Page - 75 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

3.4 Exercises 75 if a < b: print(’\na is the smallest of the two numbers’) elif a == b: print(’\na and b are equal’) else: print(’\na is the largest of the two numbers’) Proceedbywriting theprogram,andthenrunit a fewtimeswithdifferentvalues fora andb to confirmthat it worksas intended. In particular, choosecombinations foraandb so thatall threebranchesof theifconstructionget tested. Filename:compare_a_and_b.py. Remarks Theprogramisnot too robust, since it assumes the user typesan integer as input (a realnumbergives trouble). Exercise3.6:AreaofRectangleVersusCircle Consider one circle and one rectangle. The circle has a radius r = 10.6. The rectangle has sides a and b, but only a is known from the outset. Let a = 1.3 andwriteaprogramthatusesawhile looptofindthe largestpossible integerb that givesa rectangleareasmaller than,butascloseaspossible to, theareaof thecircle. Run theprogramandconfirmthat it gives the rightanswer (which isb=271). Filename:area_rectangle_vs_circle.py. Exercise3.7:FrequencyofRandomNumbers Write a programthat takes a positive integerN as input and then drawsN random integers from the interval [1,6]. In the program, count how many of the numbers, M, that equal6andprintout the fractionM/N. Also,printall the randomnumbers to thescreenso thatyoucancheckforyourself that thecounting iscorrect.Run the programwithasmallvalueforN (e.g.,N = 10) toconfirmthat itworksas intended. Hint Userandom.randint(1,6) todrawa randomintegerbetween1and6. Filename:count_random_numbers.py. Remarks For largeN, this programcomputes the probabilityM/N of getting six eyeswhen throwingadice. Exercise3.8:Game21 Consider some game where each participant draws a series of random integers evenly distributed between 0 and 10, with the aim of getting the sum as close as possible to21,butnot larger than21.Youareoutof thegameif thesumpasses21. After each draw, you are told the number and your total sum, and are asked whetheryouwantanotherdrawornot.Theonecomingclosest to21 is the winner. Implement thisgamein aprogram. Hint Userandom.randint(0,10) to drawrandomintegers in [0,10]. Filename:game_21.py.