#pragma once
enum Colour
{
RED,
BLACK,
};
template
struct RBTreeNode
{
RBTreeNode* _left;
RBTreeNode* _right;
RBTreeNode* _parent;
pair _kv;
Colour _col;
RBTreeNode(const pair& kv)
:_left(nullptr)
, _right(nullptr)
, _parent(nullptr)
, _kv(kv)
, _col(RED)
{}
};
template
class RBTree
{
typedef RBTreeNode Node;
public:
~RBTree()
{
_Destroy(_root);
_root = nullptr;
}
public:
Node* Find(const K& key)
{
Node* cur = _root;
while (cur)
{
if (cur->_kv.first < key)
{
cur = cur->_right;
}
else if (cur->_kv.first > key)
{
cur = cur->_left;
}
else
{
return cur;
}
}
return nullptr;
}
bool Insert(const pair& kv)
{
if (_root == nullptr)
{
_root = new Node(kv);
_root->_col = BLACK;
return true;
}
Node* parent = nullptr;
Node* cur = _root;
while (cur)
{
if (cur->_kv.first < kv.first)
{
parent = cur;
cur = cur->_right;
}
else if (cur->_kv.first > kv.first)
{
parent = cur;
cur = cur->_left;
}
else
{
return false;
}
}
cur = new Node(kv);
if (parent->_kv.first > kv.first)
{
parent->_left = cur;
}
else
{
parent->_right = cur;
}
cur->_parent = parent;
while (parent && parent->_col == RED)
{
Node* grandfather = parent->_parent;
if (grandfather->_left == parent)
{
Node* uncle = grandfather->_right;
// 情况1:u存在且为红,变色处理,并继续往上处理
if (uncle && uncle->_col == RED)
{
parent->_col = BLACK;
uncle->_col = BLACK;
grandfather->_col = RED;
// 继续往上调整
cur = grandfather;
parent = cur->_parent;
}
else // 情况2+3:u不存在/u存在且为黑,旋转+变色
{
// g
// p u
// c
if (cur == parent->_left)
{
RotateR(grandfather);
parent->_col = BLACK;
grandfather->_col = RED;
}
else
{
// g
// p u
// c
RotateL(parent);
RotateR(grandfather);
cur->_col = BLACK;
//parent->_col = RED;
grandfather->_col = RED;
}
break;
}
}
else // (grandfather->_right == parent)
{
// g
// u p
// c
Node* uncle = grandfather->_left;
// 情况1:u存在且为红,变色处理,并继续往上处理
if (uncle && uncle->_col == RED)
{
parent->_col = BLACK;
uncle->_col = BLACK;
grandfather->_col = RED;
// 继续往上调整
cur = grandfather;
parent = cur->_parent;
}
else // 情况2+3:u不存在/u存在且为黑,旋转+变色
{
// g
// u p
// c
if (cur == parent->_right)
{
RotateL(grandfather);
grandfather->_col = RED;
parent->_col = BLACK;
}
else
{
// g
// u p
// c
RotateR(parent);
RotateL(grandfather);
cur->_col = BLACK;
grandfather->_col = RED;
}
break;
}
}
}
_root->_col = BLACK;
return true;
}
void InOrder()
{
_InOrder(_root);
}
bool IsBalance()
{
if (_root && _root->_col == RED)
{
cout << "根节点颜色是红色" << endl;
return false;
}
int benchmark = 0;
Node* cur = _root;
while (cur)
{
if (cur->_col == BLACK)
++benchmark;
cur = cur->_left;
}
// 连续红色节点
return _Check(_root, 0, benchmark);
}
int Height()
{
return _Height(_root);
}
private:
void _Destroy(Node* root)
{
if (root == nullptr)
{
return;
}
_Destroy(root->_left);
_Destroy(root->_right);
delete root;
}
int _Height(Node* root)
{
if (root == NULL)
return 0;
int leftH = _Height(root->_left);
int rightH = _Height(root->_right);
return leftH > rightH ? leftH + 1 : rightH + 1;
}
bool _Check(Node* root, int blackNum, int benchmark)
{
if (root == nullptr)
{
if (benchmark != blackNum)
{
