实现随机二进制搜索树的C ++程序

2024-05-09 18:14:03 13

二进制搜索树是一个排序的二进制树，其中所有节点都具有以下几个属性-

节点的右子树的键大于其父节点的键。

节点的左子树的键小于或等于其父节点的键。

每个节点不应有两个以上的子节点。

这是一个实现随机二叉树的C++程序。

算法

Begin
   class BST to declare following functions:
      search() = To search an item in BST.
      initialize temp = root;
   while(temp != NULL)
      Increase depth
   if(temp->info == data)
      print Data and depth
   else if(temp->info >data)
      temp = temp->l;
   else
      temp = temp->r;
   insert() = To insert items in the tree:
      If tree is empty insert data as root.
      If tree is not empty
         data<root
         Insert data as left child.
      Else
         Insert data as right child.
         del() = To delete an item from tree.
         casea() = Called from del() if l = r = null.
         caseb() = Called from del() if l != null, r = null.
         caseb() = Called from del() if l = null, r != null.
         casec() = Called from del() if l != null, r != null.
         inorder() to traverse the node as inorder as:
            left – root – right.
         preorder() to traverse the node as preorder as:
            root – Left – right.
         postorder() to traverse the node as preorder as:
            left – right – root
End

范例程式码

# include <iostream>
# include <cstdlib>
using namespace std;
struct nod//node declaration {
   int info;
   struct nod *l;
   struct nod *r;
}*r;

class BST {
   public:
      //函数声明
      void search(nod *, int);
      void find(int, nod **, nod **);
      void insert(nod *, nod *);
      void del(int);
      void casea(nod *,nod *);
      void caseb(nod *,nod *);
      void casec(nod *,nod *);
      void preorder(nod *);
      void inorder(nod *);
      void postorder(nod *);
      void show(nod *, int);
   BST() {
      r = NULL;
   }
};

void BST::find(int i, nod **par, nod **loc)//find the position of element {
   nod *ptr, *ptrsave;
   if (r == NULL) {
      *loc = NULL;
      *par = NULL;
      return;
   }
   if (i == r->info) {
      *loc = r;
      *par = NULL;
      return;
   } if (i < r->info)
      ptr = r->l;
   else
      ptr = r->r;
      ptrsave = r;
   while (ptr != NULL) {
      if (i == ptr->info) {
         *loc = ptr;
         *par = ptrsave;
         return;
      }
      ptrsave = ptr;
      if (i < ptr->info)
         ptr = ptr->l;
      else
         ptr = ptr->r;
   }
   *loc = NULL;
   *par = ptrsave;
}

void BST::search(nod *root, int data) {
   int depth = 0;
   nod *temp = new nod;
   temp = root;
   while(temp != NULL) {
      depth++;
      if(temp->info == data) {
         cout<<"\nData found at depth: "<<depth<<endl;
         return;
      } else if(temp->info >data)
         temp = temp->l;
      else
         temp = temp->r;
   }
   cout<<"\n Data not found"<<endl;
   return;
}

void BST::insert(nod *tree, nod *newnode) {
   if (r == NULL) {
      r = new nod;
      r->info = newnode->info;
      r->l = NULL;
      r->r = NULL;
      cout<<"Root Node is Added"<<endl;
      return;
   }
   if (tree->info == newnode->info) {
      cout<<"Element already in the tree"<<endl;
      return;
   }
   if (tree->info >newnode->info) {
      if (tree->l != NULL) {
         insert(tree->l, newnode);
      } else {
         tree->l= newnode;
         (tree->l)->l = NULL;
         (tree->l)->r= NULL;
         cout<<"Node Added to Left"<<endl;
         return;
      }
   } else {
      if (tree->r != NULL) {
         insert(tree->r, newnode);
      } else {
         tree->r = newnode;
         (tree->r)->l= NULL;
         (tree->r)->r = NULL;
         cout<<"Node Added to Right"<<endl;
         return;
      }
   }
}

void BST::del(int i) {
   nod *par, *loc;
   if (r == NULL) {
      cout<<"Tree empty"<<endl;
      return;
   }
   find(i, &par, &loc);
   if (loc == NULL) {
      cout<<"Item not present in tree"<<endl;
      return;
   }
   if(loc->l == NULL && loc->r == NULL) {
      casea(par, loc);
      cout<<"item deleted"<<endl;
   }
   if (loc->l!= NULL && loc->r == NULL) {
      caseb(par, loc);
      cout<<"item deleted"<<endl;
   }
   if (loc->l== NULL && loc->r != NULL) {
      caseb(par, loc);
      cout<<"item deleted"<<endl;
   }
   if (loc->l != NULL && loc->r != NULL) {
      casec(par, loc);
      cout<<"item deleted"<<endl;
   }
   free(loc);
}

void BST::casea(nod *par, nod *loc ) {
   if (par == NULL) {
      r = NULL;
   } else {
      if (loc == par->l)
         par->l = NULL;
      else
         par->r = NULL;
   }
}

