#include <stdio.h>#include <string.h>#include <stdlib.h>typedef struct red_black_tree_type *tree;enum color_enum {color_red,color_black};struct tree_node {void *key;enum color_enum color;struct tree_node *parent;struct tree_node *left;struct tree_node *right;};struct red_black_tree_type {int (*comp) (const void *, const void *);struct tree_node *root;struct tree_node *nil;};void tree_node_ini(struct tree_node *p, void *key){p->key = key;p->parent = NULL;p->left = NULL;p->right = NULL;p->color = color_black;}void tree_left_rotate(tree t, struct tree_node *x){struct tree_node *y = x->right;x->right = y->left;if (y->left != t->nil) {y->left->parent = x;}y->parent = x->parent;if (x->parent == t->nil) {t->root = y;} else {if (x == x->parent->left) {x->parent->left = y;} else {x->parent->right = y;}}y->left = x;x->parent = y;}void tree_right_rotate(tree t, struct tree_node *x){struct tree_node *y = x->left;x->left = y->right;if (y->right != t->nil) {y->right->parent = x;}y->parent = x->parent;if (x->parent == t->nil) {t->root = y;} else {if (x == x->parent->left) {x->parent->left = y;} else {x->parent->right = y;}}y->right = x;x->parent = y;}tree tree_create(int (*comp) (const void *, const void *)){tree t = malloc(sizeof(struct red_black_tree_type));t->comp = comp;t->nil = malloc(sizeof(struct tree_node));tree_node_ini(t->nil, NULL);t->root = t->nil;return t;}void tree_destroy_all_node(tree t, struct tree_node *x, void (*free_key) (void *)){if (x != t->nil) {tree_destroy_all_node(t, x->left, free_key);tree_destroy_all_node(t, x->right, free_key);free_key(x->key);free(x);}}void tree_destroy(tree t, void (*free_key) (void *)){tree_destroy_all_node(t, t->root, free_key);free(t->nil);free(t);}void tree_inorder_walk(tree t, struct tree_node *x, void (*handle) (const void *)){if (x != t->nil) {tree_inorder_walk(t, x->left, handle);handle(x->key);printf(" ");tree_inorder_walk(t, x->right, handle);}}struct tree_node *tree_search(tree t, struct tree_node *x, void *key){if (x == t->nil || t->comp(key, x->key) == 0) {return x;}if (t->comp(key, x->key) < 0) {return tree_search(t, x->left, key);} else {return tree_search(t, x->right, key);}}void tree_count_leaf(tree t, struct tree_node *x, struct tree_node *leaf_array[], int *num){if (x != t->nil) {if (x->left == t->nil && x->right == t->nil) {leaf_array[++*num] = x;}tree_count_leaf(t, x->left, leaf_array, num);tree_count_leaf(t, x->right, leaf_array, num);}}void tree_black_height(tree t, struct tree_node *x, struct tree_node *leaf_node, int *black_height){if (x->color == color_black) {++*black_height;}if (x == t->nil) {return;}if (t->comp(leaf_node->key , x->key)<0) {tree_black_height(t, x->left, leaf_node, black_height);} else {tree_black_height(t, x->right, leaf_node, black_height);}}struct tree_node *tree_minimum(tree t, struct tree_node *x){while (x != t->nil && x->left != t->nil) {x = x->left;}return x;}struct tree_node *tree_successor(tree t, struct tree_node *x){if (x->right != t->nil) {return tree_minimum(t, x->right);}struct tree_node *y = x->parent;while (y != t->nil && x == y->right) {x = y;y = y->parent;}return y;}void tree_insert_fixup(tree t, struct tree_node *z){struct tree_node *y = t->nil;while (z->parent->color == color_red) {if (z->parent == z->parent->parent->left) {y = z->parent->parent->right;//情况1:z的叔叔y是红色的if (y->color == color_red) {z->parent->color = color_black;y->color = color_black;z->parent->parent->color = color_red;z = z->parent->parent;} else {//情况2:z的叔叔y是黑色的,z是右孩子if (z == z->parent->right) {z = z->parent;tree_left_rotate(t, z);}//情况3:z的叔叔y是黑色的,z是左孩子z->parent->color = color_black;z->parent->parent->color = color_red;tree_right_rotate(t, z->parent->parent);}} else {y = z->parent->parent->left;if (y->color == color_red) {z->parent->color = color_black;y->color = color_black;z->parent->parent->color = color_red;z = z->parent->parent;} else {if (z == z->parent->left) {z = z->parent;tree_right_rotate(t, z);}z->parent->color = color_black;z->parent->parent->color = color_red;tree_left_rotate(t, z->parent->parent);}}}t->root->color = color_black;}void tree_insert(tree t, struct tree_node *z){struct tree_node *y = t->nil;struct tree_node *x = t->root;while (x != t->nil) {y = x;if (t->comp(z->key, x->key) < 0) {x = x->left;} else {x = x->right;}}z->parent = y;if (y == t->nil) {t->root = z;} else {if (t->comp(z->key, y->key) < 0) {y->left = z;} else {y->right = z;}}z->left = t->nil;z->right = t->nil;z->color = color_red;tree_insert_fixup(t, z);}void tree_delete_fixup(tree t, struct tree_node *x){struct tree_node *w = t->nil;while (x != t->root && x->color == color_black) {if (x == x->parent->left) {w = x->parent->right;//情况1:x的兄弟w是红色的if (w->color == color_red) {w->color = color_black;x->parent->color = color_red;tree_left_rotate(t, x->parent);w = x->parent->right;} else {//情况2:x的兄弟w是黑色的,而且w的两个孩子都是黑色的if (w->left->color == color_black && w->right->color == color_black) {w->color = color_red;x = x->parent;} else {//情况3:x的兄弟w是黑色的,w的左孩子是红的，右孩子是黑的if (w->right->color == color_black) {w->left->color = color_black;w->color = color_red;tree_right_rotate(t, w);w = x->parent->right;}//情况4:x的兄弟w是黑色的,而且w的右孩子是红色的w->color = x->parent->color;x->parent->color = color_black;w->right->color = color_black;tree_left_rotate(t, x->parent);x = t->root;}}} else {w = x->parent->left;if (w->color == color_red) {w->color = color_black;x->parent->color = color_red;tree_right_rotate(t, x->parent);w = x->parent->left;} else {if (w->right->color == color_black && w->left->color == color_black) {w->color = color_red;x = x->parent;} else {if (w->left->color == color_black) {w->right->color = color_black;w->color = color_red;tree_left_rotate(t, w);w = x->parent->left;}w->color = x->parent->color;x->parent->color = color_black;w->left->color = color_black;tree_right_rotate(t, x->parent);x = t->root;}}}}x->color = color_black;}void swap(void *a, void *b, size_t elem_size){if (a == NULL || b == NULL || a == b)return;char temp[elem_size];/*变长数组 */memcpy(temp, a, elem_size);memcpy(a, b, elem_size);memcpy(b, temp, elem_size);}struct tree_node *tree_delete(tree t, struct tree_node *z){struct tree_node *y;struct tree_node *x;if (z->left == t->nil || z->right == t->nil) {y = z;} else {y = tree_successor(t, z);}if (y->left != t->nil) {x = y->left;} else {x = y->right;}x->parent = y->parent;if (y->parent == t->nil) {t->root = x;} else {if (y == y->parent->left) {y->parent->left = x;} else {y->parent->right = x;}}if (y != z) {/*要删除的结点y是z的后继,交换z和y结点的内容 */swap(&z->key, &y->key, sizeof(void *));}if (y->color == color_black) {tree_delete_fixup(t, x);}return y;}int cmp_int(const void *p1, const void *p2){const int *pa = p1;const int *pb = p2;if (*pa < *pb)return -1;if (*pa == *pb)return 0;return 1;}void print_key(const void *key){const int *p = key;printf("%-2d", *p);}int main(){tree t = tree_create(cmp_int);for (int i = 0; i < 10; i++) {struct tree_node *node = malloc(sizeof(struct tree_node));int *ip = malloc(sizeof(int));*ip = i;tree_node_ini(node, ip);tree_insert(t, node);}printf("中序遍历结果:\n");tree_inorder_walk(t, t->root, print_key);printf("\n");int k = 0;struct tree_node *result = tree_search(t, t->root, &k);printf("查找关键字:%d的结果:%s\n", k, result != t->nil ? "成功" : "失败");struct tree_node *del_node = tree_delete(t, result);free(del_node->key);free(del_node);result = tree_search(t, t->root, &k);printf("删除关键字:%d的结果:%s\n", k, result == t->nil ? "成功" : "失败");printf("查看黑高度:\n");struct tree_node *left_array[100];int num = -1;/*统计叶子结点 */tree_count_leaf(t, t->root, left_array, &num);for (int i = 0; i < num; i++) {/*黑高度不包括自身,所以初始值为-1 */int black_height = -1;tree_black_height(t, t->root, left_array[i], &black_height);/*测试黑高度，从根到叶的路径上，黑结点数是一样的 */printf("根到叶子:%d的黑高度:%d\n", *(int *)left_array[i]->key, black_height);}printf("中序遍历结果:\n");tree_inorder_walk(t, t->root, print_key);printf("\n");/*遍历树，释放结点的key */tree_destroy(t, free);return 0;}
