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 3.1, Problem 3E
Program Plan Intro
To explain the reason of the statement that the running time of
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I need the answer in a specific format like this:
Algorithm
Proof of Correctness
Runtime Analysis
As stated in the question the algorithm should have a runtime of O(n log n)
What is the leading term for the following expressions and specify the lowest Big O Complexity for each algorithm?
2) A computer science student designed two candidate algorithms for a problem while working
on his part-time job The time complexity of these two algorithms are
T1(n) = 3 n logn and T2(n) = nº/5 .
a) Which algorithm is better? Why?
b) If we run both algorithms at the same time with an input size of 10°, which algorithm
produces results faster than the other one? Why?
Chapter 3 Solutions
Introduction to Algorithms
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- Question What is the computational (time) complexity of the following piece of an algorithm? while (iarrow_forward2) A computer science student designed two candidate algorithms for a problem while working on his part-time job The time complexity of these two algorithms are T1(n) = 3 n log n and T2(n) = nº/5 . a) Which algorithm is better? Why? b) If we run both algorithms at the same time with an input size of 105, which algorithm produces results faster than the other one? Why?arrow_forwardA computer science student designed two candidate algorithms for a problem while working on his part-time job The time complexity of these two algorithms are T,(n) = 3 n logn and T2(n) = n6/5 a) Which algorithm is better? Why? b) If we run both algorithms at the same time with an input size of 105, which algorithm produces results faster than the other one? Why?arrow_forwardLet w(n) and A(n) denote respectively, the worst case and average case running time of an algorithm executed on an input of size n. which of the following is ALWAYS TRUEarrow_forwardint fun1(int n) Algorithm 3 Analyze the following Algorithms. Find their running time and asymptotic { if (n <= 1) return n; return 2*fun1(n-1); notations.arrow_forwardGive the time complexity for the following algorithm. You need to identify the basic operation first. F(int n) { if (n>1) Return F(n/3)+F(n/3)+5; else return 1; } 1) What is the basic operation? 2) Set up the recurrence. Let T(n) be the # of basic operations 3) Solve the recurrence using the Master theoremarrow_forwardEnter the time complexity of the algorithm below. Justify the answer.arrow_forwardQuestion 16 Choose the incorrect option from the following: An algorithm with O(n) time complexity consumes less time than an O(n log n) algorithm. O(1) time complexity is called as constant time. An algorithm with O(log n) time complexity consumes more time than an O(n) algorithm. A good algorithm must be space and time efficientarrow_forwardI. Compute for the running time for each algorithm 1. for i = 1 to n do Statement B 2. for(j=1; js n*n*n;j++) for (k=1; ksn) Statement f; for(m=1;marrow_forwardAssume that each of the expressions below gives the processing time T(n) spent by an algorithm for solving a problem of size n. Select the dominant term(s) having the steepest increase in n and specify the lowest Big-Oh complexity of each algorithm. For example, the dominant term in 0.1n + 10n4 is 10n4 and it is O(n4). Expression Dominant term(s) O(. . .) 5 + 0.001n3 + 0.025n 500n + 100n1.5 + 50n log10 n 0.3n + 5n1.5 + 2.5 · n1.75 n2 log2 n + n(log2 n)2 n log3 n + n log2 n 100n + 0.01n2 0.01n + 100n2 2n + n0.5 + 0.5n1.25 0.01n log2 n + n(log2 n)2 100n log3 n + n3 + 100narrow_forwardThe 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?arrow_forward7. Suppose that you have two different algorithms for solving a problem. To solve a problem of size n, the first algorithm uses exactly n(log2 n) operations and the second algorithm uses exactly n3/2 operations. As n grows, which algorithm uses fewer operations?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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