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Engineering Computer Science EBK DATA STRUCTURES AND ALGORITHMS IN C

Program Plan: The functions used in the program are given as below: adjustTreeAfterNewNode()function is used to make the tree sorted if any new node is inserted. traverseTree() function is used to traverse the tree. The variables used are given below: k and num where p represents array of items and n represent number of elements in a row. Program Description: To write a function that prints the contents of a B-tree in ascending order. Function: voidadjustTreeAfterNewNode(int *k, int num){ // adjust already constricted tree when new node is inserted, this will ensure the tree remains sorted //*k represents the array of items in a node, num is the number of elements in a node int x, y, t; for (x = 0; x< num; x++) { for (y = i; y<= num; y++) { if (k[x]>k[y]) { // swap the key values if old key value is greater than the newely inserted value t = k[x]; k[x] = k[y]; k[y] = t; } } } } Once all the elements are added and the tree is adjusted by the above function on addition of each element. The below function can be used to traverse the sorted tree: void traverseTree(BTree *k){ // traverse the sorted tree cout<<end; int x; for (x = 0; x< k->n; x++) { if (k->l == false) { traverseTree(k->child_ptr[x]); } cout<< " " << k->d[x]; } if (k->l == false) { traverseTree(k->child_ptr[x]); } cout<<end; } Program Explanation: The adjustTreeAfterNewNode() function adjusts the newly inserted element in the given tree. The position of the newly inserted element is determined by this function to ensure that the tree remains sorted. The adjustTreeAfterNewNode() swaps the new value with already inserted values at given node if it satisfies the underlying condition − “k[x] > k[y]”. Each element is compared with other elements using the - for loops. The traverseTree() function prints the elements in a sorted tree. It visits each node and checksif it is a leaf node then it prints the value(s) for that node, else it moves to children of that node. The traverseTree() function can be termed as a function for in-order-traversal of the tree. Sample Program: #include<iostream> struct BTree { int *d; BTree &child_ptr; bool l; // identify if the node is a leaf node, l is true for leaf node int n; }*r = NULL, *np = NULL, *x = NULL; BTree* createTree() { int i; np = new BTree; np->d = new int[6];// assumimg order 6 np->child_ptr = new BTree *[7]; // possible children np->l = true; np->n = 0; for (i = 0; i< 7; i++) { np->child_ptr[i] = NULL; } return np; } void traverseTree(BTree *k){ // traverse the sorted tree cout<<end; int x; for (x = 0; x< k->n; x++) { if (k->l == false) { traverseTree (k->child_ptr[x]); } cout<< " " << k->d[x]; } if (k->l == false) { traverseTree (k->child_ptr[x]); } cout<<end; } voidadjustTreeAfterNewNode(int *k, int num){ // adjust already constricted tree when new node is inserted, this will ensure the tree remains sorted //*k represents the array of items in a node, num is the number of elements in a node int x, y, t; for (x = 0; x< num; x++) { for (y = i; y<= num; y++) { if (k[x] >k[y]) { // swap the key values if old key value is greater than the newely inserted value t = k[x]; k[x] = k[y]; k[y] = t; } } } } int split_child(BTree *x, int i) { // split the child node when height and order condition voilates int j, mid; BTree *np1, *np3, *y; np3 = createTree();//create new node np3->l = true; if (i == -1) { mid = x->d[2];//find mid x->d[2] = 0; x->n--; np1 = createTree(); np1->l= false; x->l= true; for (j = 3; j < 6; j++) { np3->d[j - 3] = x->d[j]; np3->child_ptr[j - 3] = x->child_ptr[j]; np3->n++; x->d[j] = 0; x->n--; } for (j = 0; j < 6; j++) { x->child_ptr[j] = NULL; } np1->d[0] = mid; np1->child_ptr[np1->n] = x; np1->child_ptr[np1->n + 1] = np3; np1->n++; r = np1; } else { y = x->child_ptr[i]; mid = y->d[2]; y->d[2] = 0; y->n--; for (j = 3; j <6 ; j++) { np3->d[j - 3] = y->d[j]; np3->n++; y->d[j] = 0; y->n--; } x->child_ptr[i + 1] = y; x->child_ptr[i + 1] = np3; } return mid; } void insert(int a) { int i, t; x = r; if (x == NULL) { r = createTree(); x = r; } else { if (x->l== true && x->n == 6) { t = split_child(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->child_ptr[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->child_ptr[i])->n == 6) { t = split_child(x, i); x->d[x->n] = t; x->n++; continue; } else { x = x->child_ptr[i]; } } } } x->d[x->n] = a; adjustTreeAfterNewNode(x->d, x->n); x->n++; } int main() { int i, n, t; cout<<"enter the number of elements to be inserted\n"; cin>>n; for(i = 0; i< n; i++) { cout<<"enter the element\n"; cin>>t; insert(t); } cout<<"traversal of sorted B tree\n"; traverseTree(r); } Sample Output: Assuming following elements are inserted in the tree: 50, 10, 30, 20, 70, 60, 40, 80, 90, 100, 5, 1 Output: 1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

