m-WAY Search Trees | Set-1 ( Searching )

Difficulty Level : Hard
Last Updated : 20 Aug, 2019

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 $m^{h} -1$ .

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.

The structure of a node of an m-Way tree is given below:

struct node {
    int count;
    int value[MAX + 1];
    struct node* child[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

// Searches value in the node
struct 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 node
int 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;
    }
}

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

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