m-WAY Search Trees | Set-1 ( Searching )
The m-way search trees are multi-way trees which are generalised versions of binary trees where each node contains multiple elements. In an m-Way tree of order m, each node contains a maximum of m – 1 elements and m children.
The goal of m-Way search tree of height h calls for O(h) no. of accesses for an insert/delete/retrieval operation. Hence, it ensures that the height h is close to log_m(n + 1).
The number of elements in an m-Way search tree of height h ranges from a minimum of h to a maximum of 
.
An m-Way search tree of n elements ranges from a minimum height of log_m(n+1) to a maximum of n
An example of a 5-Way search tree is shown in the figure below. Observe how each node has at most 5 child nodes & therefore has at most 4 keys contained in it.
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The structure of a node of an m-Way tree is given below:
C++
struct node { int count; int value[MAX + 1]; struct node* child[MAX + 1];}; |
Python3
class node: def __init__(self): self.count = -1 self.value = [-1]*(MAX + 1) self.child = [None]*(MAX + 1) |
- Here, count represents the number of children that a particular node has
- The values of a node stored in the array value
- The addresses of child nodes are stored in the child array
- The MAX macro signifies the maximum number of values that a particular node can contain
Searching in an m-Way search tree:
- Searching for a key in an m-Way search tree is similar to that of binary search tree
- To search for 77 in the 5-Way search tree, shown in the figure, we begin at the root & as 77> 76> 44> 18, move to the fourth sub-tree
- In the root node of the fourth sub-tree, 77< 80 & therefore we move to the first sub-tree of the node. Since 77 is available in the only node of this sub-tree, we claim 77 was successfully searched
C++
// Searches value in the nodestruct node* search(int val, struct node* root, int* pos){ // if root is Null then return if (root == NULL) return NULL; else { // if node is found if (searchnode(val, root, pos)) return root; // if not then search in child nodes else return search(val, root->child[*pos], pos); }}// Searches the nodeint searchnode(int val, struct node* n, int* pos){ // if val is less than node->value[1] if (val < n->value[1]) { *pos = 0; return 0; } // if the val is greater else { *pos = n->count; // check in the child array // for correct position while ((val < n->value[*pos]) && *pos > 1) (*pos)--; if (val == n->value[*pos]) return 1; else return 0; }} |
Python3
# Searches value in the nodedef search(val, root, pos): # if root is None then return if (root == None): return None else : # if node is found if (searchnode(val, root, pos)): return root # if not then search in child nodes else: return search(val, root.child[pos], pos) # Searches the nodedef searchnode(val, n, pos): # if val is less than node.value[1] if (val < n.value[1]): pos = 0 return 0 # if the val is greater else : pos = n.count # check in the child array # for correct position while ((val < n.value[pos]) and pos > 1): pos-=1 if (val == n.value[pos]): return 1 else: return 0 |
search():
- The function search() receives three parameters
- The first parameter is the value to be searched, second is the address of the node from where the search is to be performed and third is the address of a variable that is used to store the position of the value once found
- Initially a condition is checked whether the address of the node being searched is NULL
- If it is, then simply a NULL value is returned
- Otherwise, a function searchnode() is called which actually searches the given value
- If the search is successful the address of the node in which the value is found is returned
- If the search is unsuccessful then a recursive call is made to the search() function for the child of the current node
searchnode():
- The function searchnode() receives three parameters
- The first parameter is the value that is to be searched
- The second parameter is the address of the node in which the search is to be performed and third is a pointer pos that holds the address of a variable in which the position of the value that once found is stored
- This function returns a value 0 if the search is unsuccessful and 1 if it is successful
- In this function initially it is checked whether the value that is to be searched is less than the very first value of the node
- If it is then it indicates that the value is not present in the current node. Hence, a value 0 is assigned in the variable that is pointed to by pos and 0 is returned, as the search is unsuccessful