cout << "某条路径黑色节点的数量不相等" << endl;
return false;
}
return true;
}
if (root->_col == BLACK)
{
++blackNum;
}
if (root->_col == RED
&& root->_parent
&& root->_parent->_col == RED)
{
cout << "存在连续的红色节点" << endl;
return false;
}
return _Check(root->_left, blackNum, benchmark)
&& _Check(root->_right, blackNum, benchmark);
}
void _InOrder(Node* root)
{
if (root == nullptr)
{
return;
}
_InOrder(root->_left);
cout << root->_kv.first << " ";
_InOrder(root->_right);
}
void RotateL(Node* parent)
{
Node* subR = parent->_right;
Node* subRL = subR->_left;
parent->_right = subRL;
if (subRL)
subRL->_parent = parent;
Node* ppnode = parent->_parent;
subR->_left = parent;
parent->_parent = subR;
if (ppnode == nullptr)
{
_root = subR;
_root->_parent = nullptr;
}
else
{
if (ppnode->_left == parent)
{
ppnode->_left = subR;
}
else
{
ppnode->_right = subR;
}
subR->_parent = ppnode;
}
}
void RotateR(Node* parent)
{
Node* subL = parent->_left;
Node* subLR = subL->_right;
parent->_left = subLR;
if (subLR)
subLR->_parent = parent;
Node* ppnode = parent->_parent;
subL->_right = parent;
parent->_parent = subL;
if (parent == _root)
{
_root = subL;
_root->_parent = nullptr;
}
else
{
if (ppnode->_left == parent)
{
ppnode->_left = subL;
}
else
{
ppnode->_right = subL;
}
subL->_parent = ppnode;
}
}
private:
Node* _root = nullptr;
};
set 参数只有 key,但是map除了key还有value。我们还是需要KV模型的红黑树的代码。
由于map和set都需要用到迭代器,但是两者的迭代器实际上都是封装了红黑树的迭代器,因此我们要先实现红黑树的迭代器,这里迭代器的实现和链表极其相似,因此,也是使用三个模板参数,分别代表普通类型,引用类型,指针类型,库里的实现是采用了哨兵卫的头节点的方式,但是这里并不这样做
template
struct __RBTreeIterator
{
typedef RBTreeNode Node;//方便使用节点
typedef __RBTreeIterator Self;//方便使用自己
Node* _node;//节点指针
//迭代器构造函数
__RBTreeIterator(Node* node)
:_node(node)
{}
operator*()
{}
operator->()
{}
operator++()
{}
operator++(int)
{}
operator--()
{}
operator--(int)
{}
operator!=(const Self& s) const
{}
operator==(const Self& s) const
{}
};
红黑树的正向迭代器是对结点指针进行了封装,所以这里的正向迭代器就只有一个成员变量:结点的指针,并没有什么其他的地方,迭代器的定义:
*:解引用操作,返回对应结点数据的引用:
Ref operator*()
{
return _node->_data;
}
->:成员访问操作符,返回结点数据的引用:
Ptr operator->()
{
return &_node->_data;
}
!=、==:比较两个对象中的节点即可
bool operator !=(const Self & s) const
{
return _node != s._node;
}
bool operator ==(const Self& s) const
{
return _node == s._node;
}
++,--:
一个结点的正向迭代器进行++
操作后,根据红黑树中序(左、根、右)找到当前结点的下一个结点,中序的第一个节点是最左,迭代器的++
怎么去找:
如果节点的右子树不为空,++
就是找右子树的最左节点
如果节点的右子树为空,++
就是找祖先(孩子是父亲的左的那个祖先)
Self& operator++()
{
if (_node->_right)
{
// 1、右不为空,下一个就是右子树的最左节点
Node* subLeft = _node->_right;
while (subLeft->_left)
{
subLeft = subLeft->_left;
}
_node = subLeft;
}
else
{
// 2、右为空,沿着到根的路径,找孩子是父亲左的那个祖先
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && cur == parent->_right)
{
cur = parent;
parent = parent->_parent;
}
_node = parent;
}
return *this;
}
迭代器的--
对于–,如果是根,–就是左子树,找到左子树最大的那一个(最右节点),如果节点的左子树不为空,--
找左子树最右的节点,如果节点的左子树为空,--
找祖先(孩子是父亲的右的祖先)
Self& operator--()
{
if (_node->_left)
{
// 1、左不为空,找左子树最右节点
Node* subRight = _node->_left;
while (subRight->_right)
{
subRight = subRight->_right;
}
_node = subRight;
}
else
{
// 2、左为空,孩子是父亲的右的那个祖先
