#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; }