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【B-树、B+树:适用于 文件很大且存放于计算机外存的查找】
7.3.3 B-树(属于动态查找树,适用于动态查找表)
▲课本算法实现/▲09 查找/08 B-Tree/B-Tree.c —— kangjianwei
【仅包括 查找、插入、分裂、创建、中序遍历打印,不包括删除】
#include <stdio.h>
#include <stdlib.h>
#include <math.h>#define m 3
#define TRUE 1
#define FALSE 0typedef int KeyType;
typedef char Record; //假设位置存储类型是char型的typedef struct BTNode
{int keynum;struct BTNode* parent;KeyType key[m + 1];struct BTNode* ptr[m + 2];Record* recptr[m + 1];
}BTNode, * BTree;typedef struct
{BTNode* pt;int i;int tag;
}Result;void CreateBTree(BTree& T);
int InsertBTree(BTree& T, KeyType K, BTree q, int i);
void split(BTree& q, int s, BTree& ap);
void NewRoot(BTree& T, int x, BTree& ap);
void Insert(BTree& q, int i, KeyType x, BTree ap);
Result SearchBTree(BTree T, KeyType key);
int Search(BTree T, KeyType key);
void PrintBTree(BTree T);int main()
{BTree T = NULL;CreateBTree(T);printf("\n该B-树的中序序列为:");PrintBTree(T);return 0;
}//B-树的创建(通过B-树的插入实现)
void CreateBTree(BTree& T)
{T = NULL;Result r = { NULL,0,0 };int j = 0;int N = 0;KeyType KEY = 0;printf("请输入关键字总个数:");scanf_s(" %d", &N);for (j = 1; j <= N; j++){printf("请输入第%d个关键字:", j);scanf_s(" %d", &KEY);r = SearchBTree(T, KEY); //在B-树整棵树上查找key是否存在if (r.tag == 0){InsertBTree(T, KEY, r.pt, r.i);}else{printf("该关键字已存在,无法插入,请重新输入。\n");j--;}}
}//算法7.9 B-树的插入【BTree q, int i 这两个参数来自于SearchBTree函数r.tag为0时的r.pt和r.i】
int InsertBTree(BTree& T, KeyType K, BTree q, int i)
{KeyType x = K;BTree ap = NULL;bool finished = FALSE;int s = 0;while (q && !finished){Insert(q, i, x, ap);if (q->keynum < m){finished = TRUE;}else //if(q->keynum == m){s = (int)ceil((double)m / 2);//C 标准库 <math.h>函数 double ceil(double x) 返回大于或等于 x 的最小的整数值。//B树结点中关键字个数必须>=ceil(m/2)-1split(q, s, ap);x = q->key[s];q = q->parent;if (q){i = Search(q, x);}}}if (!finished) //q的初始值为空,即整棵树T是空树{NewRoot(T,x,ap); //书上是NewRoot(T,q,x,ap),但q为NULL,在NewRoot函数中无用}return 1;
}void split(BTree& q, int s, BTree& ap)
{int i = 0;ap = (BTree)malloc(sizeof(BTNode));//将q->key[s+1,..,m]保存到ap->key[1,..,m-s]中for (i = 1; i <= m-s; i++){ap->key[i] = q->key[s+i];q->key[s + i] = 0;}//将q->ptr[s,..,m]保存到ap->ptr[0,..,m-s]中for (i= 0; i <= m-s; i++){ap->ptr[i] = q->ptr[s+i];if (ap->ptr[i]){ap->ptr[i]->parent = ap;}q->ptr[s + i] = NULL;}ap->keynum = m - s;q->keynum = s-1;ap->parent = q->parent;
}//生成含信息(T, x, ap)的新的根结点*T,原T和ap为子树指针
void NewRoot(BTree& T, int x, BTree& ap)
