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- Give an example of an algorithm that is O(1), an algorithm that is O(n) and an algorithm that is O(n2). Discuss the difference between them.Computer Science Find the correct asymptotic complexity of an algorithm with runtime T(n) and step-by-step workings where T(x) = O(n) + T((2*x)/8) Assume x and n are the same. If it is different, how will the working be like?Consider the problem of counting, in a given text, the number of substrings that start with an A and end with a B. For example, there are four such substrings in CABAAXBYA.a. Design a brute-force algorithm for this problem and determine its efficiency class.b. Design a more efficient algorithm for this problem with complexity O (n)
- Prove 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(.)Although the A* algorithm performs better with a more educated heuristic function, the overall computation time with a less informed heuristic can be reduced. How is that possible?Perform an experimental analysis on the two algorithms & Visualize their running times as a function of the input size with a log-log chart. 1. prefixAverage12. prefixAverage2. RPgramming language: Java
- Develop a brute-force algorithm that finds the longest common sequential elements of two given lists with the Java programming language. For example, the following two lists are given: S1 = [B,C,D,A,A,C,D] S2 = [A,C,D,B,A,C] Common lists are: [B,C], [C,D,A,C], [D,A,C], [A,A,C], [A,C], [C,D], … Note that although both lists have a common [C,D,A,C] (sub)list, both list items are skipped and the left-to-right order is intact. Apply the brute force algorithm. Explain Time Complexity?The doubling test will result in the hypothesis that the running time is a N for a constant a when an algorithm's order of development is N log N. Is that an issue, then?Select the asymptotic worst-case time complexity of the following algorithm:AlgorithmInput: a1, a2, ..., an, a sequence of numbersn, the length of the sequencex, a numberOutput: ??For i = 1 to n-1For j = i+1 to nFor k = 1 to nIf ((ai)^2 + (aj)^2 = (ak)^2) Return( "True" )End-forEnd-forEnd-forReturn( "False" )a. ?(1)b. ?(?)c. ?(?2)d. ?(?3)
- There are two algorithms called Alg1 and Alg2 for a problem of size n. Alg1 runs in n^2 microseconds and Alg2 runs in 100nlogn microseconds. Alg1 can be implemented using 4 hours of programmer time and needs 2 minutes of CPU time. On the other hand, Alg2 requires 15 hours of programmer time and 6 minutes of CPU time. If programmers are paid 20 dollars per hour and CPU time costs 50 dollars per minute, how many times must a problem instance of size 500 be solved using Alg2 in order to justify its development cost?Develop a piece of code for following four cases and measure the processing time of different inputs starting from 1 to 50. Plot your processing time as a graph and explain the differences. A) g(n) (Recursively)B) g(n) (Iteratively)C) Fibonacci (Recursively) D) Fibonacci (Iteratively) PLEASE DO PARTS A B C AND D in C/C++!The travel time function of an algorithm has the form: f(n) = 3n^2+4n+8.a. Determine the values of c and n0, so that big-oh O(n^2) satisfies the rule f(n) <= cg(n); n≥n0,b. Show (picture) the graphs of f(n) and g(n).