实用算法实现-第 5 篇二分查找树

5.1    二分查找树算法

《算法导论》中，二分查找树的伪代码如下：

ITERATIVE-TREE-SEARCH(x,k)

1  while x ≠ NIL and k ≠ key[x]

2      do if k < key[x]

3            thenx ← left[x]

4            elsex ← right[x]

5  return x

TREE-INSERT(T,z)

1  y ← NIL

2  x ← root[T]

3  while x ≠ NIL

4       do y ← x

5          ifkey[z] < key[x]

6             thenx ← left[x]

7             elsex ← right[x]

8  p[z] ← y

9  if y = NIL

10      thenroot[T] ← z

11      else if key[z] < key[y]

12              thenleft[y] ← z

13              elseright[y] ← z

5.1.1   实例

PKU JudgeOnline, 2418, Hardwood Species.

5.1.2   问题描述

输入一串树木的名字，统计树木在所有树木中所占的百分比。

5.1.3   输入

RedAlder

Ash

Aspen

Basswood

Ash

Beech

YellowBirch

Ash

Cherry

Cottonwood

Ash

Cypress

RedElm

Gum

Hackberry

WhiteOak

Hickory

Pecan

HardMaple

WhiteOak

SoftMaple

RedOak

RedOak

WhiteOak

Poplan

Sassafras

Sycamore

BlackWalnut

Willow

5.1.4   输出

Ash13.7931

Aspen3.4483

Basswood3.4483

Beech3.4483

BlackWalnut 3.4483

Cherry3.4483

Cottonwood3.4483

Cypress3.4483

Gum3.4483

Hackberry3.4483

HardMaple 3.4483

Hickory3.4483

Pecan3.4483

Poplan3.4483

RedAlder 3.4483

RedElm 3.4483

RedOak 6.8966

Sassafras3.4483

SoftMaple 3.4483

Sycamore3.4483

WhiteOak 10.3448

Willow3.4483

YellowBirch 3.4483

5.1.5   程序

#define MAX_WORD_LENGTH 31#include <stdio.h>#include <stdlib.h>#include <malloc.h>#include <string.h>#include <iostream.h>//定义BST结点typedef struct BSTNode{    charkey[MAX_WORD_LENGTH];    int value;    BSTNode *lchild;    BSTNode *rchild;}BSTNode,*BSTree;BSTreet=NULL;int sum = 0;//向BST插入结点void insert_tree(char * key){    //x指示查找过程中下降的路径，y始终指向x的父结点    BSTree y=NULL;    BSTree x=t;    //x下降    while(x)    {              y = x;         if(strcmp(x->key,key) == 0){              x->value++;              return;         }else if(strcmp(x->key, key) >0){              x = x->lchild;         }else{              x = x->rchild;         }    }     BSTreenew_node = (BSTree)malloc(sizeof(BSTNode));     new_node->lchild = NULL;     new_node->rchild = NULL;     strcpy(new_node->key, key);     new_node->value = 1;     //如果树为空    if(t==NULL)        t=new_node;    else    {        //设置父结点的孩子结点        if(strcmp(y->key,key) >= 0)            y->lchild = new_node;        else            y->rchild=new_node;    }}void inorder_tree_walk(BSTree x){     if(x !=NULL)     {         inorder_tree_walk(x->lchild);         printf("%s", x->key);     //   printf("%d\n", x->value);         printf("%.4f\n",(x->value * 100.0) / sum);         inorder_tree_walk(x->rchild);        }}int main(){     chartemp[31];     while(gets(temp))/*&& temp[0] != '#')*/     {         insert_tree(temp);     //   cout << temp << endl;         sum++;     }     inorder_tree_walk(t);     return 1;}

5.2    实例

PKU JudgeOnline, 2503, Babelfish.

PKU JudgeOnline, 2418, Hardwood Species.

PKU JudgeOnline, 1002, Exponentiation.

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