{BTree newT = (BTree)malloc(sizeof(BTNode));newT->key[1] = x;newT->ptr[0] = T; //必须等于T,而不能等于q,q指向NULLnewT->ptr[1] = ap;newT->keynum = 1;newT->parent = NULL;//第一次创建节点时,即树的根结点,该结点/树中只有一个关键字,且该关键字的左右子树都是空的,还无法指定其父节点为其本身。if (newT->ptr[0]){newT->ptr[0]->parent = newT;}if (newT->ptr[1]){newT->ptr[1]->parent = newT;}T = newT;
}//将x和ap分别插入到q->key[i + l]和q->ptr[i+1]
void Insert(BTree &q, int i, KeyType x, BTree ap)
{int a = 0;int b = 0;//将q->key中K(i+1)个到K(keynum)整体往后移动一个单位for (a = q->keynum + 1; a >= i + 2; a--){q->key[a] = q->key[a - 1];}//将q->ptr中的P(i+1)到第P(keynum)整体往后移动一个单位for (b = q->keynum + 1; b >= i + 2; b--){q->ptr[b] = q->ptr[b - 1];}q->key[i + 1] = x;q->ptr[i + 1] = ap;q->keynum++;
}//算法7.8 B-树的查找
//在磁盘上(外存)进行的:在B-树整棵树上查找结点
Result SearchBTree(BTree T, KeyType key)
{BTree p = T;BTree q = NULL;bool found = FALSE;int i = 0;Result r = { NULL,0,0 };while (p && !found){i = Search(p, key);/* 在内存中的Search函数中找到p中目标关键字的位置i之后,在外存磁盘上是不能将p->key[i]直接拿来使用的。在外存上,要先从Record指针类型的一维数组中,读取到该BTNode结点指针p中存储第i个关键字Ki的物理(实际)存放位置recptr[i],也就是说是p->key[i]的索引项,才能在外存上使用关键字p->key[i]. 书上没有体现。 */if (i > 0 && p->key[i] == key){found = TRUE;}else //if( p->key[i] != key ){q = p;p = p->ptr[i];}}//找到了或者p指向了叶子结点,跳出while循环if (found){r.pt = p;r.i = i;r.tag = 1;}else{r.pt = q;r.i = i;r.tag = 0;//可以在此处由q指向结点的第i个和第i+1个关键字之间,插入关键字key}return r;
}int Search(BTree p, KeyType K)
{int i = 0; int j = 1;for (i = 0, j = 1; j <= p->keynum; j++){if (p->key[j] <= K)i = j;elsebreak;}return i;
}/*
//在内存上进行的:在结点T中找关键字key
int Search(BTree T, KeyType key)
{BTree p = T;int i = 0;int endnum = 0;if (p) //结点不为空时{endnum = p->keynum; //获得节点包含的关键字个数}else{return 0;}if(key >= p->key[endnum]) //节点不为空,但当前值比最大的key还大,返回当前关键字的下标{i = endnum;return i; }else if (key <= p->key[1]) //节点不为空,但当前值比最小的key还小,返回当前关键字的下标{return i; //i==0}else //key < p->key[endnum] && key > p->key[1]{for (i = 1; i < endnum; i++) {if (p->key[i] <= key && key < p->key[i + 1]){return i;}}}
}
*///中序遍历打印B-数
void PrintBTree(BTree T)
{int i = 0;if (T){for (i = 0; i <= T->keynum; i++){PrintBTree(T->ptr[i]);if (i < T->keynum) /* 因为关键字的下标最大值为T->keynum,若打印关键字i最大只能取到T->keynum-1(打印时下标为i+1)若打印子树指针指向的树,那么i可取到T->keynum */{printf("%d ", T->key[i + 1]);}}}
}
7.3.4 B+ 树(属于动态查找树,适用于动态查找表)
▲课本算法实现/▲09 查找/09 B+Tree/B+Tree.c —— kangjianwei
【不包含删除代码】
B+ 树 ——OI Wiki
数据结构之B+树删除详解 —— 每天都要进步一点点
7.4 散列表的查找
7.4.4 散列表的创建与查找
#include <stdio.h>
#include <stdlib.h>
#include <math.h>#define m 16 //表长,能容纳的最多的元素个数
