(p193)顺序统计数及相关操作

代码和红黑树的基本一样，只是由于多了size属性，需要和color，bh等属性一样，在对其进行操作时需要维护这个属性

leftrotate和rightrotate以及insert和delete里面自然要进行维护,这里要说的是，由于维护过程都在前面四个里面操作了，transplant里面并不需要进行维护，另外，尽管delete里面情况较多，实际上还是只需要共用一个维护过程

/* * source.c * *  Created on: Mar 2, 2016 *      Author: wing */#include<stdio.h>#include<stdlib.h>#define max 6#define black 1#define red 0struct node{int n;int color,size;struct node *p,*l,*r;};struct tree{struct node *root,*nil;};int leftrotate(struct tree *t,struct node *x){struct node *y;y=x->r;x->r=y->l;if (y->l!=t->nil)y->l->p=x;/*x->p=y;千万千万注意顺序啊!*/y->l=x;y->p=x->p;if (x==t->root)t->root=y;elseif (x==x->p->l)x->p->l=y;elsex->p->r=y;x->p=y;y->size=x->size;/**/x->size=x->l->size+x->r->size+1;/*旋转会改变size属性，着色不会*/return 0;}int rightrotate(struct tree *t,struct node *x){struct node *y;y=x->l;x->l=y->r;if (y->r!=t->nil)y->r->p=x;/*x->p=y;*/y->r=x;y->p=x->p;if (x==t->root)t->root=y;elseif (x==x->p->l)x->p->l=y;elsex->p->r=y;x->p=y;y->size=x->size;/**/x->size=x->l->size+x->r->size+1;/*修改size属性*/return 0;}int rbinsertfixup(struct tree *t,struct node *x){while (x->p->color==red)if (x->p==x->p->p->l)if (x->p->p->r->color==red){x=x->p->p;x->color=red;x->l->color=black;x->r->color=black;}/*case1,只有这种情况循环才会继续*/else{if (x==x->p->r){x=x->p;leftrotate(t,x);}/*case2*/x->p->color=black;x->p->p->color=red;rightrotate(t,x->p->p);/*case3*/}elseif (x->p->p->l->color==red){x=x->p->p;x->color=red;x->l->color=black;x->r->color=black;}else{if (x==x->p->l){x=x->p;rightrotate(t,x);}x->p->color=black;x->p->p->color=red;leftrotate(t,x->p->p);}t->root->color=black;return 0;}int rbinsert(struct tree *t,struct node *new){struct node *next=t->root,*prev=t->nil;while (next!=t->nil){prev=next;(prev->size)++;/*插入时经过节点size+1，不需要考虑新增节点是根节点的情况*/next=new->n<next->n?next->l:next->r;}new->p=prev;new->l=t->nil;new->r=t->nil;if (t->root==t->nil)t->root=new;elseif (new->n<prev->n)prev->l=new;elseprev->r=new;/*和二叉搜索树几乎是一样的，区别只在于NULL换成了t.nil*/rbinsertfixup(t,new);return 0;}struct node *search(struct tree *t,struct node *root,int key){if (root==t->nil||root->n==key)return root;elseif (key<root->n)return search(t,root->l,key);elsereturn search(t,root->r,key);}int print(struct tree *t,struct node *root){if (root==t->nil){printf("#/%d(%d) ",root->size,root->color);return 0;}else{printf("%d/%d(%d) ",root->n,root->size,root->color);print(t,root->l);print(t,root->r);return 0;}}int rbtransplant(struct tree *t,struct node *u,struct node *v){if (u==t->root)t->root=v;elseif (u==u->p->l)u->p->l=v;elseu->p->r=v;v->p=u->p;/*注意即使u是t.nil也要赋值，便于fixup*/return 0;}struct node *rbminnum(struct tree *t,struct node *root){struct node *next=root;while (next->l!