算法-二叉查找树

二叉查找树（Binary Search Tree），也称有序二叉树（ordered binary tree）,排序二叉树（sorted binary tree），是指一棵空树或者具有下列性质的二叉树：

1. 若任意节点的左子树不空，则左子树上所有结点的值均小于它的根结点的值；

2. 若任意节点的右子树不空，则右子树上所有结点的值均大于它的根结点的值；

3. 任意节点的左、右子树也分别为二叉查找树；

4. 没有键值相等的节点；

本文跟前文一样只是实现了增加和查找功能，需要一个节点辅助类:

@interface BinaryNode:NSObject

@property  (strong,nonatomic)  NSString  *key;//键

@property  (strong,nonatomic)  NSString  *value;//值

@property (strong,nonatomic) BinaryNode  *left;//左子树的节点

@property (strong,nonatomic) BinaryNode  *right;//右子树的节点

@property  (assign,nonatomic)  NSInteger childCount;//以该结点为根的自述中的结点总数

-(void)initWithData:(NSString *)key  value:(NSString *)value  childCount:(NSInteger)childCount;

@end

BinaryNode实现代码：

@implementation BinaryNode

-(void)initWithData:(NSString *)key value:(NSString *)value childCount:(NSInteger)childCount{
    self.key=key;
    self.value=value;
    self.childCount=childCount;
}

@end

二叉查找树需要定义一个根结点:

@interface BinarySearchTree : NSObject

@property  (strong,nonatomic)  BinaryNode  *root;//二叉平衡树的根节点

-(NSString  *)get:(NSString *)key;//获取键对应的值

-(void)put:(NSString *)key  value:(NSString *)value;//插入键值对

@end

实现代码:

@implementation BinarySearchTree

-(NSString *)get:(NSString *)key{
    return [self getByKey:self.root key:key];
}

-(NSString *)getByKey:(BinaryNode *)node  key:(NSString *)key{
    //在node为根结点的子树种查找并返回key所对应的值
    //如果找不到返回null
    if (node==nil) {
        return nil;
    }
    //左右节点进行比较，每个结点的键值大于左子树的结点值小于右子树的结点值
    NSInteger  compare=[key integerValue]-[node.key integerValue];
    if (compare>0) {
        return [self getByKey:node.right key:key];
    }else if(compare<0){
        return [self getByKey:node.left key:key];
    }else{
        return node.value;
    }
}
//http://www.cnblogs.com/xiaofeixiang
-(void)put:(NSString *)key value:(NSString *)value{
    //查找键值，找到则更新它的值，否则为它创建一个新的结点
    self.root=[self putNode:self.root key:key value:value];
}

-(BinaryNode *)putNode:(BinaryNode *)node  key:(NSString *)key  value:(NSString *)value{
    if (node==nil) {
        BinaryNode  *newNode=[[BinaryNode alloc]init];
        [newNode initWithData:key value:value childCount:1];
        return newNode;
    }
    NSInteger  compare=[key integerValue]-[node.key integerValue];
    if (compare>0) {
        node.right=[self putNode:node.right key:key value:value];
    }else if(compare<0){
        node.left=[self putNode:node.left key:key value:value];
    }else{
        node.value=value;
    }
    node.childCount=[self childSizeCount:node.left]+[self childSizeCount:node.right]+1;
    return node;
}

-(NSInteger)childSize{
    return [self childSizeCount:self.root];
}

-(NSInteger)childSizeCount:(BinaryNode *)node{
    if (node==nil) {
        return 0;
    }else{
        return node.childCount;
    }
}
@end

测试:

        BinarySearchTree  *binaryTree=[[BinarySearchTree alloc]init];
        [binaryTree put:@"3" value:@"FlyElephant"];
        [binaryTree put:@"9" value:@"http://www.cnblogs.com/xiaofeixiang"];
        [binaryTree put:@"10" value:@"博客园"];
        [binaryTree put:@"0" value:@"228407086"];
        NSString  *temp=[binaryTree get:@"9"];
        NSLog(@"二叉查找树:%@",temp);

效果如下: