算法导论第十八章-B树-Cpp代码实现

B数的实现。删除有点复杂且没有伪代码，以后有时间再补上。

b_tree.h

#pragma once

/*************************************************
Author:董小歪
Date:2016-06-20
Description:算法导论第十八章-B树-Cpp代码实现
**************************************************/

#ifndef B_TREE_H
#define B_TREE_H

#include <iostream>
#include <vector>
#include <utility>
using namespace std;

#define t 3 //最小度数

template <typename T>
struct BTreeNode
{
int n; //关键字数量
bool leaf; //是否为叶结点
vector<T> keys; //关键字
vector<BTreeNode<T>*> children; //孩子结点

public:
BTreeNode(bool _leaf = false):n(0), //关键字数量开始为0
leaf(_leaf), //初始化为叶子
keys(vector<T>(2*t-1)), //关键字最大个数
children(vector<BTreeNode<T>*>(2*t, nullptr)) //最多可以有的孩子数量
{}
};

template <typename T>
class BTree
{
public:
BTree(bool _leaf = true) { root = new BTreeNode<T>(); root->leaf = _leaf; }

typedef pair<BTreeNode<T>*, int> mypair; //定义搜索结果数据结构
mypair b_tree_search(T k); //搜索B树
void b_tree_insert(T k); //插入关键字
void b_tree_delete(T k);
inline BTreeNode<T>* get_root() { return root; } //得到树根

private:
void b_tree_split_child(BTreeNode<T>*x, int i); //分裂B树中的节点
void b_tree_insert_nonfull(BTreeNode<T>* x, T k); //插入非满的根结点为根的树中
mypair b_tree_search(BTreeNode<T>* x, T k); //搜索B树
BTreeNode<T>* root; //树根
};

template <typename T>
pair<BTreeNode<T>*, int> BTree<T>::b_tree_search(T k)
{
return b_tree_search(root, k);
}

template <typename T>
pair<BTreeNode<T>*, int> BTree<T>::b_tree_search(BTreeNode<T>* x, T k)
{
int i = 1;
while (i <= x->n && k > x->keys[i - 1])
++i;
if (i <= x->n && k == x->keys[i - 1])
return make_pair(x, i - 1);
else if (x->leaf) //如果是叶节点
return make_pair(nullptr, 0);
else
return b_tree_search(x->children[i - 1], k);
}

template <typename T>
void BTree<T>::b_tree_split_child(BTreeNode<T>*x, int i)
{
BTreeNode<T>* z = new BTreeNode<T>();
BTreeNode<T>* y = x->children[i];
z->leaf = y->leaf;
z->n = t - 1;
//************1.建立新结点z************
for (int j = 0; j <= t - 2; ++j)
z->keys[j] = y->keys[t + j];
if (!y->leaf)
for (int j = 0; j <= t - 1; ++j)
z->children[j] = y->children[t + j];

//************2.修改y的关键字数量************
y->n = t - 1;

//************3.增加x结点的关键字和孩子************
for (int j = x->n; j >= i + 1; --j)
x->children[j + 1] = x->children[j];
x->children[i + 1] = z;
for (int j = x->n; j >= i + 1; --j)
x->keys[j] = x->keys[j - 1];
x->keys[i] = y->keys[t - 1];
x->n = x->n + 1;
}

template <typename T>
void BTree<T>::b_tree_insert(T k)
{
BTreeNode<T>* r = root;
if (r->n == 2 * t - 1)
{
BTreeNode<T>* s = new BTreeNode<T>();
root = s;
s->children[0] = r;
b_tree_split_child(s, 0);
b_tree_insert_nonfull(s, k);
}
else
b_tree_insert_nonfull(r, k);
}

template <typename T>
void BTree<T>::b_tree_insert_nonfull(BTreeNode<T>* x, T k)
{
int i = x->n;
if (x->leaf)
{
while (i >= 1 && k < x->keys[i - 1])
{
x->keys[i] = x->keys[i - 1];
--i;
}
x->keys[i] = k;
x->n = x->n + 1;
}
else
{
while (i >= 1 && k < x->keys[i - 1])
--i;
++i;
if (x->children[i - 1]->n == 2 * t - 1)
{
b_tree_split_child(x, i - 1);
if (k > x->keys[i - 1])
++i;

}
b_tree_insert_nonfull(x->children[i - 1], k);
}
}

template <typename T>
void BTree<T>::b_tree_delete(T k)
{

}

#endif // !B_TREE_H


测试代码：
main_entrance.cpp

#include "b_tree.h"

int main()
{
BTree<char> btree;
btree.b_tree_insert('G');
btree.b_tree_insert('M');
btree.b_tree_insert('P');
btree.b_tree_insert('X');
BTreeNode<char>* c0 = new BTreeNode<char>(true);
BTreeNode<char>* c1 = new BTreeNode<char>(true);
BTreeNode<char>* c2 = new BTreeNode<char>(true);
BTreeNode<char>* c3 = new BTreeNode<char>(true);
BTreeNode<char>* c4 = new BTreeNode<char>(true);
c0->n = 4; c0->keys[0] = 'A'; c0->keys[1] = 'C'; c0->keys[2] = 'D'; c0->keys[3] = 'E';
c1->n = 2; c1->keys[0] = 'J'; c1->keys[1] = 'K';
c2->n = 2; c2->keys[0] = 'N'; c2->keys[1] = 'O';
c3->n = 5; c3->keys[0] = 'R'; c3->keys[1] = 'S'; c3->keys[2] = 'T'; c3->keys[3] = 'U'; c3->keys[4] = 'V';
c4->n = 2; c4->keys[0] = 'Y'; c4->keys[1] = 'Z';
btree.get_root()->children[0] = c0;
btree.get_root()->children[1] = c1;
btree.get_root()->children[2] = c2;
btree.get_root()->children[3] = c3;
btree.get_root()->children[4] = c4;
btree.get_root()->leaf = false;

btree.b_tree_insert('B');
btree.b_tree_insert('Q');
btree.b_tree_insert('L');
btree.b_tree_insert('F');

system("pause");
}

没有测试结果。