Floating in a Tree

If you have a priority queue setup of many nodes. Lets say we want to bring the node with the highest value to the top . IN orther words if i have given a heap than how do i modify the heap so that the biggest element is always present at the root.

One simple logic can be . Given a root node of a subtree .

• Assume the root node is the largest node .
  
• Now compare the value of root node with left child and mark the one with the bigger value as biggest
• Then compare biggest with the right child now and make the bigger of the two as the new biggest.
• now repeat the above mentioned steps with the new largest node

In terms of code this looks like :

void maxHeapify(int * a,int rootIndex, int heapLength){
int largest = rootIndex;
int leftIndex = left(rootIndex);
int rightIndex = right(rootIndex);

if(leftIndex < heapLength && a[rootIndex] < a[leftIndex]){
largest = leftIndex;
}
if(rightIndex < heapLength && a[largest] < a[rightIndex]){
largest = rightIndex;
}
if(largest != rootIndex){
swap(a[largest],a[rootIndex]);
maxHeapify(a,largest,heapLength);
}
}

The worst case time for floating a node to any another node depending on your optimization would be approximately equal to the height of the tree , which would generally result in something like ~ lg(N) . To give a counter example for a max Heap operating in a heap . lets give a value of 0 to the root , and let all the other nodes be 1 . In that case the program would go all the way down the heap till the last leaf .