From the given inputs, your task is to create a B Tree and perform insertion, deletion operations. At last, traverse the resultant B Tree (Pre Order Traversal) and print the result.

Input:

First line contains an integer T: represents the degree of the B Tree   (T>2)

Second line contains an Array A: represents the elements to be inserted into the B Tree from left to right (A can contain zero or more elements)

Third Line contains an Array B: represents the element to be deleted from the B Tree from left to right (After the completion of insertion of Array A)   (B can contain zero or more elements)


Output:

Print the Pre-order traversal of the B Tree and “None” if there are no elements in the tree.

Using Java code

To implement a B-Tree in Java and perform the specified insertion, deletion, and traversal operations, we need to follow these steps:

1. Define the structure of the B-Tree node.
2. Implement the insertion and deletion operations.
3. Implement the pre-order traversal.
4. Handle input/output according to the problem statement.

Here is the Java code to achieve this:

```java
import java.util.ArrayList;
import java.util.Scanner;

// Class to represent a B-Tree node
class BTreeNode {
    int[] keys;  // Array of keys
    int t;  // Minimum degree (defines the range for number of keys)
    BTreeNode[] children;  // Array of child pointers
    int n;  // Current number of keys
    boolean leaf;  // Is true when node is leaf. Otherwise false

    // Constructor
    BTreeNode(int t, boolean leaf) {
        this.t = t;
        this.leaf = leaf;
        this.keys = new int[2 * t - 1];
        this.children = new BTreeNode[2 * t];
        this.n = 0;
    }

    // A utility function to insert a new key in this node
    void insertNonFull(int key) {
        int i = n - 1;
        
        if (leaf) {
            while (i >= 0 && keys[i] > key) {
                keys[i + 1] = keys[i];
                i--;
            }
            keys[i + 1] = key;
            n = n + 1;
        } else {
            while (i >= 0 && keys[i] > key) {
                i--;
            }
            if (children[i + 1].n == 2 * t - 1) {
                splitChild(i + 1, children[i + 1]);
                if (keys[i + 1] < key) {
                    i++;
                }
            }
            children[i + 1].insertNonFull(key);
        }
    }

    // A utility function to split the child y of this node
    void 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) {
            for (int j = 0; j < t; j++) {
                z.children[j] = y.children[j + t];
            }
        }
        
        y.n = t - 1;
        
        for (int j = n; j >= i + 1; j--) {
            children[j + 1] = children[j];
        }
        
        children[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;
    }

    // A function to perform Pre-order traversal of the tree
    void traversePreOrder() {
        for (int i = 0; i < n; i++) {
            System.out.print(keys[i] + " ");
        }
        if (!leaf) {
            for (int i = 0; i <= n; i++) {
                children[i].traversePreOrder();
            }
        }
    }

    // Function to remove a key from the sub-tree rooted with this node
    void remove(int key) {
        int idx = findKey(key);

        if (idx < n && keys[idx] == key) {
            if (leaf) {
                removeFromLeaf(idx);
            } else {
                removeFromNonLeaf(idx);
            }
        } else {
            if (leaf) {
                return;
            }

            boolean flag = (idx == n);
            if (children[idx].n < t) {
                fill(idx);
            }

            if (flag && idx > n) {
                children[idx - 1].remove(key);
            } else {
                children[idx].remove(key);
            }
        }
    }

    int findKey(int key) {
        int idx = 0;
        while (idx < n && keys[idx] < key) {
            idx++;
        }
        return idx;
    }

    void removeFromLeaf(int idx) {
        for (int i = idx + 1; i < n; i++) {
            keys[i - 1] = keys[i];
        }
        n--;
    }

    void removeFromNonLeaf(int idx) {
        int key = keys[idx];
        
        if (children[idx].n >= t) {
            int pred = getPredecessor(idx);
