[問題] 紅黑樹construct設root = nil遇到的問題

[superme7 (Bonbodi)]

開發平台(Platform): (Ex: Win10, Linux, ...) 
Win10

編譯器(Ex: GCC, clang, VC++...)+目標環境(跟開發平台不同的話需列出)
GCC

額外使用到的函數庫(Library Used): (Ex: OpenGL, ...) 
無

問題(Question)：
RBT，Tree的construct把root = nil，Insert node 後 root 無法更新 依然指向nil

餵入的資料(Input)：
在int main 中

預的正確確結果(Expected Output)：
Black/5 Black/8 Red/11 Black/9

錯誤結果(Wrong Output)：
沒有顯示

程式碼(Code)：(請善用置底文網頁, 記得排版，禁止使用圖檔) 
#include <iostream>
#include <string>
using namespace std;

class Node
{
public:

    int key;
    Node* p, * left, * right;
    string color;

    Node() :key(0), p(0), left(0), right(0), color("") {};
    Node(int a) :key(a), left(0), right(0), p(0), color("") {};

};

class Tree
{
public:

    Node* nil;
    Node* root;
    Tree()
    {
        nil = new Node;
        nil->color = "black";
        root = nil;
        root->p = nil;
    }
};

void left_Rotate(Tree t, Node* x)
{
    Node* y = x->right;
    x->right = y->left;
    if (y->left != t.nil)
        y->left->p = x;

    if (x->p == t.nil)
        t.root = y;
    else if (x == x->p->left)
        x->p->left = y;
    else
        x->p->right = y;
    y->p = x->p;
    y->left = x;
    x->p = y;
}

void right_Rotate(Tree t, Node* x)
{
    Node* y = x->left;
    x->left = y->right;
    if (y->right != t.nil)
        y->right->p = x;

    if (x->p == t.nil)
        t.root = y;
    else if (x->p->left == x)
        y = x->p->left;
    else
        y = x->p->right;
    y->p = x->p;
    y->right = x;
    x->p = y;
}

void InsertFixup(Tree t, Node* z)
{
    while (z->p->color == "red")
    {
        if (z->p == z->p->p->left)
        {
            Node* y = z->p->p->right;
            if (y->color == "red")
            {
                y->color = "black";
                z->p->color = "black";
                z->p->p->color = "red";
                z = z->p->p;
            }
            else
            {
                if (z == z->p->right)
                {
                    z = z->p;
                    left_Rotate(t, z);
                }
                z->p->color = "black";
                z->p->p->color = "red";
                right_Rotate(t, z->p->p);
            }
        }
        else
        {
            Node* y = z->p->p->left;
            if (y->color == "red")
            {
                y->color = "black";
                y->p->p->color = "red";
                z->p->color = "black";
                z = z->p->p;
            }
            else
            {
                if (z == z->p->left)
                {
                    z = z->p;
                    right_Rotate(t, z);
                }
                z->p->color = "black";
                z->p->p->color = "red";
                left_Rotate(t, z->p->p);
            }
        }
    }
    t.root->color = "black";
}

void Insert(Tree t, Node* z)
{
    Node* y = t.nil;
    Node* x = t.root;

    while (x != t.nil)
    {
        y = x;
        if (z->key < x->key)
            x = x->left;
        else
            x = x->right;
    }

    z->p = y;
    if (y == t.nil)
        t.root = z;

    else if (z->key < y->key)
        y->left = z;
    else
        y->right = z;
    z->color = "red";
    z->left = t.nil;
    z->right = t.nil;

    InsertFixup(t, z);
}

void Inorder(Tree t, Node* z)
{
    if (z != t.nil)
    {
        Inorder(t, z->left);
        cout << z->color << "/" << z->key << " ";
        Inorder(t, z->right);
    }
}

int main()
{
    Tree a;
    Node* b = new Node(8);
    Node* c = new Node(11);
    Node* d = new Node(9);
    Node* e = new Node(5);
    Insert(a, b);
    Insert(a, c);
    Insert(a, d);
    Insert(a, e);

    Inorder(a,a.root);

    return 0;

}

補充說明(Supplement)：
我在想root是不是還是指向nil，所以Inorder Print不出來

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