關於紅黑樹的c語言實現代碼。

根據之前一節，描述了紅黑樹原理，這次把相關代碼進行實現一下。
原理如下：

https://blog.csdn.net/jenie/article/details/105871388

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define RED             1
#define BLACK        2

typedef int KEY_TYPE;

typedef struct _rbtree_node {
   unsigned char color;
   struct _rbtree_node *right;
   struct _rbtree_node *left;
   struct _rbtree_node *parent;
   KEY_TYPE key;
   void *value;
} rbtree_node;

typedef struct _rbtree {
   rbtree_node *root;
   rbtree_node *nil;
} rbtree;

rbtree_node *rbtree_mini(rbtree *T, rbtree_node *x) {
   while (x->left != T->nil) {
      x = x->left;
   }
   return x;
}

rbtree_node *rbtree_maxi(rbtree *T, rbtree_node *x) {
   while (x->right != T->nil) {
      x = x->right;
   }
   return x;
}

rbtree_node *rbtree_successor(rbtree *T, rbtree_node *x) {
   rbtree_node *y = x->parent;

   if (x->right != T->nil) {
      return rbtree_mini(T, x->right);
   }

   while ((y != T->nil) && (x == y->right)) {
      x = y;
      y = y->parent;
   }
   return y;
}


void rbtree_left_rotate(rbtree *T, rbtree_node *x) {

   rbtree_node *y = x->right;  // x  --> y  ,  y --> x,   right --> left,  left --> right

   x->right = y->left; //1 1
   if (y->left != T->nil) { //1 2
      y->left->parent = x;
   }

   y->parent = x->parent; //1 3
   if (x->parent == T->nil) { //1 4
      T->root = y;
   } else if (x == x->parent->left) {
      x->parent->left = y;
   } else {
      x->parent->right = y;
   }

   y->left = x; //1 5
   x->parent = y; //1 6
}


void rbtree_right_rotate(rbtree *T, rbtree_node *y) {

   rbtree_node *x = y->left;

   y->left = x->right;
   if (x->right != T->nil) {
      x->right->parent = y;
   }

   x->parent = y->parent;
   if (y->parent == T->nil) {
      T->root = x;
   } else if (y == y->parent->right) {
      y->parent->right = x;
   } else {
      y->parent->left = x;
   }

   x->right = y;
   y->parent = x;
}

void rbtree_insert_fixup(rbtree *T, rbtree_node *z) {
    //z--->RED 當前永遠是紅色的
   while (z->parent->color == RED) { //z ---> RED
      if (z->parent == z->parent->parent->left) {
         rbtree_node *y = z->parent->parent->right;
         if (y->color == RED) {   //叔父節點是紅色的,不需要旋轉,他的黑高一樣的，通過變色就能保證黑高相同
            z->parent->color = BLACK;
            y->color = BLACK;
            z->parent->parent->color = RED;

            z = z->parent->parent; //z --> RED
         } else {

            if (z == z->parent->right) {
               z = z->parent;
               rbtree_left_rotate(T, z);
            }

            z->parent->color = BLACK;
            z->parent->parent->color = RED;
            rbtree_right_rotate(T, z->parent->parent);
         }
      }else {
         rbtree_node *y = z->parent->parent->left;
         if (y->color == RED) {
            z->parent->color = BLACK;
            y->color = BLACK;
            z->parent->parent->color = RED;

            z = z->parent->parent; //z --> RED
         } else {
            if (z == z->parent->left) {
               z = z->parent;
               rbtree_right_rotate(T, z);
            }

            z->parent->color = BLACK;
            z->parent->parent->color = RED;
            rbtree_left_rotate(T, z->parent->parent);
         }
      }
      
