[試題] 107-1 林祥泰 計算機程式 期末考
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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