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && cur == parent->_left)
{
cur = parent;
parent = parent->_parent;
}
_node = parent;
}
return *this;
}
begin()
:返回中序(左、根、右)第一个结点的正向迭代器,即最左节点,返回的是最左节点,直接找最左节点即可
end()
:返回中序(左、根、右)最后一个结点下一个位置的正向迭代器,这里直接用空指针
itertaor begin()
{
Node* cur = _root;
while (cur && cur->_left)
{
cur = cur->_left;
}
return itertaor(cur);
}
itertaor end()
{
return itertaor(nullptr);
}
至此迭代器的基本实现已完成。
由于模板参数的改变和迭代器的实现,使RBTree的实现更加完整,需要对RBTree类进行改变。
首先就是对insert进行改变,有了迭代器的实现,我们应该和库里面的一样,返回的是pair
pair Insert(const T& data)
{
// 1、搜索树的规则插入
// 2、看是否违反平衡规则,如果违反就需要处理:旋转
if (_root == nullptr)
{
_root = new Node(data);
_root->_col = BLACK;
return make_pair(iterator(_root), true);
}
KeyOfT kot;
Node* parent = nullptr;
Node* cur = _root;
while (cur)
{
if (kot(cur->_data) < kot(data))
{
parent = cur;
cur = cur->_right;
}
else if (kot(cur->_data) > kot(data))
{
parent = cur;
cur = cur->_left;
}
else
{
return make_pair(iterator(cur), true);
}
}
cur = new Node(data);
Node* newnode = cur;
cur->_col = RED;
if (kot(parent->_data) < kot(data))
{
parent->_right = cur;
}
else
{
parent->_left = cur;
}
cur->_parent = parent;
// 存在连续红色节点
while (parent && parent->_col == RED)
{
Node* grandfater = parent->_parent;
assert(grandfater);
if (grandfater->_left == parent)
{
Node* uncle = grandfater->_right;
// 情况一:
if (uncle && uncle->_col == RED) // 叔叔存在且为红
{
// 变色
parent->_col = uncle->_col = BLACK;
grandfater->_col = RED;
// 继续往上处理
cur = grandfater;
parent = cur->_parent;
}
else // 叔叔不存在 或者 叔叔存在且为黑
{
if (cur == parent->_left) // 单旋
{
// g
// p
// c
RotateR(grandfater);
parent->_col = BLACK;
grandfater->_col = RED;
}
else // 双旋
{
// g
// p
// c
RotateL(parent);
RotateR(grandfater);
cur->_col = BLACK;
grandfater->_col = RED;
}
break;
}
}
else //(grandfater->_right == parent)
{
Node* uncle = grandfater->_left;
// 情况一:
if (uncle && uncle->_col == RED)
{
// 变色
parent->_col = uncle->_col = BLACK;
grandfater->_col = RED;
// 继续往上处理
cur = grandfater;
parent = cur->_parent;
}
else
{
if (cur == parent->_right)
{
// g
// p
// c
RotateL(grandfater);
parent->_col = BLACK;
grandfater->_col = RED;
}
else // 双旋
{
// g
// p
// c
RotateR(parent);
RotateL(grandfater);
cur->_col = BLACK;
grandfater->_col = RED;
}
break;
}
}
}
_root->_col = BLACK;
return make_pair(iterator(newnode), true);//创建并返回iterator对象
}
相比原来的insert对返回值做了修改,并用KeyOfT仿函数创建对象来接受其中的K,来进行比较
利用KeyOfT提取T中的K来进行比较找想要找的元素,找到返回迭代器元素位置的迭代器否则返回end(),具体代码实现如下:
iterator Find(const K& key)
{
Node* cur = _root;
KeyOfT kot;
while (cur)
{
if (kot(cur->_data) < key)
{
cur = cur->_right;
}
else if (kot(cur->_data) > key)
{
cur = cur->_left;
}
else
{
return iterator(cur);
}
}
return End();
}
#pragma once
enum Colour
{
RED,
BLACK,
};
template
struct RBTreeNode
{
RBTreeNode* _left;
RBTreeNode* _right;
RBTreeNode* _parent;
T _data;
Colour _col;
RBTreeNode(const T& data)
:_left(nullptr)
, _right(nullptr)
, _parent(nullptr)
, _data(data)
, _col(RED)
{}
};
template
struct __RBTreeIterator
{
typedef RBTreeNode Node;
typedef __RBTreeIterator Self;
Node* _node;