   }

   T->root->color = BLACK;
}


void rbtree_insert(rbtree *T, rbtree_node *z) {

   rbtree_node *y = T->nil;
   rbtree_node *x = T->root;

   while (x != T->nil) {
      y = x;
      if (z->key < x->key) {
         x = x->left;
      } else if (z->key > x->key) {
         x = x->right;
      } else { //Exist
         return ;
      }
   }

   z->parent = y;
   if (y == T->nil) {
      T->root = z;
   } else if (z->key < y->key) {
      y->left = z;
   } else {
      y->right = z;
   }

   z->left = T->nil;
   z->right = T->nil;
   z->color = RED;//插入紅節點，不會影響黑高

   rbtree_insert_fixup(T, z);  //調整
}

void rbtree_delete_fixup(rbtree *T, rbtree_node *x) {

   while ((x != T->root) && (x->color == BLACK)) {
      if (x == x->parent->left) {

         rbtree_node *w= x->parent->right;
         if (w->color == RED) {
            w->color = BLACK;
            x->parent->color = RED;

            rbtree_left_rotate(T, x->parent);
            w = x->parent->right;
         }

         if ((w->left->color == BLACK) && (w->right->color == BLACK)) {
            w->color = RED;
            x = x->parent;
         } else {

            if (w->right->color == BLACK) {
               w->left->color = BLACK;
               w->color = RED;
               rbtree_right_rotate(T, w);
               w = x->parent->right;
            }

            w->color = x->parent->color;
            x->parent->color = BLACK;
            w->right->color = BLACK;
            rbtree_left_rotate(T, x->parent);

            x = T->root;
         }

      } else {

         rbtree_node *w = x->parent->left;
         if (w->color == RED) {
            w->color = BLACK;
            x->parent->color = RED;
            rbtree_right_rotate(T, x->parent);
            w = x->parent->left;
         }

         if ((w->left->color == BLACK) && (w->right->color == BLACK)) {
            w->color = RED;
            x = x->parent;
         } else {

            if (w->left->color == BLACK) {
               w->right->color = BLACK;
               w->color = RED;
               rbtree_left_rotate(T, w);
               w = x->parent->left;
            }

            w->color = x->parent->color;
            x->parent->color = BLACK;
            w->left->color = BLACK;
            rbtree_right_rotate(T, x->parent);

            x = T->root;
         }

      }
   }

   x->color = BLACK;
}

rbtree_node *rbtree_delete(rbtree *T, rbtree_node *z) {

   rbtree_node *y = T->nil;
   rbtree_node *x = T->nil;

   if ((z->left == T->nil) || (z->right == T->nil)) {
      y = z;
   } else {
      y = rbtree_successor(T, z);
   }

   if (y->left != T->nil) {
      x = y->left;
   } else if (y->right != T->nil) {
      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) {
      z->key = y->key;
      z->value = y->value;
   }

   if (y->color == BLACK) {   //只要等於黑色的纔要調整，因爲影響了黑高，否則不需要調整
      rbtree_delete_fixup(T, x);
   }

   return y;
}

rbtree_node *rbtree_search(rbtree *T, KEY_TYPE key) {

   rbtree_node *node = T->root;
   while (node != T->nil) {
      if (key < node->key) {
         node = node->left;
      } else if (key > node->key) {
         node = node->right;
      } else {
         return node;
      }  
   }
   return T->nil;
}


void rbtree_traversal(rbtree *T, rbtree_node *node) {
   if (node != T->nil) {
      rbtree_traversal(T, node->left);
      printf("key:%d, color:%d\n", node->key, node->color);
      rbtree_traversal(T, node->right);
   }
}

int main() {

   int keyArray[20] = {24,25,13,35,23, 26,67,47,38,98, 20,19,17,49,12, 21,9,18,14,15};

   rbtree *T = (rbtree *)malloc(sizeof(rbtree));
   if (T == NULL) {
      printf("malloc failed\n");
      return -1;
   }
   
   T->nil = (rbtree_node*)malloc(sizeof(rbtree_node));
   T->nil->color = BLACK;
   T->root = T->nil;

   rbtree_node *node = T->nil;
   int i = 0;
   for (i = 0;i < 20;i ++) {
      node = (rbtree_node*)malloc(sizeof(rbtree_node));
      node->key = keyArray[i];
      node->value = NULL;

      rbtree_insert(T, node);
      
   }

   rbtree_traversal(T, T->root);
   printf("----------------------------------------\n");

   for (i = 0;i < 20;i ++) {

      rbtree_node *node = rbtree_search(T, keyArray[i]);
      rbtree_node *cur = rbtree_delete(T, node);
      free(cur);

      rbtree_traversal(T, T->root);
      printf("----------------------------------------\n");
   }
   

   
}