#define NULLKEY 0typedef int KeyType;
typedef char OtherInfo;typedef struct elem
{KeyType key;OtherInfo otherinfo;
}elem;/* elem HashTable[m];HashTable是一个一维数组名称,里面包含m个元素,每个元素类型为一个结构体elem。HashTable 也是指向该数基地址/第一个元素地址的指针 */void CreateHash(elem HT[]);
void Insert(elem HT[], KeyType key);
int SearchHash(elem HT[], KeyType key);
int H(KeyType key);
int maxPrimeNumber(int n);
int checkPrimeNumber(int n);
void printHashTable(elem HT[]);int main()
{elem HT[m] = { 0 };CreateHash(HT);printHashTable(HT);return 0;
}//散列表的创建
void CreateHash(elem HT[])
{int i = 0;int j = 0;int KEY = 0;int flag = 0;/*HT = (elem*)malloc(sizeof(elem) * m); //HT已经被定义为一个具有固定大小的数组。 */for (i = 0; i < m; i++){HT[i].key = NULLKEY; //将所有位置置为空}for (i = 1; i <= m; i++){printf("请输入第%d个关键字(结束时输入-1):", i);scanf_s(" %d", &KEY);if (KEY != -1){flag = SearchHash(HT, KEY);if (flag == -1){Insert(HT, KEY);}else{printf("该元素已存在,无法插入,请重新输入。\n");i--;}}else{break;}}if (i > m){printf("散列表已满。");return;}
}//将查找不存在的元素,插入哈希表中
void Insert(elem HT[],KeyType key)
{int H0 = 0;int Hi = 0;int i = 0;H0 = H(key);if (HT[H0].key == NULLKEY){HT[H0].key = key;}else{for (i = 1; i < m; i++){Hi = (H0 + i) % m;if (HT[Hi].key == NULLKEY){HT[Hi].key = key;break;}//如果HT[Hi].key是其它元素,那么继续计算下一个散列值}}
}//算法7.10 散列表的查找
int SearchHash(elem HT[], KeyType key)
{int i = 0;int H0 = H(key);int Hi = 0;if (HT[H0].key == NULLKEY){return -1;}else if(HT[H0].key == key){return H0;}else //HT[H0].key是其它元素{for (i = 1; i < m; i++){Hi = (H0 + i) % m;if (HT[Hi].key == NULLKEY){return -1;}else if (HT[Hi].key == key){return Hi;}else {; //如果HT[Hi].key是其它元素,那么继续计算下一个散列值}}return -1;}
}//散列函数
/* 采用除留余数法构造散列函数,选择p为小于表长m的最大质数 */
int H(KeyType key)
{int p = maxPrimeNumber(m);return key % p;
}//确定[0,n]范围内的最大质数
int maxPrimeNumber(int n)
{int i = 0;int status = checkPrimeNumber(0);int max = 0;for (i = 0; i <= n; i++){status = checkPrimeNumber(i);if (status){max = i;}}return max;
}//判断一个数是否是素数(是的话返回1,不是返回0)
int checkPrimeNumber(int n)
{int i = 0;int sq = floor(sqrt(n)); //不大于√n的最大整数/*floor向下取整,ceil向上取整 */if (n <= 1) {return 0; //负数、0 和1 均不是素数}for (i = 2; i <= sq; i++){if (n % 2 == 0 || n % i == 0) //n%2==0,说明n是偶数,而质数一定不是偶数{return 0;}}return 1;
}void printHashTable(elem HT[])
{int i = 0;printf("\n散列表中的元素为:");for (i = 0; i < m ; i++){if (HT[i].key != NULLKEY){printf("\n HT[%d].key = %d",i, HT[i].key);}//空槽不输出,但是其它的元素还是要输出}
}
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