Double Linked List

#include<iostream>

using namespace std;

struct elem
{
    int key;
    elem *prev;
    elem *next;
} *start;

void init();
void add_b(int n);
void add_mid1(int n, int k);
void add_mid2(int n, int k);
void add_e(int n);
int del_b(int &n);
int del_n(int n);
int del_e(int &n);
void invert();
void list();
void printBack();
int search(int k);
int searchAt(int k);

int main()
{
    int num, k, ch;
    init();
    do {
        cout << "\n Menu \n";
        cout << "1. Add the first element\n";
        cout << "2. Add element before k\n";
        cout << "3. Add element after k\n";
        cout << "4. Add the last element\n";
        cout << "5. Del the first element\n";
        cout << "6. Del the element with value num\n";
        cout << "7. Del the last element\n";
        cout << "8. Invert element\n";
        cout << "9. Show the list\n";
        cout << "10. Print backwards\n";
        cout << "11. Count elements matching k\n";
        cout << "12. Print position of first k\n";
        cout << "0. Exit\n";
        cout << "Your choice:";
        cin >> ch;
        switch (ch)
        {
            case 1:
                cout << "num=";
                cin >> num;
                add_b(num);
                break;
            case 2:
                cout << "num=";
                cin >> num;
                cout << "k=";
                cin >> k;
                add_mid1(num, k);
                break;
            case 3:
                cout << "num=";
                cin >> num;
                cout << "k=";
                cin >> k;
                add_mid2(num, k);
                break;
            case 4:
                cout << "num=";
                cin >> num;
                add_e(num);
                break;
            case 5:
                if(del_b(num))
                    list();
                break;
            case 6:
                cout << "num=";
                cin >> num;
                if (del_n(num))
                    list();
                break;
            case 7:
                if (del_e(num))
                    list();
                break;
            case 8:
                invert();
                list();
                break;
            case 9:
                list();
                break;
            case 10:
                printBack();
                break;
            case 11:
            {
                int c = 0;
                cout << "Enter key ";
                cin >> c;
                cout << "Count elements matching " << c << " " << search(c);
                break;
            }

            case 12:
            {
                int c = 0;
                cout << "Enter key ";
                cin >> c;
                cout << "Key " << c << " at pos " << searchAt(c);
                break;
            }
        }
    } while (ch != 0);
    system("pause");
    return 0;

}

void  init()
{
    start = NULL;
}

void add_b(int n)
{
    elem *p = start;
    start = new elem;
    start->key = n;
    start->next = p;
    start->prev = NULL;
    if (p)
        p->prev = start;
}

void add_mid1(int n, int k)
{
    elem *q=NULL, *p = start;
    while (p->key != k)
        p = p->next;
    q = new elem;
    q->next = p->next;
    q->key = p->key;
    q->prev = p;
    if(p)
        p->next = q;
    p->key = n;
    q->next->prev = q;
}

void add_mid2(int n, int k)
{
    elem *q;
    elem *p = start;
    while (p->key != k)
        p = p->next;
    q = new elem;
    q->key = n;
    q->next = p->next;
    p->next = q;
    q->prev = p;
       q->next->prev=q;
}

void add_e(int n)
{
    elem *p = start, *q;
    q = new elem;
    q->key = n;
    q->next = NULL;
    if (start)
    {
        while (p->next)
            p = p->next;
        p->next = q;
    }
    else
        start = q;
    q->prev = p;
}

int del_b(int &n)
{
    elem *p = start;
    if (start)
    {
        n = start->key;
        if (start->next)
        {
            start = start->next;
            start->prev = NULL;
        }
        else
            start = NULL;
        delete p;
        return 1;
    }
    else
        return 0;
}

int del_n(int n)
{
    elem *q=NULL, *p = start;
    if (start)
    {
        while ((p->key != n) && (p->next != NULL))
            p = p->next;

        if (p->key == n)
        {
            if (p->prev)
            {
                p->prev->next = p->next;
                if (p->next)
                    p->next->prev = p->prev;
            }
            else
            {
                if (p->next)
                {
                    p->next->prev = NULL;
                    start = p->next;
                }
                else
                    start = NULL;
            }
            delete p;
            return 1;
        }
        else
            return 0;
    }
    else
        return 0;
}

int del_e(int &n)
{
    elem *p = start;
    if (start)
    {
        while (p->next)
            p = p->next;
        n = p->key;
        if (p->prev)
            p->prev->next = NULL;
        else
            start = NULL;
        delete p;
        return 1;
    }
    else
        return 0;
}
void invert()
{
    elem *p = start, *q = NULL;
    while (p)
    {
        q = p->next;
        p->next = p->prev;
        p->prev = q;
        if (q == NULL)
            start = p;
        p = q;
    }
}

void list()
{
    elem *p = start;
    if (start)
        while (p)
        {   cout << p->key << "\t";
            p = p->next;
        }
    cout << "\n\n";
}

void printBack()
{
    elem *p = start;
    elem *b = NULL;
    cout << "Print back\n";
    while (p->next)
    {
        p = p->next;
    }
    b = p;
    while (b)
    {
        cout << b->key << endl;
        b = b->prev;
    }
}

int search(int k)
{
    int count = 0;
    elem *p = start;
    while (p) {
        if (p->key == k)
            count++;
        p = p->next;
    }
    return count;
}

int searchAt(int k)
{
    int count = 0;
    elem *p = start;
    bool found = true;
    while (p)
    {
        if (p->key == k)
        {
            found = true;
            break;
        }
        p = p->next;
        count++;
    }
    if (found)
        return count;
    else return -1;
}