算法（5）—— 二叉查找树

这个几天前写过一遍，现在写就发现又差点很快忘掉，常复习，顺便通过这段时间的学习，把常见的树结构都搞懂。

1. 头文件

#ifndef  TREE_H
#define  TREE_H

typedef int ElementType;

struct TreeNode;
typedef struct TreeNode *Position;
typedef struct TreeNode *SearchTree;

SearchTree MakeEmpty( SearchTree T );
Position Find( ElementType X, SearchTree T );
Position FindMin( SearchTree T );
Position FindMax( SearchTree T );
SearchTree Insert( ElementType X, SearchTree T );
SearchTree Delete( ElementType X, SearchTree T );
ElementType Retrieve( Position P );
void PrintElement(ElementType X);
void PrintTree(SearchTree T);

#endif  /* TREE_H */

2.实现

#include "tree.h"
#include <stdlib.h>
#include "fatal.h"
#include <stdio.h>


struct TreeNode  {
  ElementType Element;
  SearchTree  Left;
  SearchTree  Right;
};

SearchTree  MakeEmpty( SearchTree T )  {
  if( T != NULL )
    {
      MakeEmpty( T->Left );
      MakeEmpty( T->Right );
      free( T );
    }
  return NULL;
}

Position   Find( ElementType X, SearchTree T )   {
  if( T == NULL )
    return NULL;
  if  ( X < T->Element )
         return Find( X, T->Left );
  else if( X > T->Element )
      return Find( X, T->Right );
  else
      return T;
}

Position   FindMin( SearchTree T )  {
  if( T == NULL )
    return NULL;
  else if( T->Left == NULL )
      return T;
  else
      return FindMin( T->Left );
}

Position  FindMax( SearchTree T )    {
  if( T != NULL )
    while( T->Right != NULL )
      T = T->Right;

  return T;
}

SearchTree Insert( ElementType X, SearchTree T )  {
  if( T == NULL )  {
    /* Create and return a one-node tree */
    T = malloc( sizeof( struct TreeNode ) );
    if( T == NULL )
      FatalError( "Out of space!!!" );
    else  {
      T->Element = X;
      T->Left = T->Right = NULL;
    }
  }
  else if( X < T->Element )
      T->Left = Insert( X, T->Left );
  else if( X > T->Element )
    T->Right = Insert( X, T->Right );
  /* Else X is in the tree already; we'll do nothing */

  return T;  /* Do not forget this line!! */
}

SearchTree   Delete( ElementType X, SearchTree T )  {
  Position TmpCell;

  if( T == NULL )
    Error( "Element not found" );
  else  if( X < T->Element )  /* Go left */
      T->Left = Delete( X, T->Left );
  else  if( X > T->Element )  /* Go right */
            T->Right = Delete( X, T->Right );
    else     if ( T->Left && T->Right ) /* Two children */  {
        /* Found element to be deleted */
      /* Replace with smallest in right subtree */
      TmpCell = FindMin( T->Right );
      T->Element = TmpCell->Element;
      T->Right = Delete( T->Element, T->Right );
    }
    else  /* One or zero children */ {
      TmpCell = T;
      if( T->Left == NULL ) /* Also handles 0 children */
        T = T->Right;
      else if( T->Right == NULL )
        T = T->Left;
      free( TmpCell );
    }

  return T;
}

ElementType Retrieve( Position P )  {
  return P->Element;
}

void PrintElement(ElementType X)  {
  printf("%d
",X);
}

void PrintTree (SearchTree T)  {
  if (T != NULL)  {
    PrintTree(T->Left);
    PrintElement(T->Element);
    PrintTree(T->Right);
  }
}

3.测试

#include "tree.c"
#include <stdio.h>

int main(int argc,char **argv )    {
  SearchTree T;
  Position P;
  int i;

  T = MakeEmpty  ( NULL );
  for( i = 0; i < 50; i += 5)
    T = Insert  ( i, T );
  PrintTree  (T);
    printf  ("
");

    for  (i = 0;i < 50; i += 10)
    T = Delete (i,T);
    PrintTree  (T);
  printf ("
");
  printf ("Min is %d,Max is %d. 
",Retrieve(FindMin(T)),Retrieve((FindMax(T))));
  
    return 0;
}