Program Plan: The functions used in the program are given as below: adjustTreeAfterNewNode()function is used to make the tree sorted if any new node is inserted. traverseTree() function is used to traverse the tree. The variables used are given below: k and num where p represents array of items and n represent number of elements in a row. Program Description: To write a function that prints the contents of a B-tree in ascending order. Function: voidadjustTreeAfterNewNode(int k, int num){ // adjust already constricted tree when new node is inserted, this will ensure the tree remains sorted //k represents the array of items in a node, num is the number of elements in a node int x, y, t; for (x = 0; x< num; x++) { for (y = i; y<= num; y++) { if (k[x]>k[y]) { // swap the key values if old key value is greater than the newely inserted value t = k[x]; k[x] = k[y]; k[y] = t; } } } } Once all the elements are added and the tree is adjusted by the above function on addition of each element. The below function can be used to traverse the sorted tree: void traverseTree(BTree k){ // traverse the sorted tree cout<<end; int x; for (x = 0; x< k->n; x++) { if (k->l == false) { traverseTree(k->child_ptr[x]); } cout<< " " << k->d[x]; } if (k->l == false) { traverseTree(k->child_ptr[x]); } cout<<end; } Program Explanation: The adjustTreeAfterNewNode() function adjusts the newly inserted element in the given tree. The position of the newly inserted element is determined by this function to ensure that the tree remains sorted. The adjustTreeAfterNewNode() swaps the new value with already inserted values at given node if it satisfies the underlying condition − “k[x] > k[y]”. Each element is compared with other elements using the - for loops. The traverseTree() function prints the elements in a sorted tree. It visits each node and checksif it is a leaf node then it prints the value(s) for that node, else it moves to children of that node. The traverseTree() function can be termed as a function for in-order-traversal of the tree. Sample Program: #include<iostream> struct BTree { int d; BTree &child_ptr; bool l; // identify if the node is a leaf node, l is true for leaf node int n; }r = NULL, np = NULL, x = NULL; BTree createTree() { int i; np = new BTree; np->d = new int[6];// assumimg order 6 np->child_ptr = new BTree [7]; // possible children np->l = true; np->n = 0; for (i = 0; i< 7; i++) { np->child_ptr[i] = NULL; } return np; } void traverseTree(BTree k){ // traverse the sorted tree cout<<end; int x; for (x = 0; x< k->n; x++) { if (k->l == false) { traverseTree (k->child_ptr[x]); } cout<< " " << k->d[x]; } if (k->l == false) { traverseTree (k->child_ptr[x]); } cout<<end; } voidadjustTreeAfterNewNode(int k, int num){ // adjust already constricted tree when new node is inserted, this will ensure the tree remains sorted //k represents the array of items in a node, num is the number of elements in a node int x, y, t; for (x = 0; x< num; x++) { for (y = i; y<= num; y++) { if (k[x] >k[y]) { // swap the key values if old key value is greater than the newely inserted value t = k[x]; k[x] = k[y]; k[y] = t; } } } } int split_child(BTree x, int i) { // split the child node when height and order condition voilates int j, mid; BTree np1, np3, y; np3 = createTree();//create new node np3->l = true; if (i == -1) { mid = x->d[2];//find mid x->d[2] = 0; x->n--; np1 = createTree(); np1->l= false; x->l= true; for (j = 3; j < 6; j++) { np3->d[j - 3] = x->d[j]; np3->child_ptr[j - 3] = x->child_ptr[j]; np3->n++; x->d[j] = 0; x->n--; } for (j = 0; j < 6; j++) { x->child_ptr[j] = NULL; } np1->d[0] = mid; np1->child_ptr[np1->n] = x; np1->child_ptr[np1->n + 1] = np3; np1->n++; r = np1; } else { y = x->child_ptr[i]; mid = y->d[2]; y->d[2] = 0; y->n--; for (j = 3; j <6 ; j++) { np3->d[j - 3] = y->d[j]; np3->n++; y->d[j] = 0; y->n--; } x->child_ptr[i + 1] = y; x->child_ptr[i + 1] = np3; } return mid; } void insert(int a) { int i, t; x = r; if (x == NULL) { r = createTree(); x = r; } else { if (x->l== true && x->n == 6) { t = split_child(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->child_ptr[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->child_ptr[i])->n == 6) { t = split_child(x, i); x->d[x->n] = t; x->n++; continue; } else { x = x->child_ptr[i]; } } } } x->d[x->n] = a; adjustTreeAfterNewNode(x->d, x->n); x->n++; } int main() { int i, n, t; cout<<"enter the number of elements to be inserted\n"; cin>>n; for(i = 0; i< n; i++) { cout<<"enter the element\n"; cin>>t; insert(t); } cout<<"traversal of sorted B tree\n"; traverseTree(r); } Sample Output: Assuming following elements are inserted in the tree: 50, 10, 30, 20, 70, 60, 40, 80, 90, 100, 5, 1 Output: 1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

Solution Summary: The author explains how the adjustTreeAfterNewNode() function is used to make the tree sorted if any new node is inserted.

EBK DATA STRUCTURES AND ALGORITHMS IN C

EBK DATA STRUCTURES AND ALGORITHMS IN C

4th Edition

ISBN: 9781285415017

Author: DROZDEK

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EBK DATA STRUCTURES AND ALGORITHMS IN C

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