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Objective-C实现霍夫曼树
Huffman树（Huffman Tree）是一种用于数据压缩的二叉树结构，常用于构建霍夫曼编码。以下是用Objective-C语言实现霍夫曼树的详细示例和解释。
   
    
  #import 
    
     
  @interface HuffmanNode : NSObject
  @property (nonatomic, assign) char character;
  @end
  @interface HuffmanTree : NSObject
  @property (nonatomic, strong) HuffmanNode *root;
  @property (nonatomic, strong) NSArray *nodes;
  -(id)initWithCharacters:(NSArray *)characters;
  -(HuffmanNode*)buildTree;
  -(NSString*)huffmanCode:(char)char;
  @end
  @implementation HuffmanTree
  -(id)initWithCharacters:(NSArray *)characters {
    self = [super init];
    self.nodes = [HuffmanNode nodesWithCharacters:characters];
    return self;
  }
  -(HuffmanNode*)buildTree {
    if ([self.nodes count] == 1) {
      HuffmanNode *node = [self.nodes firstObject];
      node.isLeaf = YES;
      return node;
    }
    HuffmanNode *left = [self buildTreeForNodes:self.nodes range:0...([self.nodes count]/2)];
    HuffmanNode *right = [self buildTreeForNodes:self.nodes range:([self.nodes count]/2)...[self.nodes count]];
    if (left.character < right.character) {
      left = [right swapWithLeft:left];
    }
    left.right = right;
    right.left = left;
    return left;
  }
  -(HuffmanNode*)buildTreeForNodes:(NSArray *)nodes range:(NSRange)range {
    if (range.length == 1) {
      HuffmanNode *node = [[HuffmanNode alloc] init];
      node.character = [nodes[range.location]];
      node.isLeaf = YES;
      return node;
    }
    NSArray *subNodes = [nodes range:range];
    HuffmanNode *left = [self buildTreeForNodes:subNodes range:0...([subNodes count]/2)];
    HuffmanNode *right = [self buildTreeForNodes:subNodes range:([subNodes count]/2)...[subNodes count]];
    if (left.character < right.character) {
      left = [right swapWithLeft:left];
    }
    left.right = right;
    right.left = left;
    return left;
  }
  -(HuffmanNode*)swapWithLeft:(HuffmanNode*)left {
    HuffmanNode *temp = left.right;
    left.right = temp.right;
    temp.right = left;
    left = temp;
    return left;
  }
  -(NSString*)huffmanCode:(char)char {
    return [self buildTree].right.huffmanCode(char);
  }
  @end
    
   
Huffman树是一种基于频率的编码树，其核心思想是将最频繁出现的字符放在树的根部，递减到叶子节点。通过这种方式，高频字符可以使用较短的编码，而低频字符则需要更长的编码，从而实现压缩率的提升。