Dalam tutorial ini, anda akan belajar bagaimana memasukkan kunci ke dalam btree. Anda juga akan mendapat contoh kerja memasukkan kunci ke dalam pohon B di C, C ++, Java dan Python.
Memasukkan elemen pada B-tree terdiri daripada dua peristiwa: mencari nod yang sesuai untuk memasukkan elemen dan membelah nod jika diperlukan. Operasi pemasukan selalu berlaku dalam pendekatan bawah-atas.
Mari kita fahami peristiwa ini di bawah.
Operasi Pemasangan
- Sekiranya pokok kosong, peruntukkan simpul akar dan masukkan kuncinya.
- Kemas kini bilangan kunci yang dibenarkan dalam nod.
- Cari node yang sesuai untuk dimasukkan.
- Sekiranya simpul penuh, ikuti langkah di bawah.
- Masukkan elemen dalam urutan yang semakin meningkat.
- Sekarang, ada unsur yang lebih besar daripada hadnya. Jadi, berpecah di median.
- Tekan kekunci median ke atas dan jadikan kekunci kiri sebagai anak kiri dan kunci kanan sebagai anak kanan.
- Sekiranya nod tidak penuh, ikuti langkah di bawah.
- Masukkan nod dalam urutan yang semakin meningkat.
Contoh Penyisipan
Mari kita fahami operasi penyisipan dengan ilustrasi di bawah.
Elemen yang akan dimasukkan ialah 8, 9, 10, 11, 15, 16, 17, 18, 20, 23.
Memasukkan unsur ke dalam pokok B
Algoritma untuk Memasukkan Elemen
BreeInsertion(T, k) r root(T) if n(r) = 2t - 1 s = AllocateNode() root(T) = s leaf(s) = FALSE n(s) <- 0 c1(s) <- r BtreeSplitChild(s, 1, r) BtreeInsertNonFull(s, k) else BtreeInsertNonFull(r, k) BtreeInsertNonFull(x, k) i = n(x) if leaf(x) while i ≧ 1 and k < keyi(x) keyi+1 (x) = keyi(x) i = i - 1 keyi+1(x) = k n(x) = n(x) + 1 else while i ≧ 1 and k < keyi(x) i = i - 1 i = i + 1 if n(ci(x)) == 2t - 1 BtreeSplitChild(x, i, ci(x)) if k &rt; keyi(x) i = i + 1 BtreeInsertNonFull(ci(x), k) BtreeSplitChild(x, i) BtreeSplitChild(x, i, y) z = AllocateNode() leaf(z) = leaf(y) n(z) = t - 1 for j = 1 to t - 1 keyj(z) = keyj+t(y) if not leaf (y) for j = 1 to t cj(z) = cj + t(y) n(y) = t - 1 for j = n(x) + 1 to i + 1 cj+1(x) = cj(x) ci+1(x) = z for j = n(x) to i keyj+1(x) = keyj(x) keyi(x) = keyt(y) n(x) = n(x) + 1
Contoh Python, Java dan C / C ++
Python Java C C ++# Inserting a key on a B-tree in Python # Create a node class BTreeNode: def __init__(self, leaf=False): self.leaf = leaf self.keys = () self.child = () # Tree class BTree: def __init__(self, t): self.root = BTreeNode(True) self.t = t # Insert node def insert(self, k): root = self.root if len(root.keys) == (2 * self.t) - 1: temp = BTreeNode() self.root = temp temp.child.insert(0, root) self.split_child(temp, 0) self.insert_non_full(temp, k) else: self.insert_non_full(root, k) # Insert nonfull def insert_non_full(self, x, k): i = len(x.keys) - 1 if x.leaf: x.keys.append((None, None)) while i>= 0 and k(0) = 0 and k(0) x.keys(i)(0): i += 1 self.insert_non_full(x.child(i), k) # Split the child def split_child(self, x, i): t = self.t y = x.child(i) z = BTreeNode(y.leaf) x.child.insert(i + 1, z) x.keys.insert(i, y.keys(t - 1)) z.keys = y.keys(t: (2 * t) - 1) y.keys = y.keys(0: t - 1) if not y.leaf: z.child = y.child(t: 2 * t) y.child = y.child(0: t - 1) # Print the tree def print_tree(self, x, l=0): print("Level ", l, " ", len(x.keys), end=":") for i in x.keys: print(i, end=" ") print() l += 1 if len(x.child)> 0: for i in x.child: self.print_tree(i, l) def main(): B = BTree(3) for i in range(10): B.insert((i, 2 * i)) B.print_tree(B.root) if __name__ == '__main__': main() // Inserting a key on a B-tree in Java public class BTree ( private int T; // Node Creation