红黑树

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/* * 红黑树 *      1 提供基本的操作集： *          得到最大结点 *          得到最小结点 *          得到后继结点 *          得到前驱结点 *          插入结点 *          删除结点 *      2 可以扩展的操作 *          输出一个有序列 * 本例中没有对重复的元素进行控制 * * NIL 这个思想是从《算法导论》中来的 * 有了 NIL 所有的结点都是内结点，便于算法的操作 * * Successor 算法需要明白两种情况，没有右孩子，有右孩子 * InsertNode 算法只插入叶子 * DeleteNode 算法不删除既有右孩子又有左孩子的结点，这种情况需要转化 * */#include <cstdio>#define RED    1#define BLACK  0struct RBNode {    int key;    int color;    RBNode *pParent;    RBNode *pLChild;    RBNode *pRChild;};class CRBTree {public:    CRBTree() {        NIL = new RBNode;        NIL->color = BLACK;        NIL->pParent = NIL;        NIL->pLChild = NIL;        NIL->pRChild = NIL;        root = NIL;    }    ~CRBTree() {        delete NIL;    }    int GetMaxKey() {        RBNode *node = GetMaxNode(root);        if (node == NIL) return 0;        else return node->key;    }    int GetMinKey() {        RBNode *node = GetMinNode(root);        if (node == NIL) return 0;        else return node->key;    }    void InsertKey(int key) {        RBNode *node = new RBNode;        node->key = key;        node->color = RED;        node->pParent = NIL;        node->pLChild = NIL;        node->pRChild = NIL;        InsertNode(node);    }    void DeleteKey(int key) {        RBNode *node;        while ((node=FindInTree(key)) != NIL) {            node = DeleteNode(node);            if (node != NIL) delete node;        }    }    bool KeyInTree(int key) {        return FindInTree(key) != NIL;    }private:    RBNode *GetMaxNode(RBNode *node) {        RBNode *p = node;        while (p->pRChild != NIL) {            p = p->pRChild;        }        return p;    }    RBNode *GetMinNode(RBNode *node) {        RBNode *p = node;        while (p->pLChild != NIL) {            p = p->pLChild;        }        return p;    }    RBNode *FindInTree(int key) {        RBNode *p = root;        while (p!=NIL && p->key!=key) {            if (p->key < key) p = p->pRChild;            else p = p->pLChild;        }        return  p;    }    RBNode *Successor(RBNode *node) {        if (node->pRChild != NIL) return GetMinNode(node->pRChild);        RBNode *p = node;        RBNode *pParent = p->pParent;        while (pParent!=NIL && pParent->pRChild==p) {            p = pParent;            pParent = p->pParent;        }        return pParent;    }    RBNode *Predecessor(RBNode *node) {        if (node->pLChild != NIL) return GetMaxNode(node->pLChild);        RBNode *p = node;        RBNode *pParent = p->pParent;        while (pParent!=NIL && pParent->pLChild==p) {            p = pParent;            pParent = p->pParent;        }        return pParent;    }    void LeftRotate(RBNode *node) {        // x y 都不是 NIL        RBNode *x = node;        RBNode *y = node->pRChild;        y->pParent = x->pParent;        if (x->pParent == NIL) root = y;        else if (x->pParent->pLChild == x) x->pParent->pLChild = y;        else x->pParent->pRChild = y;        x->pRChild = y->pLChild;        if (x->pRChild != NIL) x->pRChild->pParent = x;        y->pLChild = x;        x->pParent = y;    }    void RightRotate(RBNode *node) {        // x y 都不是 NIL        RBNode *x = node;        RBNode *y = node->pLChild;        y->pParent = x->pParent;        if (x->pParent == NIL) root = y;        else if (x->pParent->pLChild == x) x->pParent->pLChild = y;        else x->pParent->pRChild = y;        x->pLChild = y->pRChild;        if (x->pLChild != NIL) x->pLChild->pParent = x;        y->pRChild = x;        x->pParent = y;    }    void InsertNode(RBNode *node) {        RBNode *p = root;        RBNode *pParent = NIL;        while (p != NIL) {            pParent = p;            if (p->key < node->key) p = p->pRChild;            else p = p->pLChild;        }        node->pParent = pParent;        if (pParent == NIL) root = node;        else if (pParent->key < node->key) pParent->pRChild = node;        else pParent->pLChild = node;        node->pLChild = NIL;        node->pRChild = NIL;        node->color = RED;        InsertFixup(node);    }    void InsertFixup(RBNode *node) {        RBNode *z = node;        while (z->pParent->color==RED) {            if (z->pParent==z->pParent->pParent->pLChild) {                if (z->pParent->pParent->pRChild->color==RED) {                    z->pParent->color =  BLACK;                    z->pParent->pParent->pRChild->color= BLACK;                    z->pParent->pParent->color = RED;                    z = z->pParent->pParent;                }                else {                    if (z->pParent->pRChild == z) {                        z = z->pParent;                        LeftRotate(z);                    }                    z->pParent->color = BLACK;                    z->pParent->pParent->color = RED;                    RightRotate(z->pParent->pParent);                }            }            else {                if (z->pParent->pParent->pLChild->color == RED) {                    z->pParent->color = BLACK;                    z->pParent->pParent->pLChild->color = BLACK;                    z->pParent->pParent->color = RED;                    z = z->pParent->pParent;                }                else {                    if (z->pParent->pLChild == z) {                        z = z->pParent;                        RightRotate(z);                    }                    z->pParent->color = BLACK;                    z->pParent->pParent->color = RED;                    LeftRotate(z->pParent->pParent);                }            }        }        root->color = BLACK;    }    RBNode *DeleteNode(RBNode *node) {        RBNode *p = NIL;        if (node->pLChild==NIL || node->pRChild==NIL) p = node;        else p = Successor(node);        RBNode *pChild = NIL;        if (p->pLChild != NIL)  pChild= p->pLChild;        else pChild = p->pRChild;        pChild->pParent = p->pParent;        if (p->pParent == NIL) root = NIL;        else if (p->pParent->pLChild == p) p->pParent->pLChild = pChild;        else p->pParent->pRChild = pChild;        if (p != node) {            int tmp = node->key;            node->key = p->key;            p->key = tmp;        }        if (p->color == BLACK) DeleteFixup(pChild);        if (pChild == NIL) pChild->pParent = NIL;        return p;    }    void DeleteFixup(RBNode *x) {        RBNode *w = NIL;        while (x != root && x->color==BLACK) {            if (x->pParent->pLChild == x) {                w = x->pParent->pRChild;                if (w->color == RED) {                    w->color = BLACK;                    x->pParent->color = RED;                    LeftRotate(x->pParent);                    w = x->pParent->pRChild;                }                if (w->pLChild->color==BLACK && w->pRChild->color==BLACK) {                    w->color = RED;                    x = x->pParent;                }                else {                    if (w->pRChild->color == BLACK) {                        w->pLChild->color = BLACK;                        w->color = RED;                        RightRotate(w);                        w = w->pParent;                    }                    w->color = x->pParent->color;                    x->pParent->color = BLACK;                    w->pRChild->color = BLACK;                    LeftRotate(x->pParent);                    x = root;                }            }            else {                w = x->pParent->pLChild;                if (w->color == RED) {                    w->color = BLACK;                    x->pParent->color = RED;                    RightRotate(x->pParent);                    w = x->pParent->pLChild;                }                if (w->pLChild->color==BLACK && w->pRChild->color==BLACK) {                    w->color = RED;                    x = x->pParent;                }                else {                    if (w->pLChild == BLACK) {                        w->pRChild->color = BLACK;                        w->color = RED;                        LeftRotate(w);                        w = w->pParent;                    }                    w->color = x->pParent->color;                    x->pParent->color = BLACK;                    w->pLChild->color = BLACK;                    RightRotate(x->pParent);                    x = root;                }            }        }        x->color = BLACK;    }private:    RBNode *NIL;    RBNode *root;};int main() {    int a[10] = {2, 5, 7, 8, 1, 9 ,10, 3, 4, 6};    CRBTree btree;    for (int i=0; i<10; ++i)        btree.InsertKey(a[i]);    printf("%d %d\n", btree.GetMinKey(), btree.GetMaxKey());    btree.DeleteKey(1);    btree.DeleteKey(10);    printf("%d %d\n", btree.GetMinKey(), btree.GetMaxKey());    btree.DeleteKey(5);    if (btree.KeyInTree(5))        puts("have found 5 in btree");    else        puts("can not find 5 in btree");    if (btree.KeyInTree(4))        puts("have found 4 in btree");    else        puts("can not find 4 in btree");    return 0;}
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