;,p-next=NULL;,Lp-rear-next=p;,Lp-rear=p;,入队,a,1,a,n,Lp.front,Lp.rear,x,p,16,int ExitLQue (LinkQue* Lp , DataType* x),/*,将队头元素出队，将值送,x,*/,QueNode* p;,if (Lp-front= Lp-rear,) /*,判队列是否为空的条件*,/,printf(,“,队空,!);,return 0;,else,p=Lp-front-next;,*x=p-data;,Lp-front-next= p-next;,free(p);,return 1;,出队,p,Lp-front,Lp-,rear,A,出队,A,B,a,n,17,划分子集问题,优先级队列,离散时间模拟,图的广度优先遍历,基数排序,4.5,队列应用,18,例,A=1,2,3,4,5,6,7,8,9,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,可行的子集划分为：,A1= 1,3,4,8 ,A2= 2,7 ,A3= 5 ,A4= 6,9 ,问题描述,：,已知集合,A=a1,a2,an,，,及集合上的关系,R= (ai,aj) | ai,aj,A, ij,，,其中(,ai,aj),表示,ai,与,aj,间存在冲突关系。要求将,A,划分成,互不相交,的子集,A1,A2,Ak,(kn),，,使任何子集中的元素均无冲突关系，同时要求,分子集个数尽可能少,。,队列应用举例,划分子集问题,19,算法思想,：利用,循环筛选,。,从第一个元素开始，凡与第一个元素无冲突的元素划归一组；再将剩下的元素重新找出互不冲突的划归第二组；直到所有元素进组。,所用数据结构,冲突关系矩阵,rij=1, i,j,有冲突,rij=0, i,j,无冲突,循环队列,cqn,；,数组,groupn,存放每个元素的分组号，如,group3=5,表示第,3,个元素的分组号为,5,；,工作数组,clashn,：记录和当前已入组元素发生冲突的元素的信息。如,clash2=1,，表示第,2,个元素与当前已入组元素发生冲突。,20,工作过程,初始状态：,A,中元素放于,cq,中，,group,和,clash,数组清零，组号,group=1,第一个元素出队，将,r,矩阵中第一行“1”拷入,clash,中对应位置，这样，凡与第一个元素有冲突的元素在,clash,中对应位置处均为“1”,下一个元素出队,若其在,clash,中对应位置为“1”，有冲突，重新插入,cq,队尾，参加下一次分组,若其在,clash,中对应位置为“0”, 无冲突，可划归本组；再将,r,矩阵中该元素对应行中的“1”拷入,clash,中,如此反复，直到9个元素依次出队，由,clash,中为“0”的单元对应的元素构成第1组,将组号,group,值“1”写入,group,对应单元中,令,group=2,clash,清零，对,cq,中元素重复上述操作，直到,cq,中,front=rear,即队空，运算结束,21,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,1 2 3 4 5 6 7 8 9,0 1 2 3 4 5 6 7 8,cq,f,r,0 0 0 0 0 0 0 0 0,0 1 2 3 4 5 6 7 8,clash,0 0 0 0 0 0 0 0 0,0 1 2 3 4 5 6 7 8,group,初始,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,22,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,2 3 4 5 6 7 8 9,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,0 0 0 0 0 0 0,0 1 2 3 4 5 6 7 8,clash,1,0 0 0 0 0 0 0 0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,A1= 1, ,23,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,2,3 4 5 6 7 8 9,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,0 0 0 0 0 0 0,0 1 2 3 4 5 6 7 8,clash,1,0 0 0 0 0 0 0 0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,A1= 1, ,24,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,2,4 5 6 7 8 9,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,0 0 0,1,1,0 0,0 1 2 3 4 5 6 7 8,clash,1,0,1,0 0 0 0 0 0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,A1= 1, 3 ,25,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,2,5 6 7 8 9,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,0 0,1,1,1,0,1,0 1 2 3 4 5 6 7 8,clash,1,0,1,1,0 0 0 0 0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,A1= 1, 3, 4 ,26,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,2,5,6 7 8 9,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,0 0,1,1,1,0,1,0 1 2 3 4 5 6 7 8,clash,1,0,1,1,0 0 0 0 0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,27,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,2,5,6,7 8 9,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,0 0,1,1,1,0,1,0 1 2 3 4 5 6 7 8,clash,1,0,1,1,0 0 0 0 0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,28,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,2,5,6,7,8 