            keys[idx] = pred;
            children[idx].remove(pred);
        } else if (children[idx + 1].n >= t) {
            int succ = getSuccessor(idx);
            keys[idx] = succ;
            children[idx + 1].remove(succ);
        } else {
            merge(idx);
            children[idx].remove(key);
        }
    }

    int getPredecessor(int idx) {
        BTreeNode curr = children[idx];
        while (!curr.leaf) {
            curr = curr.children[curr.n];
        }
        return curr.keys[curr.n - 1];
    }

    int getSuccessor(int idx) {
        BTreeNode curr = children[idx + 1];
        while (!curr.leaf) {
            curr = curr.children[0];
        }
        return curr.keys[0];
    }

    void fill(int idx) {
        if (idx != 0 && children[idx - 1].n >= t) {
            borrowFromPrev(idx);
        } else if (idx != n && children[idx + 1].n >= t) {
            borrowFromNext(idx);
        } else {
            if (idx != n) {
                merge(idx);
            } else {
                merge(idx - 1);
            }
        }
    }

    void borrowFromPrev(int idx) {
        BTreeNode child = children[idx];
        BTreeNode sibling = children[idx - 1];

        for (int i = child.n - 1; i >= 0; i--) {
            child.keys[i + 1] = child.keys[i];
        }

        if (!child.leaf) {
            for (int i = child.n; i >= 0; i--) {
                child.children[i + 1] = child.children[i];
            }
        }

        child.keys[0] = keys[idx - 1];

        if (!leaf) {
            child.children[0] = sibling.children[sibling.n];
        }

        keys[idx - 1] = sibling.keys[sibling.n - 1];
        child.n++;
        sibling.n--;
    }

    void borrowFromNext(int idx) {
        BTreeNode child = children[idx];
        BTreeNode sibling = children[idx + 1];

        child.keys[child.n] = keys[idx];

        if (!child.leaf) {
            child.children[child.n + 1] = sibling.children[0];
        }

        keys[idx] = sibling.keys[0];

        for (int i = 1; i < sibling.n; i++) {
            sibling.keys[i - 1] = sibling.keys[i];
        }

        if (!sibling.leaf) {
            for (int i = 1; i <= sibling.n; i++) {
                sibling.children[i - 1] = sibling.children[i];
            }
        }

        child.n++;
        sibling.n--;
    }

    void merge(int idx) {
        BTreeNode child = children[idx];
        BTreeNode sibling = children[idx + 1];

        child.keys[t - 1] = keys[idx];

        for (int i = 0; i < sibling.n; i++) {
            child.keys[i + t] = sibling.keys[i];
        }

        if (!child.leaf) {
            for (int i = 0; i <= sibling.n; i++) {
                child.children[i + t] = sibling.children[i];
            }
        }

        for (int i = idx + 1; i < n; i++) {
            keys[i - 1] = keys[i];
        }

        for (int i = idx + 2; i <= n; i++) {
            children[i - 1] = children[i];
        }

        child.n += sibling.n + 1;
        n--;
    }
}

// Class for the B-Tree
class BTree {
    BTreeNode root;  // Pointer to root node
    int t;  // Minimum degree

    // Constructor
    BTree(int t) {
        this.root = null;
        this.t = t;
    }

    // Function to traverse the tree in Pre-order
    void traversePreOrder() {
        if (root != null) {
            root.traversePreOrder();
        } else {
            System.out.print("None");
        }
        System.out.println();
    }

    // Function to insert a new key in the B-Tree
    void insert(int key) {
        if (root == null) {
            root = new BTreeNode(t, true);
            root.keys[0] = key;
            root.n = 1;
        } else {
            if (root.n == 2 * t - 1) {
                BTreeNode newRoot = new BTreeNode(t, false);
                newRoot.children[0] = root;
                newRoot.splitChild(0, root);

                int i = 0;
                if (newRoot.keys[0] < key) {
                    i++;
                }
                newRoot.children[i

Learn how to implement B-Tree operations (insertion, deletion, and traversal) in Java. This tutorial covers step-by-step instructions for creating and manipulating B-Trees using Java code. Suitable for college-level computer science students and professionals.

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