課程名稱︰計算機程式 課程性質︰必修 課程教師︰林祥泰 開課學院：工學院 開課系所︰化工系 考試日期（年月日）︰2019.01.09 考試時限（分鐘）：110+10 試題 : 1.(25%) Write the class interface and the definition of class functions so that the following program would produce the output on its right. ┌─────────────────┐ │int main(){ │ Program Output: │ VECTOR a(1,2), b(3,4), c; │ a=(1,2) │ double d; │ b=(3,4) │ cout<<"a="<<a<<endl; │ c=a+b=(4,6) │ cout<<"b="<<b<<endl; │ c=a-b=(-2,-2) │ c=a+b; │ d=a*b=11 │ cout<<"c=a+b="<<c<<endl; │ c=b*1.5=(1.5,3) ｜ c=a-b; │ c=1.5*b=(1.5,3) ｜ cout<<"c=a-b="<<c<<endl; │ ｜ d=a*b; │ ｜ cout<<"d=a*b="<<d<<endl; │ ｜ c=b*1.5; │ ｜ cout<<"c=b*1.5="<<c<<endl; │ ｜ c=1.5*b; │ ｜ cout<<"c=1.5*b="<<c<<endl; ｜ ｜ return 0; ｜ ｜} ｜ └─────────────────┘ 2.(20%) Modify your C++ code to solve the following set of linear equations. 4 x1 - 3 x2 + 2 x3 - 1 x4 = 2 3 x1 + 4 x2 + 5 x3 + 6 x4 = 0 2 x1 + 3 x2 - 4 x3 - 5 x4 = 1 1 x1 - 3 x2 + 5 x3 - 7 x4 = 9 3.(20%) Modify your program for homework 4 to solve the following nonlinear equations. x^2 + y^2 + z^2 = 8 xyz = sin(x)cos(y) y/x - 2xy + 3z = 4 Using initial guesses for (x,y,z) using (1,2,3),(3,2,1),(2,1,3), (-1,-2,-3), respectively. 4.(20%) In a casino, you are playing a game that you can bet on either Head or Tail from tossing a coin. As a fair game, the chance of winning is 50%. If you win, you can take away twice the amount of your bet. Otherwise, you lose your bet. Someone comes up with a strategy that ensures to increase his/her wealth by playing this game as follows (known as the martingale betting) (a) Place an initial bet of 1 dollar. (b) If you win a game, your next bet is 1 dollar. (c) If you lose a game, your next bet is doubled. Write a program to check if this betting strategy ensures winning in the long run. What do you think could be the problem of this strategy? 5.(15%) a) Write a program to generate 100 sets of (x,y) data in a text file. In particular, the values of x should be generated randomly using 123 as the random seed with a value between -1 and 1, i.e., -1≦x≦1. The corresponding values of y are calculated as y = sin(x) + x^2. b) Write a program to read the previous data file, sort the data in an ascending order of x, and save the result to a new text file. c) Use your linear regression program to read the previous data file, and determine the slope b and intercept a if these data were to fit in a line y = a + bx. What is the correlation coefficient, the standard errors in a and b? 備註：可以帶上課練習的程式、投影片等應考。 --

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