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a) Give a formula for triangular numbers (show first 7 elements of triangular numbers with explanation). b) Give a formula for Fibonacci numbers (show first 5 elements with explanation). c) How does Hanoi Tower work? (explain).

a) Give a formula for triangular numbers (show first 7 elements of triangular numbers with explanation). b) Give a formula for Fibonacci numbers (show first 5 elements with explanation). c) How does Hanoi Tower work? (explain).

C++ for Engineers and Scientists
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter4: Selection Structures
Section: Chapter Questions
Problem 14PP
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Question 6: a) Give a formula for triangular numbers (show first 7 elements of triangular numbers with explanation). b) Give a formula for Fibonacci numbers (show first 5 elements with explanation). c) How does Hanoi Tower work? (explain). d) Give a pseudocode for factorial (show how it works). Question 7: d) Show that 5x² + 25x - 9 is 0(x²). e) Suppose a computer can perform 10¹2 bit operations per second. Find the largest problem size that could be solved in 1 second if an algorithm requires: n³ and 3¹. f) Suppose a computer can perform 10¹2 bit operations per second. Find the time it would take an algorithm that requires n³ + logn operations with a problem size of: n = 3000 and n = 10⁹. Question 8: Calculate time and space complexity for given algorithms. a) procedure function(){ answer = 0 for i=1 to n for j = 1 to log(i) answer += 1 print(answer) } b) { int i; for (i=1;i<n³; i = i*5) print ("Hello World"); } c) for (i = 1; i <n; i++){ for (k = 1; k <= i; k = k + 1) print ("Hello World"); }
Transcribed Image Text:Question 6: a) Give a formula for triangular numbers (show first 7 elements of triangular numbers with explanation). b) Give a formula for Fibonacci numbers (show first 5 elements with explanation). c) How does Hanoi Tower work? (explain). d) Give a pseudocode for factorial (show how it works). Question 7: d) Show that 5x² + 25x - 9 is 0(x²). e) Suppose a computer can perform 10¹2 bit operations per second. Find the largest problem size that could be solved in 1 second if an algorithm requires: n³ and 3¹. f) Suppose a computer can perform 10¹2 bit operations per second. Find the time it would take an algorithm that requires n³ + logn operations with a problem size of: n = 3000 and n = 10⁹. Question 8: Calculate time and space complexity for given algorithms. a) procedure function(){ answer = 0 for i=1 to n for j = 1 to log(i) answer += 1 print(answer) } b) { int i; for (i=1;i<n³; i = i*5) print ("Hello World"); } c) for (i = 1; i <n; i++){ for (k = 1; k <= i; k = k + 1) print ("Hello World"); }
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