__RBTreeIterator(Node* node)
:_node(node)
{}
// 1、typedef __RBTreeIterator itertaor; 拷贝构造
// 2、 typedef __RBTreeIterator const_itertaor;
// 支持普通迭代器构造const迭代器的构造函数
__RBTreeIterator(const __RBTreeIterator& it)
:_node(it._node)
{}
Ref operator*()
{
return _node->_data;
}
Ptr operator->()
{
return &_node->_data;
}
bool operator!=(const Self& s)
{
return _node != s._node;
}
Self& operator++()
{
if (_node->_right)
{
// 1、右不为空,下一个就是右子树的最左节点
Node* subLeft = _node->_right;
while (subLeft->_left)
{
subLeft = subLeft->_left;
}
_node = subLeft;
}
else
{
// 2、右为空,沿着到根的路径,找孩子是父亲左的那个祖先
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && cur == parent->_right)
{
cur = parent;
parent = parent->_parent;
}
_node = parent;
}
return *this;
}
Self& operator--()
{
if (_node->_left)
{
// 1、左不为空,找左子树最右节点
Node* subRight = _node->_left;
while (subRight->_right)
{
subRight = subRight->_right;
}
_node = subRight;
}
else
{
// 2、左为空,孩子是父亲的右的那个祖先
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && cur == parent->_left)
{
cur = parent;
parent = parent->_parent;
}
_node = parent;
}
return *this;
}
};
// 仿函数
template
class RBTree
{
typedef RBTreeNode Node;
public:
~RBTree()
{
_Destroy(_root);
_root = nullptr;
}
public:
typedef __RBTreeIterator itertaor;
typedef __RBTreeIterator const_itertaor;
itertaor begin()
{
Node* cur = _root;
while (cur && cur->_left)
{
cur = cur->_left;
}
return itertaor(cur);
}
itertaor end()
{
return itertaor(nullptr);
}
const_itertaor begin() const
{
Node* cur = _root;
while (cur && cur->_left)
{
cur = cur->_left;
}
return const_itertaor(cur);
}
const_itertaor end() const
{
return const_itertaor(nullptr);
}
Node* Find(const K& key)
{
Node* cur = _root;
KeyOfT kot;
while (cur)
{
if (kot(cur->_data) < key)
{
cur = cur->_right;
}
else if (kot(cur->_data) > key)
{
cur = cur->_left;
}
else
{
return cur;
}
}
return nullptr;
}
pair Insert(const T& data)
{
if (_root == nullptr)
{
_root = new Node(data);
_root->_col = BLACK;
return make_pair(itertaor(_root), true);
}
KeyOfT kot;
Node* parent = nullptr;
Node* cur = _root;
while (cur)
{
if (kot(cur->_data) < kot(data))
{
parent = cur;
cur = cur->_right;
}
else if (kot(cur->_data) > kot(data))
{
parent = cur;
cur = cur->_left;
}
else
{
return make_pair(itertaor(cur), false);
}
}
cur = new Node(data);
Node* newnode = cur;
if (kot(parent->_data) > kot(data))
{
parent->_left = cur;
}
else
{
parent->_right = cur;
}
cur->_parent = parent;
while (parent && parent->_col == RED)
{
Node* grandfather = parent->_parent;
if (grandfather->_left == parent)
{
Node* uncle = grandfather->_right;
// 情况1:u存在且为红,变色处理,并继续往上处理
if (uncle && uncle->_col == RED)
{
parent->_col = BLACK;
uncle->_col = BLACK;
grandfather->_col = RED;
// 继续往上调整
cur = grandfather;
parent = cur->_parent;
}
else // 情况2+3:u不存在/u存在且为黑,旋转+变色
{
// g
// p u
// c
if (cur == parent->_left)
{
RotateR(grandfather);
parent->_col = BLACK;
grandfather->_col = RED;
}
else
{
// g
// p u
// c
RotateL(parent);
RotateR(grandfather);
cur->_col = BLACK;
//parent->_col = RED;
grandfather->_col = RED;
