This question is concerned with hashing with open addressing where the (linear) probing sequence is defined by h'(k) = k mod 10 and h(k, i) = (h'(k) + i) mod 10. Assume that the content of the hash table T is as follows: T(0) = 49 T(1) = 1 T(2) = NIL T(3) = NIL T(4) = DELETED T(5) = 25 T(6) = DELETED T(7) = 36 T(8) = 64 T(9) = 9 Note that I have used parentheses (rather than brackets) due to the Canvas Syntax.   (a) The first cell (index to the table) probed by Hash-Search(T, 64) is [a]   (b) The last cell (index to the table) probed by Hash-Search(T, 64) is [b]   (c) The first cell (index to the table) probed by Hash-Insert(T, 29) is [c]   (d) The last cell (index to the table) probed by Hash-Insert(T, 29) is [d]   (e) The last cell (index to the table) probed by Hash-Delete(T, 96) is [e]

Given an unsorted array A of n distinct integers and an integer k, you need to return the k smallest integers in the array in sorted order, where k may be any integer between 1 and n. Suppose that you have the following three algorithms to solve this problem. A1: Sort the array in increasing order, then list the first k integers after sorting. A2: Build a min-heap from these n integers, then call Extract-Min k times. A3: Use the linear time selection algorithm to find the k-th smallest integer in the array, then partition the array about that number to obtain the k smallest numbers in the array, and finally sort the k smallest numbers. Assume that you are using mergesort as your sorting algorithm, and use the linear time build-heap algorithm to build the heap. Let T1(n, k) denote the worst-case running time of Algorithm A1. Let T2(n, k) denote the worst-case running time of Algorithm A2. Let T3(n, k) denote the worst-case running time of Algorithm A3. Analyze the worst-case running times of the algorithms. What is the asymptotic notation for T2(n, k)? Use the most accurate big-O notation in your answer. Note that k is between 1 and n. Hence k is nominated by n.

Write a brief justification to your answer to Q1-c1.

The following figure shows red-black tree (RBT) in which a square denotes a black node, a circle denotes a red node, and the NIL nodes are omitted. The number inside a circle/square is the key value of the corresponding node. The label (upper-case letter) next to a node is a pointer pointing to the memory location of the corresponding node. You should use the label when referring to a node.   (a) Suppose that we want to insert 33 into the RBT in the figure. We first allocate memory for a tree node O and set its color to red and its key to 33. Then we insert it into tree T as if inserting into a binary search tree. After BST insertion (before RBT insertion fixup), the parent of O is [a]   (b) Suppose that we want to insert 33 into the RBT in the figure. We first allocate memory for a tree node O and set its color to red and its key to 33. Then we insert it into tree T as if inserting into a binary search tree. After BST insertion (before RBT insertion fixup), is O the left child of its parent or the right child of its parent? Write LEFT or RIGHT. [b]   (c) Suppose that we want to insert 33 into the RBT in the figure. We first allocate memory for a tree node O and set its color to red and its key to 33. Then we insert it into tree T as if inserting into a binary search tree. After BST insertion (before RBT insertion fixup), which property of the RBT is violated? Select 0 if none of the properties is violated. [c]   (d) Suppose that we want to insert 33 into the RBT in the figure. We first allocate memory for a tree node O and set its color to red and its key to 33. Then we insert it into tree T as if inserting into a binary search tree. Then we perform insertion fixup if necessary. In the resulting RBT, what is the parent of node E? [d]   (e) Suppose that we want to insert 33 into the RBT in the figure. We first allocate memory for a tree node O and set its color to red and its key to 33. Then we insert it into tree T as if inserting into a binary search tree. Then we perform insertion fixup if necessary. In the resulting RBT, what is the color of node J? [e]   (f) Suppose that we want to insert 33 into the RBT in the figure. We first allocate memory for a tree node O and set its color to red and its key to 33. Then we insert it into tree T as if inserting into a binary search tree. Then we perform insertion fixup if necessary. In the resulting RBT, what is the left child of node O? [f]   (g) Suppose that we want to insert 33 into the RBT in the figure. We first allocate memory for a tree node O and set its color to red and its key to 33. Then we insert it into tree T as if inserting into a binary search tree. Then we perform insertion fixup if necessary. In the resulting RBT, what is the right child of node O? [g]     (h) Suppose that we want to delete node M (with key=60) from the RBT  in the figure. In the resulting RBT, what is the right child of node A? [h]   (i) Suppose that we want to delete node M (with key=60) from the RBT  in the figure. In the resulting RBT, what is the color of node M? Write either BLACK or RED. [i]   (j) Suppose that we want to delete node M (with key=60) from the RBT  in the figure. In the resulting RBT, what is the left child of node M? [j]   (k) Suppose that we want to delete node M (with key=60) from the RBT  in the figure. In the resulting RBT, what is the right child of node M? [k]   (l) Suppose that we want to delete node M (with key=60) from the RBT  in the figure. In the resulting RBT, what is the color of node F? Write either BLACK or RED. [l]   (m) Suppose that we want to delete node M (with key=60) from the RBT  in the figure. In the resulting RBT, what is the color of node N? Write either BLACK or RED. [m]   (n) Suppose that we want to delete node M (with key=60) from the RBT  in the figure. In the resulting RBT, what is the color of node G? Write either BLACK or RED. [n]

Given an unsorted array A of n distinct integers and an integer k, you need to return the k smallest integers in the array in sorted order, where k may be any integer between 1 and n. Suppose that you have the following three algorithms to solve this problem. A1: Sort the array in increasing order, then list the first k integers after sorting. A2: Build a min-heap from these n integers, then call Extract-Min k times. A3: Use the linear time selection algorithm to find the k-th smallest integer in the array, then partition the array about that number to obtain the k smallest numbers in the array, and finally sort the k smallest numbers. Assume that you are using mergesort as your sorting algorithm, and use the linear time build-heap algorithm to build the heap. Let T1(n, k) denote the worst-case running time of Algorithm A1. Let T2(n, k) denote the worst-case running time of Algorithm A2. Let T3(n, k) denote the worst-case running time of Algorithm A3. Analyze the worst-case running times of the algorithms. What is the asymptotic notation for T3(n, k)? Use the most accurate big-O notation in your answer. Note that k is between 1 and n. Hence k is nominated by n.

Write a brief justification to your answer to Q1-b1.

Match each thesis statement to its description: bad in what way or good.

Why is water a good solvent for organic chemistry and life on Earth? **Note: No partial credit – no exceptions** 

Repeated encounters with a musical work will help one to

Which relatively new instrument did Mozart revise Symphony No. 40 to include?