##### An operator delete(i) for a binary heap data structure is to be designed to delete the item in the i-th node.

An operator delete(i) for a binary heap data structure is to be designed to delete the item in the i-th node. Assume that the heap is implemented in an array and i refers to the i-th index of the array. If the heap tree has depth d (number of edges on the path from the root to the farthest leaf ), then what is the time complexity to re-fix the heap efficiently after the removal of the elemts?

efficiently after the removal of the element?

A |
O(1) |

B |
O(d) but not O(1) |

C |
O(2 |

D |
O(d2 |

O(2

^{d}) but not O(d)height of heap either it is

min heapormax heaporO(logn)O(d);delete the i th node then

re-fixO(logn) or O(d) but not.O(1)Becasue tree not contain only one element also

complexity of heapre-fixisforO(logn)avgorworstandforO(1)bestcase;so answer is

B.