Question

Please provide the big oh notation for running time and space complexity for the following methods (splay, findSplay, putSplay, eraseSplay:

void

SplayTreeMap::splay(Node* x) {

  

if(x!=NULL){

while (x -> parent != NULL )

{

Node *p = x -> parent;

Node *g = p -> parent;

if (g == NULL) zig(x);

else if (g -> left == p && p -> left == x) zigZig(x);

else if (g -> right == p && p -> right == x) zigZig(x);

else zigZag(x);

}

this -> root = x;

}

}

Node*

SplayTreeMap::findSplay(string k) {

Node** wAndZ = this->find(k);

Node* w = wAndZ[0]; // w is the node with key k, if it exists, or NULL otherwise

Node* z = wAndZ[1]; // z is the parent of node w, or if w is NULL, the last node found while searching for key k

if(w!=NULL){

delete wAndZ;

Node* x = (w) ? w : z;

this->splay(x);

return x;

}

else{

return NULL;

}

}

Node*

SplayTreeMap::putSplay(string k, int v) {

Node* x = this->put(k,v);

this->splay(x);

return x;

}

Node*

SplayTreeMap::eraseSplay(string k) {

Node* x = this->erase(k);

this->splay(x);

return x;

}

Answer 1

Splay Tree is nothing but it is a self-balanced binary search tree with having some additional property that are accessing the elements which are quick to access again.

• The Big oh notation for running time and space complexity for the following method (splay or zigZig):

Time complexity in Average case:   O (log N)

Time complexity in Worst case:      O (log N)

Space complexity in Worst case:     O (N)

• The Big oh notation for running time and space complexity for the following method (findSplay):

Time complexity in Average case:   O (log N)

Time complexity in Worst case:      O (log N)

Space complexity in Worst case:     O (N)

• The Big oh notation for running time and space complexity for the following method (putSplay):

Time complexity in Average case:   O (log N)

Time complexity in Worst case:      O (log N)

Space complexity in Worst case:     O (N)

• The Big oh notation for running time and space complexity for the following method (eraseSplay):

Time complexity in Average case:   O (log N)

Time complexity in Worst case:      O (log N)

Space complexity in Worst case:     O (N)