public class Node ( int n; int key() = new int(2 * T - 1); Node child() = new Node(2 * T); boolean leaf = true; public int Find(int k) ( for (int i = 0; i < this.n; i++) ( if (this.key(i) == k) ( return i; ) ) return -1; ); ) public BTree(int t) ( T = t; root = new Node(); root.n = 0; root.leaf = true; ) private Node root; // split private void split(Node x, int pos, Node y) ( Node z = new Node(); z.leaf = y.leaf; z.n = T - 1; for (int j = 0; j < T - 1; j++) ( z.key(j) = y.key(j + T); ) if (!y.leaf) ( for (int j = 0; j = pos + 1; j--) ( x.child(j + 1) = x.child(j); ) x.child(pos + 1) = z; for (int j = x.n - 1; j>= pos; j--) ( x.key(j + 1) = x.key(j); ) x.key(pos) = y.key(T - 1); x.n = x.n + 1; ) // insert key public void insert(final int key) ( Node r = root; if (r.n == 2 * T - 1) ( Node s = new Node(); root = s; s.leaf = false; s.n = 0; s.child(0) = r; split(s, 0, r); _insert(s, key); ) else ( _insert(r, key); ) ) // insert node final private void _insert(Node x, int k) ( if (x.leaf) ( int i = 0; for (i = x.n - 1; i>= 0 && k = 0 && k x.key(i)) ( i++; ) ) _insert(x.child(i), k); ) ) public void display() ( display(root); ) // Display the tree private void display(Node x) ( assert (x == null); for (int i = 0; i < x.n; i++) ( System.out.print(x.key(i) + " "); ) if (!x.leaf) ( for (int i = 0; i < x.n + 1; i++) ( display(x.child(i)); ) ) ) public static void main(String() args) ( BTree b = new BTree(3); b.insert(8); b.insert(9); b.insert(10); b.insert(11); b.insert(15); b.insert(20); b.insert(17); b.display(); ) ) // insertioning a key on a B-tree in C #include #include #define MAX 3 #define MIN 2 struct btreeNode ( int item(MAX + 1), count; struct btreeNode *link(MAX + 1); ); struct btreeNode *root; // Node creation struct btreeNode *createNode(int item, struct btreeNode *child) ( struct btreeNode *newNode; newNode = (struct btreeNode *)malloc(sizeof(struct btreeNode)); newNode->item(1) = item; newNode->count = 1; newNode->link(0) = root; newNode->link(1) = child; return newNode; ) // Insert void insertValue(int item, int pos, struct btreeNode *node, struct btreeNode *child) ( int j = node->count; while (j> pos) ( node->item(j + 1) = node->item(j); node->link(j + 1) = node->link(j); j--; ) node->item(j + 1) = item; node->link(j + 1) = child; node->count++; ) // Split node void splitNode(int item, int *pval, int pos, struct btreeNode *node, struct btreeNode *child, struct btreeNode **newNode) ( int median, j; if (pos> MIN) median = MIN + 1; else median = MIN; *newNode = (struct btreeNode *)malloc(sizeof(struct btreeNode)); j = median + 1; while (j item(j - median) = node->item(j); (*newNode)->link(j - median) = node->link(j); j++; ) node->count = median; (*newNode)->count = MAX - median; if (pos item(node->count); (*newNode)->link(0) = node->link(node->count); node->count--; ) // Set the value of node int setNodeValue(int item, int *pval, struct btreeNode *node, struct btreeNode **child) ( int pos; if (!node) ( *pval = item; *child = NULL; return 1; ) if (item item(1)) ( pos = 0; ) else ( for (pos = node->count; (item item(pos) && pos> 1); pos--) ; if (item == node->item(pos)) ( printf("Duplicates not allowed"); return 0; ) ) if (setNodeValue(item, pval, node->link(pos), child)) ( if (node->count link(pos); for (; dummy->link(0) != NULL;) dummy = dummy->link(0); myNode->item(pos) = dummy->item(1); ) // Do rightshift void rightShift(struct btreeNode *myNode, int pos) ( struct btreeNode *x = myNode->link(pos); int j = x->count; while (j> 0) ( x->item(j + 1) = x->item(j); x->link(j + 1) = x->link(j); ) x->item(1) = myNode->item(pos); x->link(1) = x->link(0); x->count++; x = myNode->link(pos - 1); myNode->item(pos) = x->item(x->count); myNode->link(pos) = x->link(x->count); x->count--; return; ) // Do leftshift void leftShift(struct btreeNode *myNode, int pos) ( int j = 1; struct btreeNode *x = myNode->link(pos - 1); x->count++; x->item(x->count) = myNode->item(pos); x->link(x->count) = myNode->link(pos)->link(0); x = myNode->link(pos); myNode->item(pos) = x->item(1); x->link(0) = x->link(1); x->count--; while (j count) ( x->item(j) = x->item(j + 1); x->link(j) = x->link(j + 1); j++; ) return; ) // Merge the nodes void mergeNodes(struct btreeNode *myNode, int pos) ( int j = 1; struct btreeNode *x1 = myNode->link(pos), *x2 = myNode->link(pos - 1); x2->count++; x2->item(x2->count) = myNode->item(pos); x2->link(x2->count) = myNode->link(0); while (j count) ( x2->count++; x2->item(x2->count) = x1->item(j); x2->link(x2->count) = x1->link(j); j++; ) j = pos; while (j count) ( myNode->item(j) = myNode->item(j + 1); myNode->link(j) = myNode->link(j + 1); j++; ) myNode->count--; free(x1); ) // Adjust the node void adjustNode(struct btreeNode *myNode, int pos) ( if (!pos) ( if (myNode->link(1)->count> MIN) ( leftShift(myNode, 1); ) else ( mergeNodes(myNode, 1); ) ) else ( if (myNode->count != pos) ( if (myNode->link(pos - 1)->count> MIN) ( rightShift(myNode, pos); ) else ( if (myNode->link(pos + 1)->count> MIN) ( leftShift(myNode, pos + 1); ) else ( mergeNodes(myNode, pos); ) ) ) else ( if (myNode->link(pos - 1)->count> MIN) rightShift(myNode, pos); else mergeNodes(myNode, pos); ) ) ) // Traverse the tree void traversal(struct btreeNode *myNode) ( int i; if (myNode) ( for (i = 0; i count; i++) ( traversal(myNode->link(i)); printf("%d ", myNode->item(i + 1)); ) traversal(myNode->link(i)); ) ) int main() ( int item, ch; insertion(8); insertion(9); insertion(10); insertion(11); insertion(15); insertion(16); insertion(17); insertion(18); insertion(20); insertion(23); traversal(root); )// Inserting a key on a B-tree in C++ #include using namespace std; class Node ( int *keys; int t; Node **C; int n; bool leaf; public: Node(int _t, bool _leaf); void insertNonFull(int k); void splitChild(int i, Node *y); void traverse(); friend class BTree; ); class BTree ( Node *root; int t; public: BTree(int _t) ( root = NULL; t = _t; ) void traverse() ( if (root != NULL) root->traverse(); ) void insert(int k); ); Node::Node(int t1, bool leaf1) ( t = t1; leaf = leaf1; keys = new int(2 * t - 1); C = new Node *(2 * t); n = 0; ) // Traverse the nodes void Node::traverse() ( int i; for (i = 0; i traverse(); cout << " "
keys(0) = k; root->n = 1; ) else ( if (root->n == 2 * t - 1) ( Node *s = new Node(t, false); s->C(0) = root; s->splitChild(0, root); int i = 0; if (s->keys(0) C(i)->insertNonFull(k); root = s; ) else root->insertNonFull(k); ) ) // Insert non full condition void Node::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) insertNonFull(k); ) ) // split the child void Node::splitChild(int i, Node *y) ( Node *z = new Node(y->t, y->leaf); z->n = t - 1; for (int j = 0; j keys(j) = y->keys(j + t); if (y->leaf == false) ( for (int j = 0; j 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(8); t.insert(9); t.insert(10); t.insert(11); t.insert(15); t.insert(16); t.insert(17); t.insert(18); t.insert(20); t.insert(23); cout << "The B-tree is: "; t.traverse(); ) 
