Trie(特里结构,字典树)

简介

Trie是一种特殊的树，可用于
1 存储英语单词(如下图所示)
2 hash table的替代品，优点如下

1 Looking up values typically have a better worst-case time complexity.
2 Unlike a hash table, a Trie does not need to worry about key collisions.
3 Doesn’t require a hashing algorithm to guarantee a unique path to elements.
4 Trie structures can be alphabetically ordered.

当用于存储英语单词死，下图展示了Trie的结构
这个Trie包含“Cat”，“Cut”，“Cute”，“To”，“B”五个单词

示例

/**
 TrieNode存储一个字符
 */
@interface TrieNode : NSObject

@property(nonatomic, copy) NSString *value;

//用来标识一个单词的结束(如果只添加了cute,则cut是不应该在单词库里面)
@property(nonatomic, assign) BOOL isTerminating;

@property(nonatomic, weak) TrieNode *parent;

@property(nonatomic, strong, readonly) NSMutableDictionary *children;

- (instancetype)initWithValue:(NSString *)value
                       parent:(TrieNode *)parent;

- (void)addChild:(NSString *)child;

@end

@interface TrieNode ()

@property(nonatomic, strong, readwrite) NSMutableDictionary *children;


@end

@implementation TrieNode

- (instancetype)initWithValue:(NSString *)value parent:(TrieNode *)parent
{
    if (self = [super init]) {
        _value = [value copy];
        _parent = parent;
    }
    
    return self;
}

- (void)addChild:(NSString *)child
{
    if (!self.children) {
        self.children = [NSMutableDictionary new];
    }
    
    //一个节点下不能有2个一样的节点，避免重复
    if ([[self.children allKeys] containsObject:child]) {
        return;
    }
    
    TrieNode *node = [[TrieNode alloc] initWithValue:child parent:self];
    
    [self.children setObject:node forKey:child];
    
}

@end

/**
 管理所有单词
 */
@interface Trie : NSObject
//插入一个单词
- (void)insert:(NSString *)word;
//是否包含一个单词
- (BOOL)contains:(NSString *)word;
//删除一个单词
- (void)remove:(NSString *)word;
@end

@interface Trie ()

@property(nonatomic, strong) TrieNode *root;

@end

@implementation Trie

- (instancetype)init
{
    if (self = [super init]) {
        _root = [[TrieNode alloc] init];
    }
    
    return self;
}

- (void)insert:(NSString *)word
{
    if (word.length == 0) {
        return;
    }
    
    TrieNode *currentNode = _root;
    
    NSMutableArray *words = [NSMutableArray new];
    
    NSString *lowerWorld = [word lowercaseString];
    for (NSInteger i = 0; i < lowerWorld.length; i++) {
        [words addObject:[lowerWorld substringWithRange:NSMakeRange(i, 1)]];
    }
    
    NSInteger currentIndex = 0;
    
    while (currentIndex < words.count) {
        
        NSString *ch = words[currentIndex];
        
        TrieNode *node = [currentNode.children objectForKey:ch];
        if (node) {
            currentNode = node;
        } else {
            [currentNode addChild:ch];
            currentNode = [currentNode.children objectForKey:ch];
        }
        
        currentIndex += 1;
        
        if (currentIndex == words.count) {
            currentNode.isTerminating = YES;
        }
    }
}

- (BOOL)contains:(NSString *)word
{
    if (word.length == 0) {
        return NO;
    }
    
    TrieNode *currentNode = _root;
    
    NSMutableArray *words = [NSMutableArray new];
    
    NSString *lowerWorld = [word lowercaseString];
    for (NSInteger i = 0; i < lowerWorld.length; i++) {
        [words addObject:[lowerWorld substringWithRange:NSMakeRange(i, 1)]];
    }
    
    NSInteger currentIndex = 0;
    
    while (currentIndex < words.count) {
        TrieNode *node = [currentNode.children objectForKey:words[currentIndex]];
        
        if (node) {
            currentIndex += 1;
            currentNode = node;
        } else {
            break;
        }
    }
    
    if (currentIndex == words.count && currentNode.isTerminating) {
        return YES;
    }
    return NO;
}

- (void)remove:(NSString *)word
{
    if (![self contains:word]) {
        return;
    }
    
    TrieNode *currentNode = _root;
    
    NSMutableArray *words = [NSMutableArray new];
    
    NSString *lowerWorld = [word lowercaseString];
    for (NSInteger i = 0; i < lowerWorld.length; i++) {
        [words addObject:[lowerWorld substringWithRange:NSMakeRange(i, 1)]];
    }
    
    NSInteger currentIndex = 0;
    
    while (currentIndex < words.count) {
        TrieNode *node = [currentNode.children objectForKey:words[currentIndex]];
        
        if (node) {
            currentIndex += 1;
            currentNode = node;
        } else {
            break;
        }
    }
    
    //此时的currentNode为单词最后一个字符所在的节点
    //情形1和2可以参考下面的配图
    /*  
    1 如果这个节点还有子节点，将这个节点的isTerminating属性设置为NO
    例如"cute"和"cut"同时存在，删除"cut"，只要设置"t"对应节点的isTerminating=NO即可
    */
    if (currentNode.children != nil) {
        currentNode.isTerminating = NO;
    } else {
        /*
         2 这个节点是叶子，那么删除这个节点，判断上一个节点
         2.1 如果上一个节点的isTerminating=YES或者children的key数量>=2，不删除上一个节点，跳出循环
         2.2 否则，删除上一个节点，并继续判断上一个节点的上一个节点
         */
        
        while (currentNode) {
            TrieNode *parentNode = currentNode.parent;
            
            currentNode.parent = nil;
            
            NSString *key = currentNode.value;
            
            currentNode = parentNode;
            
            if (parentNode) {
        
                [parentNode.children removeObjectForKey:key];
                
                if (parentNode.isTerminating || parentNode.children.allKeys.count > 0) {
                    break;
                }
            }
        }
    }
}


@end

删除方法对应的情形

参考链接

参考1