Which is the common data structure to implement a relational database?
Answer: Relational databases commonly uses B-tree indexes for data retrieval.
Time Complexity of B-Tree:
| Sr. No. | Algorithm | Time Complexity |
| 1 | Add | O(log n) |
| 1 | Delete | O(log n) |
| 2 | Search | O(log n) |
C++ Program to implement B-tree
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// B Tree is the Common data structure to implement relational database #include<iostream> using namespace std; struct BTree//node declaration { int *d; BTree **derived_Pointer; bool l; int n; }*r = NULL, *New_Pointer = NULL, *x = NULL; BTree* init()//creation of node { int i; New_Pointer = new BTree; New_Pointer->d = new int[6];//order 6 New_Pointer->derived_Pointer = new BTree *[7]; New_Pointer->l = true; New_Pointer->n = 0; for (i = 0; i < 7; i++) { New_Pointer->derived_Pointer[i] = NULL; } return New_Pointer; } void traversal_of_B_Tree(BTree *p)//traversal_of_B_Tree { cout<<endl<<endl;; int i; for (i = 0; i < p->n; i++) { if (p->l == false) { traversal_of_B_Tree(p->derived_Pointer[i]); } cout << " " << p->d[i]; } if (p->l == false) { traversal_of_B_Tree(p->derived_Pointer[i]); } cout<<endl<<endl;; } void sort(int *p, int n)//sorting the B tree { int i, j, t; for (i = 0; i < n; i++) { for (j = i; j <= n; j++) { if (p[i] >p[j]) { t = p[i]; p[i] = p[j]; p[j] = t; } } } } int Child_Division(BTree *x, int i) { int j, mid; BTree *New_Pointer1, *New_Pointer3, *y; New_Pointer3 = init();//create new node New_Pointer3->l = true; if (i == -1) { mid = x->d[2];//find mid x->d[2] = 0; x->n--; New_Pointer1 = init(); New_Pointer1->l= false; x->l= true; for (j = 3; j < 6; j++) { New_Pointer3->d[j - 3] = x->d[j]; New_Pointer3->derived_Pointer[j - 3] = x->derived_Pointer[j]; New_Pointer3->n++; x->d[j] = 0; x->n--; } for (j = 0; j < 6; j++) { x->derived_Pointer[j] = NULL; } New_Pointer1->d[0] = mid; New_Pointer1->derived_Pointer[New_Pointer1->n] = x; New_Pointer1->derived_Pointer[New_Pointer1->n + 1] = New_Pointer3; New_Pointer1->n++; r = New_Pointer1; } else { y = x->derived_Pointer[i]; mid = y->d[2]; y->d[2] = 0; y->n--; for (j = 3; j <6 ; j++) { New_Pointer3->d[j - 3] = y->d[j]; New_Pointer3->n++; y->d[j] = 0; y->n--; } x->derived_Pointer[i + 1] = y; x->derived_Pointer[i + 1] = New_Pointer3; } return mid; } void insert(int a) { int i, t; x = r; if (x == NULL) { r = init(); x = r; } else { if (x->l== true && x->n == 6) { t = Child_Division(x, -1); x = r; for (i = 0; i < (x->n); i++) { if ((a >x->d[i]) && (a < x->d[i + 1])) { i++; break; } else if (a < x->d[0]) { break; } else { continue; } } x = x->derived_Pointer[i]; } else { while (x->l == false) { for (i = 0; i < (x->n); i++) { if ((a >x->d[i]) && (a < x->d[i + 1])) { i++; break; } else if (a < x->d[0]) { break; } else { continue; } } if ((x->derived_Pointer[i])->n == 6) { t = Child_Division(x, i); x->d[x->n] = t; x->n++; continue; } else { x = x->derived_Pointer[i]; } } } } x->d[x->n] = a; sort(x->d, x->n); x->n++; } int main() { int i, n, t; cout<<"Please tell that how much elements you want to insert?\n"; cin>>n; for(i = 0; i < n; i++) { cout<<"Please enter the element:n"; cin>>t; insert(t); } cout<<"The traversal of constructed B tree is:\n"; traversal_of_B_Tree(r); } |
Output
Please tell that how much elements you want to insert?2
Please enter the element: 3
Please enter the element: 4
The traversal of constructed B tree is:
3Â Â 4