示例
特点
BinarySearchTree(BST)是一种特殊的BinaryTree,其特点是
1 若左子树不空，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 左、右子树也分别为二叉排序树；
向二叉排序树中插入值的步骤
1 如果当前节点为空(只有没有根节点这种情况)，则插入节点,结束
2 如果插入值小于当前节点的值
- 如果左子树不存在，则将插入值对应的节点设为当前节点的leftChild，
结束 - 如果左子树存在，则对左子树执行步骤123
3 如果插入值大于当前节点的值
- 如果右子树不存在，则将插入值对应的节点设为当前节点的rightChild，
结束 - 如果右子树存在，则对左子树执行步骤123
示例
代码创建的二叉排序树结构见文章顶部的示例图
@interface BinarySortTree : NSObject
@property(nonatomic, assign) NSInteger value;
@property(nonatomic, assign, readonly) NSUInteger count;
@property(nonatomic, strong) BinarySortTree *leftChild;
@property(nonatomic, strong) BinarySortTree *rightChild;
- (void)insertValue:(NSInteger)value;
- (NSString *)traverseInOrder;
- (NSString *)traversePreOrder;
- (NSString *)traversePostOrder;
- (BinarySortTree *)search:(NSInteger)value;
@implementation BinarySortTree
- (void)insertValue:(NSInteger)value
{
if (value <= 0) return;
//当树没有一个节点的时候，把value当成根节点
if (!self.leftChild && !self.rightChild && _value == 0) {
_value = value;
return;
}
if (value == _value) {
return;
}
if (value < _value) {
//leftChild
if (_leftChild) {
[_leftChild insertValue:value];
} else {
BinarySortTree *tree = [BinarySortTree new];
tree.value = value;
_leftChild = tree;
}
} else {
//rightChild
if (_rightChild) {
[_rightChild insertValue:value];
} else {
BinarySortTree *tree = [BinarySortTree new];
tree.value = value;
_rightChild = tree;
}
}
}
- (NSUInteger)count
{
return [self.leftChild count] + (_value > 0 ? 1 : 0) + [self.rightChild count];
}
//遍历的时间复杂度为O(n)，因为每一个节点都会被访问
//顺序遍历，从小到大。先访问leftChild，然后访问当前节点，最后访问rightChild的顺序
- (NSString *)traverseInOrder
{
if (_value == 0) {
return @"";
}
return [NSString stringWithFormat:@"%@ %ld %@", [_leftChild traverseInOrder] ?: @"", _value, [_rightChild traverseInOrder] ?: @""];
}
//先访问节点，然后访问leftChild，最后访问rightChild的顺序
- (NSString *)traversePreOrder
{
if (_value == 0) return @"";
return [NSString stringWithFormat:@"%ld %@ %@", _value, [_leftChild traversePreOrder] ?: @"", [_rightChild traversePreOrder] ?: @""];
}
//先访问leftChild，然后访问rightChild，最后访问当前节点的顺序
- (NSString *)traversePostOrder
{
if (_value == 0) return @"";
return [NSString stringWithFormat:@"%@ %@ %ld", [_leftChild traversePostOrder] ?: @"", [_rightChild traversePostOrder] ?: @"" , _value];
}
//查找的平均时间复杂度为O(log n)，因为每次查找的时候只会在一个子树中查找
- (BinarySortTree *)search:(NSInteger)value
{
if (value <= 0) {
return nil;
}
if (_value == value) {
return self;
} else if (value < _value) {
return [self.leftChild search:value];
} else {
return [self.rightChild search:value];
}
}
@end
测试
- (void)binarySortTreeTest
{
BinarySortTree *tree = [BinarySortTree new];
[tree insertValue:7];
[tree insertValue:10];
[tree insertValue:2];
[tree insertValue:1];
[tree insertValue:5];
[tree insertValue:9];
NSLog(@"tree.count = %lu", (unsigned long)tree.count);
NSLog(@"traverseInOrder=%@", [tree traverseInOrder]);
NSLog(@"traversePreOrder=%@", [tree traversePreOrder]);
NSLog(@"traversePostOrder=%@", [tree traversePostOrder]);
BinarySortTree *b1 = [tree search:0];
BinarySortTree *b2 = [tree search:1];
BinarySortTree *b3 = [tree search:7];
}
