【数据结构】算法9.13-9.14 B树-插入&查找

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#include<stdio.h>#include<string.h>#include<stdlib.h>#include<math.h>#define TRUE 1#define FALSE 0#define OK 1#define ERROR 0#define INFEASIBLE -1#define OVERFLOW_SELF -2#define EQ(a,b) ((a) == (b))#define LT(a,b) ((a) <  (b))#define LQ(a,b) ((a) <= (b))#define M 3typedef int Status;typedef int ElemType;typedef int KeyType;typedef struct{    ElemType *elem; //unit elem[0] keep NULL    int length;   //length of table}SSTable;typedef struct BTNode{    int keynum;   //结点中关键字个数，即结点的大小    struct BTNode *parent;  //point to Parent node    KeyType key[M+1];    //关键字向量，0号单元未用    struct BTNode *ptr[M+1];  //子树指针向量}BTNode,*BTree;typedef struct{    BTNode *pt;  //指向找到的结点    int i;   //1...M，在结点中的关键字序号    int tag;  //1:found,0:unfound}Result;  //B-Tree 的查找结果类型/*******************************声明部分****************************************/int Search(BTree p,KeyType K);//在p->key[1...keynum]中查找，返回值i使得：p->key[i] <= K < p->key[i+1]Result SearchBTree(BTree T,KeyType K);//在M阶B树T上查找关键字K，返回结果（pt,i,tag),若查找成功，则特征值tag = 1，//指针pt所指结点中第i个关键字等于K，否则特征值tag = 0，等于K的关键字应插入//在指针pt所指结点中第i个和第i+1个关键字之间Status insert(BTree q,int i,KeyType x,BTree ap);//将x和ap分别插入到q->key[i+1]和q->ptr[i+1]Status split(BTree q,int s,BTree *ap);//将q->key[s+1...M],q->ptr[s...M]和q->recptr[s+1...M]移入新结点*apStatus NewRoot(BTree *T,BTree q,KeyType x,BTree ap);//生成含信息(T,x,ap)的新的根结点*T，原T和ap为子树指针Status InsertBTree(BTree *T,KeyType K,BTree q,int i);//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，//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Status CreateTalbe(SSTable *L);Status InitTable(SSTable *L);/*******************************函数部分****************************************/int Search(BTree p,KeyType K){    int i,j;    for(i = 0,j = 1;j <= p->keynum;j++){        if(p->key[j] <= K)            i = j;        else            break;    }    return i;}Result SearchBTree(BTree T,KeyType K){    BTree p,q;    int found,i;    p = T;  //初始化，p指向待查结点，q指向p的双亲    q = NULL;    found = FALSE;    i = 0;    while(p && !found){        i = Search(p,K);        if(i > 0 && p->key[i] == K)            found = TRUE;  //找到关键字        else{            q = p;            p = p->ptr[i];        }    }//while    if(found){        Result R1;        R1.pt = p;        R1.i = i;        R1.tag = 1;        return R1;    }    else{        Result R0;        R0.pt = q;        R0.i = i;        R0.tag = 0;        return R0;    }}Status Insert(BTree q,int i,KeyType x,BTree ap){    int j;    for(j = q->keynum;j > i;j--){   //所有元素后移        q->key[j+1] = q->key[j];        q->ptr[j+1] = q->ptr[j];    }    q->key[i+1] = x;    q->ptr[i+1] = ap;    q->keynum++;    return OK;}Status split(BTree q,int s,BTree *ap){    int i;    (*ap) = (BTree)malloc(sizeof(BTNode));    (*ap)->ptr[0] = q->ptr[s];    for(i = s+1; i <= M;i++){        (*ap)->key[i-s] = q->key[i];        (*ap)->ptr[i-s] = q->ptr[i];    }    (*ap)->keynum = M - s;    q->keynum = s-1;    (*ap)->parent = q->parent;    for(i = 0;i<=(*ap)->keynum;i++){        if((*ap)->ptr[i])            (*ap)->ptr[i]->parent = *ap;    }}Status NewRoot(BTree *T,BTree q,KeyType x,BTree ap){    BTree p;    p = (BTree)malloc(sizeof(BTNode));    p->keynum = 1;    p->parent = NULL;    p->key[1] = x;    p->ptr[0] = *T;    p->ptr[1] = ap;    if(p->ptr[0])        p->ptr[0]->parent = p;    if(p->ptr[1])        p->ptr[1]->parent = p;    *T = p;}Status InsertBTree(BTree *T,KeyType K,BTree q,int i){    KeyType x;    BTree ap;    int finished,s;    x = K;    ap = NULL;    finished = FALSE;    while(q && !finished){        Insert(q,i,x,ap);        if(q->keynum < M)            finished = TRUE;  //Insert complete        else{  //split the node *q            s =ceil((double)M/2);            split(q,s,&ap);            x = q->key[s];            q = q->parent;            if(q)                i = Search(q,x);        }//else    }//while    if(!finished)        NewRoot(T,q,x,ap);    return OK;}Status CreateTalbe(SSTable *L){  /*  int i;    printf("请输入顺序表的长度:");    scanf("%d",&L->length);    for(i = 1;i<=L->length;i++){        printf("请输入第 %d 个元素的值：",i);        scanf("%d",&L->elem[i].key);    }*/    L->length = 15;    L->elem[1] = 24;    L->elem[2] = 45;    L->elem[3] = 50;    L->elem[4] = 53;    L->elem[5] = 100;    L->elem[6] = 37;    L->elem[7] = 12;    L->elem[8] = 61;    L->elem[9] = 90;    L->elem[10] = 70;    L->elem[11] = 3;    L->elem[12] = 30;    L->elem[13] = 26;    L->elem[14] = 85;    L->elem[15] = 7;    return OK;}Status InitTable(SSTable *L){    (*L).elem = (ElemType *)malloc(100 * sizeof(ElemType));    if(!(*L).elem)        exit(OVERFLOW);    (*L).length = 0;    return OK;}Status CreateBTree(BTree *T,SSTable L){    int i;    *T = NULL;    Result R;    if(L.length){        for(i = 1;i<=L.length;i++){            R = SearchBTree(*T,L.elem[i]);            if(!InsertBTree(T, L.elem[i], R.pt, R.i)){                printf("插入失败!\n");                break;            }        }    }    printf("插入完成\n");    return OK;}void PrintBT_InOrder(BTree T){    int j;    if(T){        for(j = 0;j<= T->keynum;j++){            PrintBT_InOrder(T->ptr[j]);            if(j < T->keynum)                printf("%d ",T->key[j+1]);        }    }}/*******************************主函数部分**************************************/int main(){    SSTable L;    BTree T;    printf("\n创建一个顺序表如下：\n");    InitTable(&L);    CreateTalbe(&L);    int i;    for(i = 1;i<= L.length;i++)        printf("%d ",L.elem[i]);    printf("\n\n创建一个B树,依次插入顺序表的元素\n");    CreateBTree(&T,L);    printf("\n中序遍历B树：\n");    PrintBT_InOrder(T);    printf("\n\n寻找是否存在元素 88 ：\n");    Result R;    R = SearchBTree(T,88);    printf("结果是：%d \n",R.tag);    printf("\n将该元素 88 插入到B树中：\n");    InsertBTree(&T, 88, R.pt, R.i);    printf("插入完成\n");    printf("\n再次中序遍历B树：\n");    PrintBT_InOrder(T);    printf("\n");}
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