摘要：最近學習了，對其內部結構較為感興趣，為了進一步了解其運行原理，我打算自己動手用寫一個。本章講解的是項目中樹與的引入。樹的具體實現方法如下其中主要函數為向樹中插入一個關鍵字以及該關鍵字對應的的值。

最近學習了Redis，對其內部結構較為感興趣，為了進一步了解其運行原理，我打算自己動手用C++寫一個redis。這是我第一次造輪子，所以紀念一下 ^ _ ^。

源碼github鏈接,項目現在實現了客戶端與服務器的鏈接與交互，以及一些Redis的基本命令，下面是測試結果：

（左邊是服務端，右邊是客戶端）

上節已經實現了小型Redis的基本功能，為了完善其功能并且鍛煉一下自己的數據結構與算法，我打算參考《Redis設計與實現》一書優化其中的數據結構與算法從而完善自己的項目。

本章講解的是項目中B樹與hash的引入。

在上一章中，我們的數據庫使用的是原生的map結構，為了提高數據庫的增刪改查效率，這里我將其改為使用B_樹這一數據結構。

B樹的具體實現方法如下：
其中主要函數為
（1）void insert(int k,string stt） 向B_樹中插入一個關鍵字以及該關鍵字對應的value的值。

（2）string getone(int k) 通過關鍵字獲取其對應的value的值。

// A BTree node
class BTreeNode
{
    int *keys;  // An array of keys
    string* strs;//value的類型使用string數組
    int t;      // Minimum degree (defines the range for number of keys)
    BTreeNode **C; // An array of child pointers
    int n;     // Current number of keys
    bool leaf; // Is true when node is leaf. Otherwise false
 
public:
 
    BTreeNode(int _t, bool _leaf);   // Constructor
 
    string getOne(int k);

    // A function to traverse all nodes in a subtree rooted with this node
    void traverse();
 
    // A function to search a key in subtree rooted with this node.
    BTreeNode *search(int k);   // returns NULL if k is not present.
 
    // A function that returns the index of the first key that is greater
    // or equal to k
    int findKey(int k);
 
    // A utility function to insert a new key in the subtree rooted with
    // this node. The assumption is, the node must be non-full when this
    // function is called
    void insertNonFull(int k,string stt);
 
    // A utility function to split the child y of this node. i is index
    // of y in child array C[].  The Child y must be full when this
    // function is called
    void splitChild(int i, BTreeNode *y);
 
    // A wrapper function to remove the key k in subtree rooted with
    // this node.
    void remove(int k);
 
    // A function to remove the key present in idx-th position in
    // this node which is a leaf
    void removeFromLeaf(int idx);
 
    // A function to remove the key present in idx-th position in
    // this node which is a non-leaf node
    void removeFromNonLeaf(int idx);
 
    // A function to get the predecessor of the key- where the key
    // is present in the idx-th position in the node
    int getPred(int idx);
 
    // A function to get the successor of the key- where the key
    // is present in the idx-th position in the node
    int getSucc(int idx);
 
    // A function to fill up the child node present in the idx-th
    // position in the C[] array if that child has less than t-1 keys
    void fill(int idx);
 
    // A function to borrow a key from the C[idx-1]-th node and place
    // it in C[idx]th node
    void borrowFromPrev(int idx);
 
    // A function to borrow a key from the C[idx+1]-th node and place it
    // in C[idx]th node
    void borrowFromNext(int idx);
 
    // A function to merge idx-th child of the node with (idx+1)th child of
    // the node
    void merge(int idx);
 
    // Make BTree friend of this so that we can access private members of
    // this class in BTree functions
    friend class BTree;
};
 
class BTree
{
    BTreeNode *root; // Pointer to root node
    int t;  // Minimum degree
public:
 
    // Constructor (Initializes tree as empty)
    BTree(int _t)
    {
        root = NULL;
        t = _t;
    }
 
    void traverse()
    {
        if (root != NULL) root->traverse();
    }
 
    // function to search a key in this tree
    //查找這個關鍵字是否在樹中
    BTreeNode* search(int k)
    {
        return (root == NULL)? NULL : root->search(k);
    }
 
    // The main function that inserts a new key in this B-Tree
    void insert(int k,string stt);
 
    // The main function that removes a new key in thie B-Tree
    void remove(int k);

    string getone(int k){
        string ss=root->getOne(k);
        return ss;
    }
 