9,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,0 0,1,1,1,0,1,0 1 2 3 4 5 6 7 8,clash,1,0,1,1,0 0 0 0 0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,29,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,2,5,6,7,9,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,0 0,1,1,1,0,1,0 1 2 3 4 5 6 7 8,clash,1,0,1,1,0 0 0,1,0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,A1= 1, 3, 4 , 8 ,30,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,2,5,6,7,9,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,0 0,1,1,1,0,1,0 1 2 3 4 5 6 7 8,clash,1,0,1,1,0 0 0,1,0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,31,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,5,6,7,9,0 1 2 3 4 5 6 7 8,cq,f,r,1,0 0 0,1,1,0,1,1,0 1 2 3 4 5 6 7 8,clash,1,2,1,1,0 0 0,1,0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,A1= 1, 3, 4 , 8 ,A2= 2, ,32,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,6,7,9,5,0 1 2 3 4 5 6 7 8,cq,f,r,1,0 0 0,1,1,0,1,1,0 1 2 3 4 5 6 7 8,clash,1,2,1,1,0 0 0,1,0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,33,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,7,9,5 6,0 1 2 3 4 5 6 7 8,cq,f,r,1,0 0 0,1,1,0,1,1,0 1 2 3 4 5 6 7 8,clash,1,2,1,1,0 0 0,1,0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,34,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,9,5 6,0 1 2 3 4 5 6 7 8,cq,f,r,1,0,1,0,1,1,0,1,1,0 1 2 3 4 5 6 7 8,clash,1,2,1,1,0 0,2,1,0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,A1= 1, 3, 4 , 8 ,A2= 2, 7 ,35,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,5 6 9,0 1 2 3 4 5 6 7 8,cq,f,r,1,0,1,0,1,1,0,1,1,0 1 2 3 4 5 6 7 8,clash,1,2,1,1,0 0,2,1,0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,36,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,6 9,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,0,1,0,1,1,0,1,0 1 2 3 4 5 6 7 8,clash,1,2,1,1,3,0,2,1,0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,A1= 1, 3, 4 , 8 ,A2= 2, 7 ,A3= 5, ,37,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,9 6,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,0,1,0,1,1,0,1,0 1 2 3 4 5 6 7 8,clash,1,2,1,1,3,0,2,1,0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,38,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,9,6,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,0,1,0,1,1,0,1,0 1 2 3 4 5 6 7 8,clash,1,2,1,1,3,0,2,1,0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,39,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,9,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,1,0,1,0,1,0 0,0 1 2 3 4 5 6 7 8,clash,1,2,1,1,3,4,2,1,0,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,A1= 1, 3, 4 , 8 ,A2= 2, 7 ,A3= 5, ,A4= 6, ,40,算法描述,0 1 0 0 0 0 0 0 0,0 1 0 1 1 0 0 0 0,0 0 0 0 0 1 1 0 0,0 0 0 0 1 0 0 0 1,0 1 0 1 0 1 1 0 1,0 1 1 0 1 0 1 0 0,0 0 1 0 1 1 0 0 0,0 1 0 0 0 0 0 0 0,1 0 0 0 1 1 0 1 1,R=,0 1 2 3 4 5 6 7 8,cq,f,r,0,1,1,1,1,0,1,0 0,0 1 2 3 4 5 6 7 8,clash,1,2,1,1,3,4,2,1,4,0 1 2 3 4 5 6 7 8,group,R= (2,8), (9,4), (2,9), (2,1), (2,5), (6,2), (5,9),(5,6), (5,4), (7,5), (7,6), (3,7), (6,3) ,A1= 1, 3, 4 , 8 ,A2= 2, 7 ,A3= 5, ,A4= 6, 9 ,41,