CS2420 Midterm 2
At what index is the root index generally stored?
1
What is the location of the left child of an item at index i?
2*i
What is the location of the right child of an item at index i?
2*i+1
An ADT stands for _______________?
Abstract Data Type
Which ADT has an insert method that requires a constant cost O(1)?
Binary Heap
The binary heap supports access to the minimum item in ______________ time.
Constant
True/False: A BST allows duplicates.
False
True/False: A binary heap does not allow duplicates.
False
True/False: A complete binary tree is constructed using nodes, just like a balanced BST.
False
True/False: A data structure is defined in terms of its behavior (possible values and operations) from the point of view of the user.
False
True/False: An ADT is a concrete representation of data from the point of view of the implementer.
False
True/False: For a doubly-ended priority queue, for any node X at even depth, the key stored at X is the maximum of its subtree.
False
True/False: For a doubly-ended priority queue, for any node X at odd depth, the key stored at X is the minimum of its subtree.
False
True/False: For a max-heap order property, for every node X with parent node P, the key in P is > the key in X.
False
True/False: If k is almost equal to N, quicksort and a binary min heap approach to the k smallest items problem is expected to have a quadratic complexity.
False
True/False: If k is almost equal to N, quicksort and a binary min heap approach to the k smallest items problem is expected to have logN complexity.
False
True/False: In a binary heap, deleting a new item requires starting with a hole at the bottom and percolating to the correct placement for the item at the top of the list.
False
True/False: In a binary heap, inserting a new item requires starting with a hole at the top and percolating to the bottom.
False
True/False: The average cost for deleteMin for a binary heap is O(N)
False
True/False: The binary min-max heap has the same structure property as the binary max heap.
False
True/False: The cost of traversing a balanced BST to find the minimum element is the height of the tree, which yields a linear cost for traversal.
False
True/False: The min-heap order property requires that for every node X with parent node P, the key in p is < the key in X.
False
True/False: The min-heap order property requires that for every node X with parent node P, the key in p is > the key in X.
False
True/False: The min-heap order property requires that for every node X with parent node P, the key in p is >= the key in X.
False
True/False: The worst case performance of insert for a binary heap is linear.
False
True/False: The worst case scenario for inserting a new item to a binary heap with a min-heap structure is when the new item is greater than the root.
False
True/False: This is how a generic array is declared: Type[] array = new Object[10];
False
True/False: This is how a generic array is declared: Type[] array = new Type[10];
False
True/False: When inserting a new item to a binary heap, you must first satisfy the order property and then satisfy the structure property.
False
True/False: the buildHeap operation is logarithmic.
False
What is the property that ensures that a complete binary tree has constant time operations?
Heap-order
Using an array to store a tree is called ___________________?
Implicit Representation
The binary heap supports deletion to the minimum item in ______________ time.
Logarithmic
The binary heap supports insertion to the minimum item in ______________ time in the worst case.
Logarithmic
To get a list of items in ascending order with Heapsort, do we need a binary min- or max-heap?
Max-heap/max
To get a list of items in descending order with Heapsort, do we need a binary min- or max-heap?
Min-heap/min
Heap operations lead to a O(________) sorting algorithm
NlogN
For a basic array kept in unsorted order, what is the cost for insertion?
O(1)/Constant
What is the cost for deleteMin for a basic array kept in sorted order (that implements a priority queue)?
O(1)/Constant
What is the cost for findMin for a basic array kept in sorted order (that implements a priority queue)?
O(1)/Constant
For a basic array kept in unsorted order, what is the cost for calling findMin?
O(N)/Linear
For a basic array kept in unsorted order, what is the cost for deleteMin?
O(N)/Linear
What is the cost for insertion to a basic array kept in sorted order?
O(N)/Linear
When finding k smallest items in a list, what is the cost of using a binary min heap (using buildHeap)?
O(N*klogN)/NklogN
What is the cost of Heapsort?
O(NlogN)/NlogN
When finding k smallest items in a list, what is the cost of using quicksort (assuming good pivot choice)?
O(NlogN)/NlogN
What is the cost of deleteMin for a self-balancing BST?
O(logN)/Logarithmic
What is the cost of findMin for a self-balancing BST?
O(logN)/Logarithmic
What is the cost of insert for a self-balancing BST?
O(logN)/Logarithmic
What is the worst-case performance of insertion with a binary heap?
O(logN)/Logarithmic
True/False: A BST does not allow duplicates.
True
True/False: A binary heap allows duplicates.
True
True/False: A binary heap can be used to implement a priority queue.
True
True/False: A data structure is a concrete representation of data from the point of view of the implementer.
True
True/False: A priority queue can be implemented using a basic array in sorted order.
True
True/False: An ADT is defined in terms of its behavior (possible values and operations) from the point of view of the user.
True
True/False: For a double-ended priority queue, the root is at even depth.
True
True/False: For a doubly-ended priority queue, for any node X at even depth, the key stored at X is the minimum of its subtree.
True
True/False: For a doubly-ended priority queue, for any node X at odd depth, the key stored at X is the maximum of its subtree.
True
True/False: For a max-heap order property, for every node X with parent node P, the key in P is >= the key in X.
True
True/False: Heap sort is slower than merge sort in practice.
True
True/False: If k is almost equal to N, quicksort and a binary min heap approach to the k smallest items problem is expected to have NlogN complexity.
True
True/False: In a binary heap, deleting a new item requires starting with a hole at the top and percolating to the correct placement for the item at the bottom of the list.
True
True/False: In a binary heap, inserting a new item requires starting with a hole at the bottom and percolating to the top.
True
True/False: In a self-balancing BST, we are guaranteed that the height of the tree is logarithmic in the number of nodes.
True
True/False: The average cost for deleteMin for a binary heap is O(logN)
True
True/False: The binary min-max heap has the same structure property as the binary min heap.
True
True/False: The cost of traversing a balanced BST to find the minimum element is the height of the tree, which yields a logarithmic cost for traversal.
True
True/False: The min-heap order property requires that for every node X with parent node P, the key in p is <= the key in X.
True
True/False: The minimum item in a self-balancing BST is in the left-most node.
True
True/False: The only structure that gives dynamic logarithmic running time is the tree.
True
True/False: The root of a complete binary tree can be stored at index 0.
True
True/False: The worst case performance of insert for a binary heap is logarithmic.
True
True/False: The worst case scenario for inserting a new item to a binary heap with a min-heap structure is when the new item is less than the root.
True
True/False: This is how a generic array is declared: Type[] array = (Type[]) new Object[10];
True
True/False: When inserting a new item to a binary heap, you must first satisfy the structure property and then satisfy the order property.
True
True/False: the buildHeap operation is linear.
True
True/False: you do not need to reference the left and right for a complete binary tree.
True
If k is much smaller than N, is quick sort or a binary min heap a better algorithm for finding k smallest items?
binary min heap
What is the location of the parent of an item at index i?
i/2
For a complete binary tree, the height of an N-node tree is at most __________
log(N)/Logarithmic