};
 
BTreeNode::BTreeNode(int t1, bool leaf1)
{
    // Copy the given minimum degree and leaf property
    t = t1;
    leaf = leaf1;
 
    // Allocate memory for maximum number of possible keys
    // and child pointers
    keys = new int[2*t-1];
    strs= new string[2*t-1];
    C = new BTreeNode *[2*t];
 
    // Initialize the number of keys as 0
    n = 0;
}
 
// A utility function that returns the index of the first key that is
// greater than or equal to k
//查找關鍵字的下標
int BTreeNode::findKey(int k)
{
    int idx=0;
    while (idxn < t)
            fill(idx);
 
        // If the last child has been merged, it must have merged with the previous
        // child and so we recurse on the (idx-1)th child. Else, we recurse on the
        // (idx)th child which now has atleast t keys
        if (flag && idx > n)
            C[idx-1]->remove(k);
        else
            C[idx]->remove(k);
    }
    return;
}
 
// A function to remove the idx-th key from this node - which is a leaf node
void BTreeNode::removeFromLeaf (int idx)
{
 
    // Move all the keys after the idx-th pos one place backward
    for (int i=idx+1; in >= t)
    {
        int pred = getPred(idx);
        keys[idx] = pred;
        C[idx]->remove(pred);
    }
 
    // If the child C[idx] has less that t keys, examine C[idx+1].
    // If C[idx+1] has atleast t keys, find the successor "succ" of k in
    // the subtree rooted at C[idx+1]
    // Replace k by succ
    // Recursively delete succ in C[idx+1]
    else if  (C[idx+1]->n >= t)
    {
        int succ = getSucc(idx);
        keys[idx] = succ;
        C[idx+1]->remove(succ);
    }
 
    // If both C[idx] and C[idx+1] has less that t keys,merge k and all of C[idx+1]
    // into C[idx]
    // Now C[idx] contains 2t-1 keys
    // Free C[idx+1] and recursively delete k from C[idx]
    else
    {
        merge(idx);
        C[idx]->remove(k);
    }
    return;
}
 
// A function to get predecessor of keys[idx]
int BTreeNode::getPred(int idx)
{
    // Keep moving to the right most node until we reach a leaf
    BTreeNode *cur=C[idx];
    while (!cur->leaf)
        cur = cur->C[cur->n];
 
    // Return the last key of the leaf
    return cur->keys[cur->n-1];
}
 
int BTreeNode::getSucc(int idx)
{
 
    // Keep moving the left most node starting from C[idx+1] until we reach a leaf
    BTreeNode *cur = C[idx+1];
    while (!cur->leaf)
        cur = cur->C[0];
 
    // Return the first key of the leaf
    return cur->keys[0];
}
 
// A function to fill child C[idx] which has less than t-1 keys
void BTreeNode::fill(int idx)
{
 
    // If the previous child(C[idx-1]) has more than t-1 keys, borrow a key
    // from that child
    if (idx!=0 && C[idx-1]->n>=t)
        borrowFromPrev(idx);
 
    // If the next child(C[idx+1]) has more than t-1 keys, borrow a key
    // from that child
    else if (idx!=n && C[idx+1]->n>=t)
        borrowFromNext(idx);
 
    // Merge C[idx] with its sibling
    // If C[idx] is the last child, merge it with with its previous sibling
    // Otherwise merge it with its next sibling
    else
    {
        if (idx != n)
            merge(idx);
        else
            merge(idx-1);
    }
    return;
}
 
// A function to borrow a key from C[idx-1] and insert it
// into C[idx]
void BTreeNode::borrowFromPrev(int idx)
{
 
    BTreeNode *child=C[idx];
    BTreeNode *sibling=C[idx-1];
 
    // The last key from C[idx-1] goes up to the parent and key[idx-1]
    // from parent is inserted as the first key in C[idx]. Thus, the  loses
    // sibling one key and child gains one key
 
    // Moving all key in C[idx] one step ahead
    for (int i=child->n-1; i>=0; --i){
        child->keys[i+1] = child->keys[i];
        child->strs[i+1]=child->strs[i];
    }
 
    // If C[idx] is not a leaf, move all its child pointers one step ahead
    if (!child->leaf)
    {
        for(int i=child->n; i>=0; --i)
            child->C[i+1] = child->C[i];
    }
 
