Introduction to Java Programming and Data Structures: Brief Version (11th Global Edition)
11th Edition
ISBN: 9780134671710
Author: Y. Daniel Liang
Publisher: PEARSON
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Chapter 22.4, Problem 22.4.1CP
Program Plan Intro
Given growth functions:
The above functions are ordered as follows:
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Order the following functions by asymptotic growth rate:
4n log n +2n
3n + 100 n log n
n2 + 10n
210
4n
n3
2log n
2n
n log n
Please consider n=9.
List the functions below from the lowest order to the highest order of growth. Indicate any that are of the same order.
5n +3 2n 2n*lg(n) 5*lg(n) + 4
n - n2 + 3n4 6√n 2n3 + lg(n) (n2)*lg(5n)
3n3 8n2 2n-1
Chapter 22 Solutions
Introduction to Java Programming and Data Structures: Brief Version (11th Global Edition)
Ch. 22.2 - Prob. 22.2.1CPCh. 22.2 - What is the order of each of the following...Ch. 22.3 - Count the number of iterations in the following...Ch. 22.3 - How many stars are displayed in the following code...Ch. 22.3 - Prob. 22.3.3CPCh. 22.3 - Prob. 22.3.4CPCh. 22.3 - Example 7 in Section 22.3 assumes n = 2k. Revise...Ch. 22.4 - Prob. 22.4.1CPCh. 22.4 - Prob. 22.4.2CPCh. 22.4 - Prob. 22.4.3CP
Ch. 22.4 - Prob. 22.4.4CPCh. 22.4 - Prob. 22.4.5CPCh. 22.4 - Prob. 22.4.6CPCh. 22.5 - Prob. 22.5.1CPCh. 22.5 - Why is the recursive Fibonacci algorithm...Ch. 22.6 - Prob. 22.6.1CPCh. 22.7 - Prob. 22.7.1CPCh. 22.7 - Prob. 22.7.2CPCh. 22.8 - Prob. 22.8.1CPCh. 22.8 - What is the difference between divide-and-conquer...Ch. 22.8 - Prob. 22.8.3CPCh. 22.9 - Prob. 22.9.1CPCh. 22.9 - Prob. 22.9.2CPCh. 22.10 - Prob. 22.10.1CPCh. 22.10 - Prob. 22.10.2CPCh. 22.10 - Prob. 22.10.3CPCh. 22 - Program to display maximum consecutive...Ch. 22 - (Maximum increasingly ordered subsequence) Write a...Ch. 22 - (Pattern matching) Write an 0(n) time program that...Ch. 22 - (Pattern matching) Write a program that prompts...Ch. 22 - (Same-number subsequence) Write an O(n) time...Ch. 22 - (Execution time for GCD) Write a program that...Ch. 22 - (Geometry: gift-wrapping algorithm for finding a...Ch. 22 - (Geometry: Grahams algorithm for finding a convex...Ch. 22 - Prob. 22.13PECh. 22 - (Execution time for prime numbers) Write a program...Ch. 22 - (Geometry: noncrossed polygon) Write a program...Ch. 22 - (Linear search animation) Write a program that...Ch. 22 - (Binary search animation) Write a program that...Ch. 22 - (Find the smallest number) Write a method that...Ch. 22 - (Game: Sudoku) Revise Programming Exercise 22.21...Ch. 22 - (Bin packing with smallest object first) The bin...Ch. 22 - Prob. 22.27PE
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- 1 2 Order the following functions by growth rate: N, N, N¹5, N², Nlog N, Nlog log N, N log² N, N log(N²), 2/N, 2N, 2N/2, 37, N² log N, N³. Indicate which functions grow at the same rate. Suppose T₁ (N) = O(f(N)) and T₂(N) = O(f(N)). Which of the following are true? a. T₁(N) + T₂(N) = O(f(n)) b. T₁(N) - T₂(N) = o(f(N)) T₁ (N) C. = : 0(1) T₂(N) d. T₁(N) = O(T₂(N))arrow_forwardSort the following functions in terms of asymptotic growth from smallest to largest. In particular, the resulting order should be such that f₁ =0(f₂), f₂=0 (f 3), and so on. 1 2 I I I - ✓ 3" ✓ log (23) 14 1 1010 n 11/10 ✓ nln(12n) ✓ 52! ✓ log_²(n) ✓20200.1arrow_forwardProblem 3: Order the following functions by asymptotic growth rate 5n 4.n. log(n) n!0 2log(n) 5n + 32 log(n) 9n nlog(n) nt + n2 + 23 4"arrow_forward
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- Rank the following functions by order of growth from the slowest to the fastest (lgn means log2n) [4] 2n, n6/3, n (lg n) 4, nlog n, 22n, 2n2, lg n, n lg n,arrow_forwardPlease explain What is the Big-O complexity of the following function: f(n^2 + 100n + 15712958) Choose the following: A. O(n^2) B. O(n) C. O(15712958)arrow_forwardArrange the following functions in ascending order of growth rate. That is, if function g(n) immediately follows f(n) in your list, then it should be the case that f (n) = 0(g(n)) fi(n) = 3n – log n 32.3 f2(n) = Vn + 2"n f3(n) = 3"14 () 3 1 9 fa(n) = fs(n) = V Vn +1arrow_forward
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