}
break;
}
}
else // (grandfather->_right == parent)
{
// g
// u p
// c
Node* uncle = grandfather->_left;
// 情况1:u存在且为红,变色处理,并继续往上处理
if (uncle && uncle->_col == RED)
{
parent->_col = BLACK;
uncle->_col = BLACK;
grandfather->_col = RED;
// 继续往上调整
cur = grandfather;
parent = cur->_parent;
}
else // 情况2+3:u不存在/u存在且为黑,旋转+变色
{
// g
// u p
// c
if (cur == parent->_right)
{
RotateL(grandfather);
grandfather->_col = RED;
parent->_col = BLACK;
}
else
{
// g
// u p
// c
RotateR(parent);
RotateL(grandfather);
cur->_col = BLACK;
grandfather->_col = RED;
}
break;
}
}
}
_root->_col = BLACK;
return make_pair(itertaor(newnode), true);;
}
bool IsBalance()
{
if (_root && _root->_col == RED)
{
cout << "根节点颜色是红色" << endl;
return false;
}
int benchmark = 0;
Node* cur = _root;
while (cur)
{
if (cur->_col == BLACK)
++benchmark;
cur = cur->_left;
}
// 连续红色节点
return _Check(_root, 0, benchmark);
}
int Height()
{
return _Height(_root);
}
private:
void _Destroy(Node* root)
{
if (root == nullptr)
{
return;
}
_Destroy(root->_left);
_Destroy(root->_right);
delete root;
}
int _Height(Node* root)
{
if (root == NULL)
return 0;
int leftH = _Height(root->_left);
int rightH = _Height(root->_right);
return leftH > rightH ? leftH + 1 : rightH + 1;
}
bool _Check(Node* root, int blackNum, int benchmark)
{
if (root == nullptr)
{
if (benchmark != blackNum)
{
cout << "某条路径黑色节点的数量不相等" << endl;
return false;
}
return true;
}
if (root->_col == BLACK)
{
++blackNum;
}
if (root->_col == RED
&& root->_parent
&& root->_parent->_col == RED)
{
cout << "存在连续的红色节点" << endl;
return false;
}
return _Check(root->_left, blackNum, benchmark)
&& _Check(root->_right, blackNum, benchmark);
}
void RotateL(Node* parent)
{
Node* subR = parent->_right;
Node* subRL = subR->_left;
parent->_right = subRL;
if (subRL)
subRL->_parent = parent;
Node* ppnode = parent->_parent;
subR->_left = parent;
parent->_parent = subR;
if (ppnode == nullptr)
{
_root = subR;
_root->_parent = nullptr;
}
else
{
if (ppnode->_left == parent)
{
ppnode->_left = subR;
}
else
{
ppnode->_right = subR;
}
subR->_parent = ppnode;
}
}
void RotateR(Node* parent)
{
Node* subL = parent->_left;
Node* subLR = subL->_right;
parent->_left = subLR;
if (subLR)
subLR->_parent = parent;
Node* ppnode = parent->_parent;
subL->_right = parent;
parent->_parent = subL;
if (parent == _root)
{
_root = subL;
_root->_parent = nullptr;
}
else
{
if (ppnode->_left == parent)
{
ppnode->_left = subL;
}
else
{
ppnode->_right = subL;
}
subL->_parent = ppnode;
}
}
private:
Node* _root = nullptr;
};
注意:
这里和list实现迭代器一样,当我们typedef迭代器时,会出现内嵌类型的问题,需要使用到typename关键字
翻开源码一看,RBTree的结构源码:是KV结构的红黑树
RBTree是通过传入的Value的值来判断类型,也就是一棵泛型的RBTree,通过不同的实例化,实现出了Map和Set:
对于map:传key,对于set:传pair
map的结构简化源码
:
为了让我们的红黑树能够识别set与map我们增加一个模板参数T:
template
class RBTree
对于T模板参数可能是键值Key,也可能是由Key和Value共同构成的键值对。
如果是set容器,那么它传入底层红黑树的模板参数就是Key和Key:
template
class set
{
private:
RBTree _t;
};
如果是map容器,传入底层红黑树的模板参数就是Key和Key和value的键值对:
class map
{
private:
RBTree> _t;
};
由此可以得出,对于set和map的区别:我们只要通过第二个模板参数就能进行区分,那是不是第一个模板参数就没有意义了呢?