    // Setting child"s first key equal to keys[idx-1] from the current node
    child->keys[0] = keys[idx-1];
    child->strs[0]=strs[idx-1];
 
    // Moving sibling"s last child as C[idx]"s first child
    if (!leaf)
        child->C[0] = sibling->C[sibling->n];
 
    // Moving the key from the sibling to the parent
    // This reduces the number of keys in the sibling
    keys[idx-1] = sibling->keys[sibling->n-1];
    strs[idx-1] = sibling->strs[sibling->n-1];

    child->n += 1;
    sibling->n -= 1;
 
    return;
}
 
// A function to borrow a key from the C[idx+1] and place
// it in C[idx]
void BTreeNode::borrowFromNext(int idx)
{
 
    BTreeNode *child=C[idx];
    BTreeNode *sibling=C[idx+1];
 
    // keys[idx] is inserted as the last key in C[idx]
    child->keys[(child->n)] = keys[idx];
    child->strs[(child->n)] = strs[idx];

    // Sibling"s first child is inserted as the last child
    // into C[idx]
    if (!(child->leaf))
        child->C[(child->n)+1] = sibling->C[0];
 
    //The first key from sibling is inserted into keys[idx]
    keys[idx] = sibling->keys[0];
    strs[idx] = sibling->strs[0];

    // Moving all keys in sibling one step behind
    for (int i=1; in; ++i)
        sibling->strs[i-1] = sibling->strs[i];
 
    // Moving the child pointers one step behind
    if (!sibling->leaf)
    {
        for(int i=1; i<=sibling->n; ++i)
            sibling->C[i-1] = sibling->C[i];
    }
 
    // Increasing and decreasing the key count of C[idx] and C[idx+1]
    // respectively
    child->n += 1;
    sibling->n -= 1;
 
    return;
}
 
// A function to merge C[idx] with C[idx+1]
// C[idx+1] is freed after merging
void BTreeNode::merge(int idx)
{
    BTreeNode *child = C[idx];
    BTreeNode *sibling = C[idx+1];
 
    // Pulling a key from the current node and inserting it into (t-1)th
    // position of C[idx]
    child->keys[t-1] = keys[idx];
    child->strs[t-1] = strs[idx];
 
    int i;
    // Copying the keys from C[idx+1] to C[idx] at the end
    for (i=0; in; ++i){
        child->strs[i+t] = sibling->strs[i];    
    }
 
    // Copying the child pointers from C[idx+1] to C[idx]
    if (!child->leaf)
    {
        for(i=0; i<=sibling->n; ++i)
            child->C[i+t] = sibling->C[i];
    }
 
    // Moving all keys after idx in the current node one step before -
    // to fill the gap created by moving keys[idx] to C[idx]
    for (i=idx+1; in += sibling->n+1;
    n--;
 
    // Freeing the memory occupied by sibling
    delete(sibling);
    return;
}
 
// The main function that inserts a new key in this B-Tree
void BTree::insert(int k,string stt)
{
    // If tree is empty
    if (root == NULL)
    {
        // Allocate memory for root
        root = new BTreeNode(t, true);
        root->keys[0] = k;  // Insert key
        root->strs[0]=stt;
        root->n = 1;  // Update number of keys in root
    }
    else // If tree is not empty
    {
        // If root is full, then tree grows in height
        if (root->n == 2*t-1)
        {
            // Allocate memory for new root
            BTreeNode *s = new BTreeNode(t, false);
 
            // Make old root as child of new root
            s->C[0] = root;
 
            // Split the old root and move 1 key to the new root
            s->splitChild(0, root);
 
            // New root has two children now.  Decide which of the
            // two children is going to have new key
            int i = 0;
            if (s->keys[0] < k)
                i++;
            s->C[i]->insertNonFull(k,stt);
 
            // Change root
            root = s;
        }
        else  // If root is not full, call insertNonFull for root
            root->insertNonFull(k,stt);
    }
}
 
// A utility function to insert a new key in this node
// The assumption is, the node must be non-full when this
// function is called
void BTreeNode::insertNonFull(int k,string stt)
{
    // Initialize index as index of rightmost element
    int i = n-1;
 
