算法导论：c++实现红黑树

数据结构

性质

这里定义一个结构体保存颜色

enum colorRB{    black = 0,    red,};struct TreeNode_RB {    int val;    colorRB color;    TreeNode_RB *left;    TreeNode_RB *right;    TreeNode_RB *parent;    TreeNode_RB(int x, colorRB c) : val(x), left(NULL), right(NULL), parent(NULL),color(c) {}};

旋转

左旋

/*红黑树左旋*/void left_roate(TreeNode_RB *root,TreeNode_RB *x) //x称为y的左子树，y的左子树成为x的右子树{    TreeNode_RB *y = x->right;  //右子树左旋    x->right = y->left;    if (y->left != NULL) {        y->left->parent = x;    //y左子树非空    }    y->parent = x->parent;  //置y的父节点    if (x->parent == NULL) {        root = y;    }    else if(x->parent->left==x)    {        x->parent->left = y;    }    else    {        x->parent->right = y;    }    y->left = x;    //y成为x左子树    x->parent = y;  //y称为x的父节点}

右旋

void right_roate(TreeNode_RB *root, TreeNode_RB *y) //y成为x的右子树，x的右子树成为y的左子树{    TreeNode_RB *x = y->left;   //左子树右旋    y->left = x->right;    if (x->right != NULL) {        x->right->parent = y;   //x右子树非空    }    x->parent = y->parent;  //置x的父节点    if (y->parent == NULL) {        root = x;    }    else if (y->parent->left == y)    {        y->parent->left = x;    }    else    {        y->parent->right = x;    }    x->right = y;   //x成为y右子树    y->parent = x;  //x成为y的父节点}

测试

int main(){    TreeNode_RB *r1 = new TreeNode_RB(15,black);    TreeNode_RB *r2 = new TreeNode_RB(6,red);    TreeNode_RB *r3 = new TreeNode_RB(18,black);    TreeNode_RB *r4 = new TreeNode_RB(3,black);    TreeNode_RB *r5 = new TreeNode_RB(7,black);    r1->left = r2;    r1->right = r3;    r2->parent = r1;    r2->left = r4;    r2->right = r5;    r3->parent = r1;    r4->parent = r2;    r5->parent = r2;    right_roate(r1, r2);}

插入

插入就比较复杂了，涉及红黑树性质的调整，插入节点一致置颜色为红色，后再调整

void RB_insert_fixup(TreeNode_RB *root, TreeNode_RB *z) {    while (z->parent->color==red)    {        if (z->parent->parent->left==z->parent) //z的父节点是左子树        {            TreeNode_RB *y = z->parent->parent->right;  //叔叔节点            if (y->color == red) //叔叔节点是红色，case 1            {                z->color = black;   //重新着色                z->parent->color = black;                z->parent->parent->color = red;                z = z->parent->parent;  //指针上移            }            else if(z->parent->right==z)// 叔叔节点是黑色，且z是右子树，case 2            {                z = z->parent;                left_roate(root, z);    //左旋            }            // 叔叔节点是黑色，且z是左子树，case 3            z->parent->color = black;            z->parent->parent->color = red;            right_roate(root, z->parent->parent);        }        else        {            TreeNode_RB *y = z->parent->parent->left;   //叔叔节点            if (y->color == red) //叔叔节点是红色，case 1            {                z->color = black;   //重新着色                z->parent->color = black;                z->parent->parent->color = red;                z = z->parent->parent;  //指针上移            }            else if (z->parent->right == z)// 叔叔节点是黑色，且z是右子树，case 2            {                z = z->parent;                right_roate(root, z);   //左旋            }            // 叔叔节点是黑色，且z是左子树，case 3            z->parent->color = black;            z->parent->parent->color = red;            left_roate(root, z->parent->parent);        }    }}/*红黑树插入*/void RB_insert(TreeNode_RB *root, TreeNode_RB *z) {    TreeNode_RB *y = NULL;  //y标记node的父指针    TreeNode_RB *x = root;  //x用于向下探测    z->color = red; //将待插入节点颜色置为红色    while (x != NULL)    {        y = x;        if (root->val < x->val) {            x = x->left;        }        else        {            x = x->right;        }    }    z->parent = y;    if (y == NULL) {        root = z;    }    else if (z->val<y->val)    {        y->left = z;    }    else    {        y->right = z;    }}