Consider the online median problem: we are given a stream of integers (for simplicity assume that they are all distinct). On reading the ith input integer, we are required to quickly output the median of the i integers we have seen so far. Design and analyze an efficient algorithm that can compute the median of the current stream as soon as a new

Consider the online median problem: we are given a stream of integers (for simplicity assume that they are all distinct). On reading the ith input integer, we are required to quickly output the median of the i integers we have seen so far. Design and analyze an efficient algorithm that can compute the median of the current stream as soon as a new

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter8: Arrays And Strings

Section: Chapter Questions

Problem 24PE

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Consider the following problem: You have a large collection of music files (e.g., MP3 files), and for each file you know the artist name (as a string) and the song title (also as a string). You wish to find the name of the artist who has the largest number of songs featured in the collection. Describe an algorithm for this problem.the algorithm should be as efficient as possible. State the running time of your algorithm, assuming that there are in total n songs, across t different artists
Text reading is an integral component in our counting algorithms, and it is also ubiquitous in daily applications. Thefollowing is a very bad algorithm for reading from a text file, although it is correct and straightforward. It reads froma file line by line, and concatenate them into text. Then we split it using a regular expression. The split part isfast in linear complexity (we will learn it in Comp-2140), hence that is not our concern. Note that trim() is neededto remove empty strings.static String [] readTextBAD ( String PATH ) throws Exception {BufferedReader br =new BufferedReader (new FileReader ( PATH ) ) ;String text ="";String line ="";while (( line = br . readLine () ) != null )text = text +" "+ line . trim () ;String tokens []= text . trim () . split ("[^a-zA -Z]+") ;return tokens ;}5.4.1 Time complexity of readT extBADWrite below the time complexity of readTextBAD in terms of the text length n (number of lines), and explain youranswer. Refer to repeat1 example in the…
Problem Alice was given a number line containing every positive integer, x, where 1<=x<=n. She was also given m line segments, each having a left endpoint, l (1<=l<=n), a right endpoint, r (1<=r<=n), and an integer weight, w. Her task is to cover all numbers on the given number line using a subset of the line segments, such that the maximum weight among all the line segments in the chosen subset is minimal. In other words, let S=(l1,r1,w1),(l2,r2,w2),....,(lk,rk,wk), represent a set of k line segments chosen by Alice, max(w1,w2,...,wk) should be minimized. All numbers 1,2,....n should be covered by at least one of k the chosen line segments. It is okay for the chosen line segments to overlap. You program should output the minimized maximum weight in the chosen subset that covers all the numbers on the number line, or -1 if it is not possible to cover the number line. Input format The first line of the input contains an integer, n - denoting the range of numbers…
Binary search is significantly faster than the built-in search but requiresthat the list is sorted. As you know, the running time for the best sortingalgorithm is on the order of N log2 N, where N is the length of the list. Ifwe search a lot of times on the same list of data, it makes sense to sortit once before doing the searching. Roughly how many times do we needto search in order to make sorting and then searching faster than usingthe built-in search?
Consider the problem of searching for genes in DNA sequences using Horspool's algorithm. A DNA sequence is represented by a text on the alphabet {A, C, G, T}, and the gene segment is the pattern. Let the pattern be TAACTC C T 1.1) Construct the shift table t for the gene segment of chromosome length 8 (pattern) is given above. Character c A C T Shift t(c) Apply Horspool's algorithm to locate the pattern given above in the following DNA sequence 1.2) (text): TTATAGCTTCTTATA GGCTCGCTAACTCCT |Number of comparisons |(Karşılaştırma sayısı) TTATA GCTTCTTATA GGCTC GCTAA CTC CT Total number of comparisons:
You are given an insertion-only stream, only consisting of (add, i) updates where i e {1,...,n}. There are m such updates. Suppose you want to sample a random insertion in the stream. For example, if the insertions formed the sequence (1,3, 5, 5, 7, 1, 5) with m = 7, then the goal is to output 1 with probability 2/7, 3 with probability 1/7, 5 with probability 3/7, and 7 with probability 1/7. Consider the following algorithm that acts as follows on the t'th insertion. If t = 1, let X be the first inserted element. For t > 1, with probability 1/t, let X be the tth inserted element and with probability 1– 1/t, don't change X. At the end of the stream, return X. Show that X is indeed uniformly sampled from the m insertions.
Correct answer will be upvoted else downvoted. Computer science. We should characterize the expense of a string s as the number of file sets I and j (1≤i<j<|s|) with the end goal that si=sj and si+1=sj+1. You are given two positive integers n and k. Among all strings with length n that contain just the principal k characters of the Latin letters in order, find a string with least conceivable expense. In case there are different such strings with least expense — see as any of them. Input The main line contains two integers n and k (1≤n≤2⋅105;1≤k≤26). Output Print the string s to such an extent that it comprises of n characters, every its character is one of the k first Latin letters, and it has the base conceivable expense among this load of strings. In case there are various such strings — print any of them
A graph is a collection of vertices and edges G(V, E). A weighted graph has weights (numbers, etc.) on every edge. A multigraph can have more than one edges between any vertices. Explain why a person should use a weighted graph instead of a multigraph. Give examples. An adjacency matrix might be a better choice for speeding up a program, however, it consumes huge memory for large graphs. How this situation can be improved? What programming constructs better suit graph representation? Explain with example
Please do not give solution in image formate thanku. Write a Python code for the following scenario : 1: Use Breadth First Search and Recursive Best First Search and implement the algorithms in Python. The program should be able to dynamically take in start and goal nodes from the user at run time. Compare to interpret the results in terms of the algorithm working, performance & shortest path if obtained relevant to the given problem 2: Print the minimum connections that keep the whole network up and running. For each incremental depth limit, the corresponding node generating sequence should be legibly printed in the result Consider Heuristic Value as : The edge cost is an approximation towards the transmission cost between any pair of nodes. For heuristic design, consider all the possible paths between any arbitrary node n to the goal node. The average of the total transmission cost across all these paths is the heuristic value h(n) Consider the following undirected graph…
By using Greedy Algorithm only. How to create an efficient java code to solve the problem?
Let s = σ1. . . σk be a binary string of length k > 0. We say that a binary string w = w1 . . . wn contains s as a subsequence if there are k indices 1 ≤ i1 < i2, . . . < ik ≤ n such that wik = sr for every 1 ≤ r ≤ k. For example, if s = 11 then 10001, 1010 and 110 contain s as a subsequence whereas 000 and 1000 do not. Prove that the language of all binary strings containing a fixed binary string s of length k as a subsequence is a regular language.
Code in python only.