    // If this is a leaf node
    if (leaf == true)
    {
        // The following loop does two things
        // a) Finds the location of new key to be inserted
        // b) Moves all greater keys to one place ahead
        while (i >= 0 && keys[i] > k)
        {
            keys[i+1] = keys[i];
            strs[i+1] = strs[i];
            i--;
        }
 
        // Insert the new key at found location
        keys[i+1] = k;
        strs[i+1]=stt;
        n = n+1;
    }
    else // If this node is not leaf
    {
        // Find the child which is going to have the new key
        while (i >= 0 && keys[i] > k)
            i--;
 
        // See if the found child is full
        if (C[i+1]->n == 2*t-1)
        {
            // If the child is full, then split it
            splitChild(i+1, C[i+1]);
 
            // After split, the middle key of C[i] goes up and
            // C[i] is splitted into two.  See which of the two
            // is going to have the new key
            if (keys[i+1] < k)
                i++;
        }
        C[i+1]->insertNonFull(k,stt);
    }
}
 
// A utility function to split the child y of this node
// Note that y must be full when this function is called
void BTreeNode::splitChild(int i, BTreeNode *y)
{
    // Create a new node which is going to store (t-1) keys
    // of y
    BTreeNode *z = new BTreeNode(y->t, y->leaf);
    z->n = t - 1;
    int j;
    // Copy the last (t-1) keys of y to z
    for (j = 0; j < t-1; j++){
        z->keys[j] = y->keys[j+t];
        z->strs[j] = y->strs[j+t];
    }
 
    // Copy the last t children of y to z
    if (y->leaf == false)
    {
        for (int j = 0; j < t; j++)
            z->C[j] = y->C[j+t];
    }
 
    // Reduce the number of keys in y
    y->n = t - 1;
 
    // Since this node is going to have a new child,
    // create space of new child
    for (j = n; j >= i+1; j--)
        C[j+1] = C[j];
 
    // Link the new child to this node
    C[i+1] = z;
 
    // A key of y will move to this node. Find location of
    // new key and move all greater keys one space ahead
    for (j = n-1; j >= i; j--){
        strs[j+1] = strs[j];    
    }
 
    // Copy the middle key of y to this node
    keys[i] = y->keys[t-1];
    strs[i] = y->strs[t-1];
 
    // Increment count of keys in this node
    n = n + 1;
}
 
// Function to traverse all nodes in a subtree rooted with this node
void BTreeNode::traverse()
{
    // There are n keys and n+1 children, travers through n keys
    // and first n children
    int i;
    for (i = 0; i < n; i++)
    {
        // If this is not leaf, then before printing key[i],
        // traverse the subtree rooted with child C[i].
        if (leaf == false)
            C[i]->traverse();
        cout << " " << keys[i];
    }
 
    // Print the subtree rooted with last child
    if (leaf == false)
        C[i]->traverse();
}
 
// Function to search key k in subtree rooted with this node
BTreeNode *BTreeNode::search(int k)
{
    // Find the first key greater than or equal to k
    int i = 0;
    while (i < n && k > keys[i])
        i++;
 
    // If the found key is equal to k, return this node
    if (keys[i] == k)
        return this;
 
    // If key is not found here and this is a leaf node
    if (leaf == true)
        return NULL;
 
    // Go to the appropriate child
    return C[i]->search(k);
}
 
void BTree::remove(int k)
{
    if (!root)
    {
        cout << "The tree is empty
";
        return;
    }
 
    // Call the remove function for root
    root->remove(k);
 
    // If the root node has 0 keys, make its first child as the new root
    //  if it has a child, otherwise set root as NULL
    if (root->n==0)
    {
        BTreeNode *tmp = root;
        if (root->leaf)
            root = NULL;
        else
            root = root->C[0];
 
        // Free the old root
        delete tmp;
    }
    return;
}

由于客戶端傳入的是鍵值對，考慮到B_樹的性質以及數據庫的效率，我將作為鍵key的字符串的值hash后作為B_樹中的關鍵字進行存儲，并且仿照關鍵字數組開辟了一個字符串數組存儲值value的值。

因此get和set命令的實現做了如下的改動

int DJBHash(string str)
{
    unsigned int hash = 5381;
 
    for(int i=0;idb->getone(k);
    if(ss==""){
        cout<<"get null"<db.insert(pair(key,value));
    //需要將key進行hash轉成int
    int k=DJBHash(key);
    client->db->insert(k,value);
}