数据结构【查找】—B树

/*********************讲解后期补充*****************/

先上代码

 #include "000库函数.h"

 #define MAXSIZE 100//存储空间

 #define m 3//B树的阶
 #define N 17//数据元素的个数
 #define MAX 5//字符串的最大长度

 struct BTree
 {
     int keynum;//节点中关键字的个数 即节点大小
     BTree *parent;//指向双亲的指针
     struct Node//节点向量类型
     {
         int key;//关键字向量
         BTree *ptr;//子树指针向量
         int recptr;//记录指针向量
     };
     Node node[m + ];//0号单元未使用
 };

 struct Result{
     BTree *pt;//指向找到的节点
     int i;//在节点中的关键字序号
     int tag;//查找成功与否
 };

 int Search(BTree *p, int elem) {//p.node[i].key<=elem<p.node[i+1].key
     int j;
     for (int i = ; i < p->keynum; ++i)
         if (p->node[i].key <= elem)
             j = i;
     return j;
 }

 //查找B树中是否存在该数
 /*关键字应该插在指针pt所指节点中的第i和第i+1个关键字之间*/
 Result* SearchBTree(BTree *T, int elem) {
     BTree *p, *q;
     p = T;
     q = NULL;
     int find = false;
     Result *r = new Result;
     int i = ;
     while (p && !find) {
         i = Search(p, elem);//p.node[i].key<=elem<p.node[i+1].key
         if (i >  && p->node[i].key == elem)//查找到了关键字
             find = true;
         else {
             q = p;
             p = p->node[i].ptr;
         }
     }
     r->i = i;
     if(find){//查找成功
         r->pt = p;
         r->tag = ;
     }
     else {//查找不成功，返回elem的插入位置的信息
         r->pt = q;
         r->tag = ;
     }
     return r;
 }

 /* 将r->key、r和ap分别插入到q->key[i+1]、q->recptr[i+1]和q->ptr[i+1]中 */
 int Insert(BTree* &pt, int n, int rx, BTree *ap) {
     for (int i = pt->keynum; i > n; --i)//空出pt->node[n+1]
         pt->node[i + ] = pt->node[i];//向后挪，腾出位置来
     pt->node[n + ].key = rx;
     pt->node[n + ].ptr = ap;
     pt->node[n + ].recptr = rx;
     pt->keynum++;
     return true;
 }

 /* 将结点q分裂成两个结点，前一半保留，后一半移入新生结点ap */
 int split(BTree* &pt, BTree* &ap) {
     int s = (m + ) / ;
     ap = new BTree;//生成新的节点ap
     ap->node[].ptr = pt->node[s].ptr;//后一半移入ap中
     for (int i = s + ; i < m; ++i) {
         ap->node[i - s] = pt->node[i];
         if (ap->node[i - s].ptr)
             ap->node[i - s].ptr->parent = ap;
     }
     ap->keynum = m - s;
     ap->parent = pt->parent;
     pt->keynum = s - ;/*  q的前一半保留，修改keynum */ 

     return true;
 }

 /* 生成含信息(T,r,ap)的新的根结点&T，原T和ap为子树指针 */
 int NewRoot(BTree *T, int key, BTree *ap) {
     BTree *p = new BTree;
     p->node[].ptr = T;
     T = p;
     if (T->node[].ptr)
         T->node[].ptr->parent = T;
     T->parent = NULL;
     T->keynum = ;
     T->node[].key = key;
     T->node[].recptr = key;
     T->node[].ptr = ap;
     if (T->node[].ptr)
         T->node[].ptr->parent = T;

     return true;
 }

 /*  在m阶B树T上结点*q的key[i]与key[i+1]之间插入关键字K的指针r。若引起 */
 /*  结点过大,则沿双亲链进行必要的结点分裂调整,使T仍是m阶B树。 */
 int InsertBTree(BTree* &T, int elem, BTree *pt, int n) {
     BTree *ap;
     ap = new BTree;
     bool finished = false;
     int s, rx;
     rx = elem;
     while (pt && !finished) {
         Insert(pt, n, rx, ap);// 将r->key、r和ap分别插入到q->key[i+1]、q->recptr[n+1]和q->ptr[n+1]中  */
         if (pt->keynum < m)
             finished = true;//插入成功
         else {//对节点进行分裂
             s = (m + ) / ;
             rx = pt->node[s].recptr;
             split(pt, ap);/*  将q->key[s+1..m],q->ptr[s..m]和q->recptr[s+1..m]移入新结点*ap  */
             pt = pt->parent;
             if (pt)
                 n = Search(pt, elem);//在双亲结点中*q中查找rx->key的插入位置
         }
     }
     if (!finished)/*  T是空树(参数q初值为NULL)或根结点已分裂为结点*q和*ap */
         NewRoot(T, rx, ap);/*  生成含信息(T,rx,ap)的新的根结点*T，原T和ap为子树指针 */

     return true;
 }

 int T034()
 {
     int r[N] = { ,,,,,,,,,,,,,,,, };
     BTree *T = new BTree;
     T = NULL;
     Result *s;
     for (int i = ; i < N; i++)
     {
         s = SearchBTree(T, r[i]);
         if (!s->tag)
             InsertBTree(T, r[i], s->pt, s->i);
     }
     printf("\n请输入待查找记录的关键字: ");
     int a;
     scanf("%d", &a);
     s = SearchBTree(T, a);
     if (s->tag)
         printf("(%d)", (s->pt)->node[a].key);
     else
         printf("没找到");
     printf("\n");

     return ;
 }