(25pts) You are given two sorted lists of size m and n. Give an O(log m...
You are interested in analyzing some hard-to-obtain data from two separate databases. Each database contains n numerical values—so there are 2n values total—and you may assume that no two values are the same. You’d like to determine the median of this set of 2n values, which we will define here to be the nth smallest value. However, the only way you can access these values is through queries to the databases. In a single query, you can specify a value...
Youareinterestedinanalyzingsomehard-to-obtain data from two sepa- rate databases. Each database contains n numerical values—so there are 2n values total—and you may assume that no two values are the same. You’d like to determine the median of this set of 2n values, which we will define here to be the nth smallest value. However, the only way you can access these values is through queries to the databases. In a single query, you can specify a value k to one of the...
3. (20 pts.) You are given two sorted lists of numbers with size m and n. Give an O(logn+ logm) time algorithm for computing the k-th smallest element in the union of the two lists. 4. (20 pts.) Solve the following recurrence relations and give a bound for each of them. CMPSC 465, Fall 2019, HW 2 (a) T(n) = 117(n/5)+13n!.3 (b) T(n) = 2T (n/4)+nlogn (c) T(n) = 5T (n/3) +log-n (d) T(n) = T(n/2) +1.5" (e) T(n) =...
Suppose you are given k sorted arrays of size n. Give an algorithm, that runs in O(nk log k)time, that merges them into a single list.
9. When we have two sorted lists of numbers in non-descending order, and we need to merge them into one sorted list, we can simply compare the first two elements of the lists, extract the smaller one and attach it to the end of the new list, and repeat until one of the two original lists become empty, then we attach the remaining numbers to the end of the new list and it's done. This takes linear time. Now, try...
Given two sorted arrays A and B of numbers. The size of A is N and the size of B is n + 1. Say that the numbers in A U B are pairwise distinct (no value returns more than once). Note that A U B has odd size because its 2n + 1. Hence the median is unique. Give an algorithm that returns the median. PSEUDOCODE ONLY.
When we have two sorted lists of numbers in non-descending order, and we need to merge them into one sorted list, we can simply compare the first two elements of the lists, extract the smaller one and attach it to the end of the new list, and repeat until one of the two original lists become empty, then we attach the remaining numbers to the end of the new list and it's done. This takes linear time. Now, try to...
1. Design an algorithm to find all the non-common elements in two sorted lists of numbers. What is the maximum number of comparisons your algorithm makes if the lengths of the two given lists are m and n, ?respectively 2. Estimate how many times faster it will be to find ged(98765, 56789) by Euclid's algorithm compared with the algorithm based on checking consecutive integers from min{m, n} down to gcd(m, n). 3. For each of the following functions, indicate how...
You will be given an array of N elements sorted small to large. For the X and Y values that satisfy the X ≤ Y condition, draw the flow diagram of the algorithm that finds the start and end addresses of the region with the numbers greater than X and less than Y with the divide and manage approach and with O (logN) complexity. Also code the algorithm in c language. (not c++) Example: A[0…8] array 3, 5, 7, 9,...
We are given a red-black tree T containing n keys and two keys X and Y, key X is stored in node x, wbhile key Y is stored in node y. Give an effective algorithm that determines the smallest key value stored on the path connecting x and y in T. The running time should be O(log n).