void BST::caseb(nod *par, nod *loc) {
   nod *child;
   if (loc->l!= NULL)
      child = loc->l;
   else
      child = loc->r;
   if (par == NULL) {
      r = child;
   } else {
      if (loc == par->l)
         par->l = child;
      else
         par->r = child;
   }
}

void BST::casec(nod *par, nod *loc) {
   nod *ptr, *ptrsave, *suc, *parsuc;
   ptrsave = loc;
   ptr = loc->r;
   while (ptr->l!= NULL) {
      ptrsave = ptr;
      ptr = ptr->l;
   }
   suc = ptr;
   parsuc = ptrsave;
   if (suc->l == NULL && suc->r == NULL)
      casea(parsuc, suc);
   else
      caseb(parsuc, suc);
   if (par == NULL) {
      r = suc;
   } else {
      if (loc == par->l)
         par->l = suc;
      else
         par->r= suc;
   }
   suc->l = loc->l;
   suc->r= loc->r;
}

void BST::preorder(nod *ptr) {
   if (r == NULL) {
      cout<<"Tree is empty"<<endl;
      return;
   }
   if (ptr != NULL) {
      cout<<ptr->info<<" ";
      preorder(ptr->l);
      preorder(ptr->r);
   }
}

void BST::inorder(nod *ptr) {
   if (r == NULL) {
      cout<<"Tree is empty"<<endl;
      return;
   }
   if (ptr != NULL) {
      inorder(ptr->l);
      cout<<ptr->info<<" ";
      inorder(ptr->r);
   }
}

void BST::postorder(nod *ptr) {
   if (r == NULL) {
      cout<<"Tree is empty"<<endl;
      return;
   }
   if (ptr != NULL) {
      postorder(ptr->l);
      postorder(ptr->r);
      cout<<ptr->info<<" ";
   }
}

void BST::show(nod *ptr, int level) {
   int i;
   if (ptr != NULL) {
      show(ptr->r, level+1);
      cout<<endl;
      if (ptr == r)
         cout<<"Root->: ";
      else {
         for (i = 0;i < level;i++)
         cout<<" ";
      }
      cout<<ptr->info;
      show(ptr->l, level+1);
   }
}

int main() {
   int c, n,item;
   BST bst;
   nod *t;
   while (1) {
      cout<<"1.Insert Element "<<endl;
      cout<<"2.Delete Element "<<endl;
      cout<<"3.Search Element"<<endl;
      cout<<"4.Inorder Traversal"<<endl;
      cout<<"5.Preorder Traversal"<<endl;
      cout<<"6.Postorder Traversal"<<endl;
      cout<<"7.Display the tree"<<endl;
      cout<<"8.Quit"<<endl;
      cout<<"Enter your choice : ";
      cin>>c;
      switch©//perform switch operation {
         case 1:
            t = new nod;
            cout<<"Enter the number to be inserted : ";
            cin>>t->info;
            bst.insert(r, t);
         break;
         case 2:
            if (r == NULL) {
               cout<<"Tree is empty, nothing to delete"<<endl;
               continue;
            }
            cout<<"Enter the number to be deleted : ";
            cin>>n;
            bst.del(n);
         break;
         case 3:
            cout<<"Search:"<<endl;
            cin>>item;
            bst.search(r,item);
         break;
         case 4:
            cout<<"BST的有序遍历："<<endl;
            bst.inorder(r);
            cout<<endl;
         break;
         case 5:
            cout<<"BST的预遍历："<<endl;
            bst.preorder(r);
            cout<<endl;
         break;
         case 6:
            cout<<"BST的事后遍历："<<endl;
            bst.postorder(r);
            cout<<endl;
         break;
         case 7:
            cout<<"显示BST："<<endl;
            bst.show(r,1);
            cout<<endl;
         break;
         case 8:
            exit(1);
         default:
            cout<<"Wrong choice"<<endl;
      }
   }
}

输出结果

1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 1
Enter the number to be inserted : 6
Root Node is Added
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 1
Enter the number to be inserted : 7
Node Added to Right
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 1
Enter the number to be inserted : 5
Node Added to Left
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 1
Enter the number to be inserted : 4
Node Added to Left
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 3
Search:
7

Data found at depth: 2
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 3
Search:
1

Data not found
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 4
BST的有序遍历：
4 5 6 7
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 5
BST的预遍历：
6 5 4 7
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 6
BST的事后遍历：
4 5 7 6
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 7
显示BST：

7
Root->: 6
5
4
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 2
Enter the number to be deleted : 1
Item not present in tree
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 5
BST的预遍历：
6 5 4 7
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 2
Enter the number to be deleted : 5
item deleted
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 7
显示BST：

7
Root->: 6
4
1.Insert Element
2.Delete Element
3.Search Element
4.Inorder Traversal
5.Preorder Traversal
6.Postorder Traversal
7.Display the tree
8.Quit
Enter your choice : 8

实现随机二进制搜索树的C ++程序

算法

范例程式码

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