红黑树的节点:set容器:K和T都是键值Key; map容器:K是键值Key,T由Key和Value构成的键值对;但是底层红黑树并不知道上层容器到底是map还是set,因此红黑树的结点当中直接存储T就行了,如果是set的时候,结点当中存储的是键值Key;如果是map的时候,结点当中存储的就是键值对,所以红黑树的结点定义如下,由T类型来决定红黑树存的是key还是pair:
template
//三叉链结构
struct RBTreeNode
{
T _data;
RBTreeNode* _left;
RBTreeNode* _right;
RBTreeNode* _parent;
Color _col;
RBTreeNode(const T& data)
:_data(data)
, _left(nullptr)
, _right(nullptr)
, _parent(nullptr)
, _col(RED)
{}
};
这里存在一个问题:插入的时候data的大小如何去进行比较:我们并不知道是什么类型是key,还是pair的比较,而我们刚开始kv结构就直接用kv.first去比较了。
对于set是
Key
,可以比较对于map是
pair
,那我们要取其中的first来比较,但是pair的大小并不是直接按照first去进行比较的,而我们只需要按照first去进行比较
由于底层的红黑树不知道传的是map还是set容器,当需要进行两个结点键值的比较时,底层红黑树传入的仿函数来获取键值Key,进行两个结点键值的比较:这个时候我们就需要仿函数了,如果是set那就是用于返回T当中的键值Key,如果是map那就是用于返回pair的first:
仿函数/函数对象也是类,是一个类对象。仿函数要重载operator()。
namespace ayf
{
template
class map
{
struct MapKeyOfT
{
const K& operator()(const pair& kv)
{
return kv.first;
}
};
public:
private:
RBTree,MapKeyOfT> _t;
};
namespace ayf
{
template
class set
{
struct SetKeyOfT
{
const K& operator()(const K& key)
{
return key;
}
};
private:
RBTree _t;
};
如图:
通过前面底层红黑树的接口进行套用即可实现set的实现:
值得注意的是:typename:没有实例化的模板,区分不了是静态变量还是类型,typename告诉编译器是类型
#pragma once
#include"RBTree.h"
namespace ayf {
template
class set
{
struct SetKeyOfT
{
const K& operator()(const K& key)
{
return key;
}
};
public:
typedef typename RBTree::const_itertaor iterator;
typedef typename RBTree::const_itertaor const_iterator;
iterator begin()
{
return _t.begin();
}
iterator end()
{
return _t.end();
}
pair insert(const K& key)
{
return _t.Insert(key);
}
private:
RBTree _t;
};
void test_set1()
{
int a[] = { 16, 3, 7, 11, 9, 26, 18, 14, 15 };
set s;
for (auto e : a)
{
s.insert(e);
}
set::iterator it = s.begin();
while (it != s.end())
{
cout << *it << " ";
//*it = 1;
++it;
}
cout << endl;
for (auto e : s)
{
cout << e << " ";
}
cout << endl;
}
}
同样是套用上底层红黑树的接口,不过map的实现有一个很重要的地方,那就是[]的实现
#pragma once
#include"RBTree.h"
namespace ayf {
template
class map {
struct MapKeyOfT {
const K& operator() (const pair& kv) {
return kv.first;
}
};
public:
typedef typename RBTree, MapKeyOfT>::itertaor iterator;
iterator begin()
{
return _t.begin();
}
iterator end()
{
return _t.end();
}
V& operator[](const K& key)
{
pair ret = _t.Insert(make_pair(key, V()));
return ret.first->second;
}
pair insert(const pair& kv)
{
return _t.Insert(kv);
}
private:
RBTree, MapKeyOfT> _t;
};
void test_map2()
{
string arr[] = { "西瓜", "草莓", "苹果", "刘紫菱", "西瓜", "西瓜", "刘紫菱", "苹果", "苹果", "西瓜", "西瓜", "草莓", "草莓", "草莓" };
map countMap;
for (auto& e : arr)
{
countMap[e]++;
}
for (auto& kv : countMap)
{
cout << kv.first << ":" << kv.second << endl;
}
}
}