Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 32.1, Problem 3E
Program Plan Intro
To demonstrate that expected count of character to character comparisons build by implicit loop of line
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The Boyer-Moore algorithm is used to find the pattern P in the string T. What will be
the values of i, j, T[i], and P[j] when we perform comparison number 5 by the
algorithm. The first comparison is already given to you.
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Design and analyze asymptotically a divide-conquer algorithm for the following problem:
input: a string s of length n;output: the number of substrings of s that start and end with the letter A.example:ABACDA→→6.
According to the loop invariant theorem, a valid loop invariant I(n) must have the property
that
Select one:
O a. After the loop, P I(N) where P is the postcondition.
O b. I(n) =0 after a finite number of steps.
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O c. None of the other answers are correct
O d. I(0) → Q, where Q is the precondition.
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- Show how the Boyer-Moore string matching algorithm works for the following input.How many comparisons of characters are done in each case?(a) T = AAAAAAAAAA, P = AAAB(b) T = ratsbatsandcats, P =cathatarrow_forwardWe showed that there is at least one incompressible string of length n for every n E N. Show that it is not possible that there is exactly one incompressible strings of length n for large n. Hint: if there were, you could encode that string more succinctly. How?arrow_forwardProve the correctness of the following pattern-matching algorithm. The input consists of a string S[1..n], and a pattern P[0..m − 1], where 1 ≤ m ≤ n. The algorithmlocates the first contiguous occurrence of the pattern P in the string S, that is, . = p if S[p..p + m − 1] = P, and . = n − m + 1 if the pattern P does not occur at all in the string S. function match(P, S, n, m) comment Find the pattern P[0..m − 1] in string S[1..n] 1. . := 0; matched := false 2. while (. ≤ n − m) ∧ ¬matched do 3. . := . +1; 4. r := 0; matched := true 5. while (r<m) ∧ matched do 6. matched := matched ∧ (P[r] = S[. + r]) 7. r := r + 1 8. return(.)arrow_forward
- Given the following Truth Table: Inputs ABC Outputs Y 000 001 010 011 100 101 110 111 Y= 1. Construct a K-Map on Scrap Paper 2. Perform Grouping on Scrap Paper 3. Give the SIMPLEST Boolean Expression for x in the answer box below. 1 X 1 0 X 1 1 1 4. Give sum of minterms and sum of don't cares. Em( )+ d( Should you have an empty set please answer with N/A )arrow_forwardx² Find the maximum of f (x) = x + x using genetic algorithm, where:- The range of x:[0,1,.........,15]. The population size:4. String length: 4 bits. Crossover type: 1-point crossover. Mutation: Bitwise mutation. 8 Selection method: Roulette Wheel selection. Initialization parents are:- 01 10 1000 001 1 10 10arrow_forwardUpdate all JAVA methods of Cohen Sutherland line clipping algorithm if region code (LRBA). (Where L=left, R=right, B=bottom, A=Above; for example: Left point = (1000), Left-above point = (1001))arrow_forward
- designed an iterative algorithm for separating n VLSIchips into those that are good and those that are bad by testing two chips at a time andlearning either that they are the same or that they are different. To help, at least half ofthe chips are promised to be good. Now design (much easier) a randomized algorithmfor this problem. Here are some hints. Randomly select one of the chips. What is the probability that the chip is good? How can you learn whether or not the selected chip is good? If it is good, how can you easily partition the chips into good and bad chips? If the chip is not good, what should your algorithm do? When should the algorithm stop? What is the expected running time of this algorithm?arrow_forwardWhen the order of growth of the running time of an algorithm is N log N, the doubling test will lead to the hypothesis that the running time is ~ a N for a constant a. Isn’tthat a problem?arrow_forwardWhen trying to find a solution, you should give serious attention to employing both the selective-repeat technique and the Go-Back-N strategy if the sequence number space is wide enough to incorporate k bits of information. If the sequence number space is not big enough, you should not even bother trying to find a solution. In its whole, what is the maximum size that the sender window that we are allowed to use is authorised to be allowed to be?arrow_forward
- Write Algorithm to Generating a random number from a distribution described by a finite sequence of weights.in: sequence of n weights W describing the distribution (Wi ∈ N for i = 0, . . . , (n −1) ∧ 1 ≤ n−1 i=0 Wi)out: randomly selected index r according to W (0 ≤ r ≤ m − 1)arrow_forwardPlease written by computer source Let x be a binary string. The minimal description of x, written d(x), is the shortest string ⟨M, w⟩ where TM M on input w halts with x on its tape. If several such strings exist, select the lexicographically first among them. The descriptive complexity, or Kolmogorov complexity, of x, written K(x), is K(x) = |d(x)|. Show that the function K(x) is not a computable function. HINTS: If K is a computable function, there is some TM which computes it. That TM can be used to find strings of large complexity. Try to design a program which outputs “complex” strings but which contradicts their supposed complexity, and even contradicting the supposed complexity of a single string suffices.arrow_forwardAn evolutionary algorithm uses chromosomes that are strings over the alphabet Σ = {A, C, T, G}. Suggest an appropriate crossover operator for these chromosomes.arrow_forward
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