5

#include <iostream>
#include <vector>

using namespace std;

class BTreeNode {
    int* keys;
    int t;
    BTreeNode** C;
    int n;
    bool leaf;

public:
    BTreeNode(int _t, bool _leaf);

    void traverse();

    BTreeNode* search(int k);

    void insertNonFull(int k);

    void splitChild(int i, BTreeNode* y);

    friend class BTree;
};

class BTree {
    BTreeNode* root;
    int t;

public:
    BTree(int _t) {
        root = NULL;
        t = _t;
    }

    void traverse() {
        if (root != NULL)
            root->traverse();
    }

    BTreeNode* search(int k) {
        return (root == NULL) ? NULL : root->search(k);
    }

    void insert(int k);
};

BTreeNode::BTreeNode(int t1, bool leaf1) {
    t = t1;
    leaf = leaf1;
    keys = new int[2 * t - 1];
    C = new BTreeNode*[2 * t];
    n = 0;
}

void BTreeNode::traverse() {
    int i;
    for (i = 0; i < n; i++) {
        if (leaf == false)
            C[i]->traverse();
        cout << " " << keys[i];
    }
    if (leaf == false)
        C[i]->traverse();
}

BTreeNode* BTreeNode::search(int k) {
    int i = 0;
    while (i < n && k > keys[i])
        i++;
    if (keys[i] == k)
        return this;
    if (leaf == true)
        return NULL;
    return C[i]->search(k);
}

void BTree::insert(int k) {
    if (root == NULL) {
        root = new BTreeNode(t, true);
        root->keys[0] = k;
        root->n = 1;
    } else {
        if (root->n == 2 * t - 1) {
            BTreeNode* s = new BTreeNode(t, false);
            s->C[0] = root;
            s->splitChild(0, root);
            int i = 0;
            if (s->keys[0] < k)
                i++;
            s->C[i]->insertNonFull(k);
            root = s;
        } else
            root->insertNonFull(k);
    }
}

void BTreeNode::insertNonFull(int k) {
    int i = n - 1;
    if (leaf == true) {
        while (i >= 0 && keys[i] > k) {
            keys[i + 1] = keys[i];
            i--;
        }
        keys[i + 1] = k;
        n = n + 1;
    } else {
        while (i >= 0 && keys[i] > k)
            i--;
        if (C[i + 1]->n == 2 * t - 1) {
            splitChild(i + 1, C[i + 1]);
            if (keys[i + 1] < k)
                i++;
        }
        C[i + 1]->insertNonFull(k);
    }
}

void BTreeNode::splitChild(int i, BTreeNode* y) {
    BTreeNode* z = new BTreeNode(y->t, y->leaf);
    z->n = t - 1;
    for (int j = 0; j < t - 1; j++)
        z->keys[j] = y->keys[j + t];
    if (y->leaf == false) {
        for (int j = 0; j < t; j++)
            z->C[j] = y->C[j + t];
    }
    y->n = t - 1;
    for (int j = n; j >= i + 1; j--)
        C[j + 1] = C[j];
    C[i + 1] = z;
    for (int j = n - 1; j >= i; j--)
        keys[j + 1] = keys[j];
    keys[i] = y->keys[t - 1];
    n = n + 1;
}

int main() {
    BTree t(3); 
    t.insert(10);
    t.insert(20);
    t.insert(5);
    t.insert(6);
    t.insert(12);
    t.insert(30);
    t.insert(7);
    t.insert(17);

    cout << "Traversal of the constucted tree is ";
    t.traverse();
    cout << endl;

    int k = 6;
    cout << "Key " << k << " is: ";
    (t.search(k) != NULL) ? cout << "Present" : cout << "Not Present";
    cout << endl;

    k = 15;
    cout << "Key " << k << " is: ";
    (t.search(k) != NULL) ? cout << "Present" : cout << "Not Present";
    cout << endl;

    return 0;
}