=t->nil)next=next->l;return next;}int rbdeletefixup(struct tree *t,struct node *x){struct node*w;while (x!=t->root&&x->color==black)if (x==x->p->l){w=x->p->r;if (w->color==red){w->color=black;w->p->color=red;w=w->l;leftrotate(t,x->p);}/*case1*/if (w->l->color==black&&w->r->color==black){w->color=red;x=x->p;}/*case2，只有这种情况循环才会继续*/else{if (w->r->color==black)/*书上的代码非常精炼，没有一点多余，之前还判断了w.l.color是不是red*/{w->l->color=black;w->color=red;rightrotate(t,w);w=x->p->r;}/*case3*/w->color=x->p->color;x->p->color=black;w->r->color=black;leftrotate(t,x->p);x=t->root;/*case4*/}}else{w=x->p->l;if (w->color==red){w->color=black;w->p->color=red;w=w->r;rightrotate(t,x->p);}if (w->l->color==black&&w->r->color==black){w->color=red;x=x->p;}else{if (w->l->color==black){w->r->color=black;w->color=red;leftrotate(t,w);w=x->p->l;}w->color=x->p->color;x->p->color=black;w->l->color=black;rightrotate(t,x->p);x=t->root;}}x->color=black;/*如果x是根节点，性质2会被破坏，在这里修复*/return 0;}int rbdelete(struct tree *t,struct node *z){struct node *x,*y;int yoc;/*y_original_color*/if (z==t->nil)return 0;y=z;yoc=z->color;/*y是删除的节点*/if (y->l==t->nil){x=y->r;rbtransplant(t,y,x);/*x可能为t.nil*/}elseif (y->r==t->nil){x=y->l;rbtransplant(t,y,x);}else{y=rbminnum(t,z->r);yoc=y->color;/*y是移向内部的节点*/x=y->r;if (y->p==z)x->p=y;/*因为没有rbtransplant(t,y,x),也就没有对x.p进行赋值，这是如果x是t.nil，进行fixup是就会出错*/else{rbtransplant(t,y,x);y->r=z->r;y->r->p=y;}rbtransplant(t,z,y);y->l=z->l;y->l->p=y;y->color=z->color;y->size=z->size;/*由于使用y替换z，因此y的size属性要改成z的，别急，下面会修复这条路径上所有节点的size属性*/}struct node *p=x->p;while (p!=t->nil){(p->size)--;p=p->p;}/*这个循环修复待删除节点所在路径上节点的size属性*/if (yoc==black)/*删除（移动）黑色的y节点只会对以x为根的子树的黑节点数产生影响*/rbdeletefixup(t,x);free(z);return 0;}struct node *osselect(struct tree *t,int i)/*根据秩返回节点指针*/{struct node *next=t->root;if (i<=0||i>t->root->size)return t->nil;int r=next->l->size+1;while (r!=i){if (i<r)next=next->l;else{next=next->r;i-=r;}r=next->l->size+1;}return next;}int osrank(struct tree *t,struct node *x)/*返回节点的秩*/{struct node *next=x;int r=next->l->size+1;while (next!=t->root){if (next==next->p->r)r+=next->p->l->size+1;next=next->p;}return r;}int main(void){struct tree *t;t=(struct tree *)malloc(sizeof(struct tree));t->nil=(struct node *)malloc(sizeof(struct node));t->nil->color=black;t->nil->size=0;/*空节点的size设为0，保证正确性*/t->root=t->nil;struct node *new;int i,x[6]={41,38,31,12,19,8};for (i=0;i<max;i++){new=(struct node *)malloc(sizeof(struct node));new->n=x[i];new->color=red;new->size=1;/*新添节点size设为1*/rbinsert(t,new);}print(t,t->root);printf("\n");for (i=1;i<=max;i++)printf("%d ",osselect(t,i)->n);/*输出秩为i的节点*/printf("\n");for (i=1;i<=max;i++)printf("%d ",osrank(t,osselect(t,i)));/*osselect和osrank互为反函数*/return 0;}