國立台中師範學院九十二學年度研究所碩士班考試
程式設計 科試題
測統所、數教系 用壹、選擇題（每題 2.5 分，共 75 分）
Please answer the question (1) to question (4) after the following BASIC program is executed. 10 FOR K=2 TO 100 11 N=INT(SQR(K)) 12 FOR L=2 TO N 13 IF ( K MOD L=0) THEN GO TO 16 14 NEXT L 15 PRINT K 16 NEXT K 17 END
(1) How many values of variable K is printed? X23 Y31 Z28 [25 (2) Which is the largest number of printed K value? X100 Y97 Z96 [98 (3) Which is the smallest number of printed K value? X3 Y4 Z2 [7 (4) Which is the fifteenth number of printed K value? X47 Y61 Z54 [43
Please answer the question (5) to question (8) after the following BASIC program is executed. 10 N=23460 11 I=1 12 I=I+1 13 IF N MOD I <>0 THEN 12 14 PRINT I 15 N=N/I 16 IF N <> 1 THEN 13 17 END
(5)How many values of variable I is printed? X4 Y5 Z6 [7
(6)Which is the largest number of printed I value? X23 Y25 Z20 [27 (7)Which is the smallest number of printed I value? X5 Y3 Z4 [2 (8)Which is the fourth number of printed I value? X2 Y3 Z5 [4
(9) There is a integer array X represented in row-major order, if the address of X[3, 5] is 1000, and the address of X[5,7] is 1200. Which statement is wrong?
X The number of column is 49, Y The address of X[8, 10] is 1600, Z The address of X[3, 8] is 1016,
[ Each element in the array occupies 2 bytes.
(10) Which program segment is to insert a node in the linked list? (Suppose the inserted node named NEW, which is inserted after a node named Pointer) X NEW->Next = Pointer Pointer = NEW, Y NEW->Next = Pointer->Next Pointer->Next = NEW, Z Pointer->Next = NEW->Next NEW->Next = Pointer, [ none of the above.
(11)Which program segment is to delete a node in the linked list? (Suppose the deleted node named Pointer, which is deleted after a node named Back) X free(Pointer),
Y Back = Pointer->Next free(Pointer),
Z Back->Next = Pointer->Next free(Pointer),
[ none of the above.
(12) This is a recursive program segment. int fact(int N) { if N <=0 return 1; else return N * fact(N-1); }
Which statement is correct?
X The number of computing fact(N) is N Y fact(7) = 5040
Z fact(8) = 40302 [ none of the above
(13) What is the number of executing statement S in the following program segment? for(k = 1; k<=n; k++)
for(i = 0; i<k; i++) for(j = 0; j<k; j++)
if i≠j then S X n2
(n+1)/3 Yn(n+1)/2 Z n2(n+1)/2 [ none of above
(14) There is a sequence, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16. What is the number of key comparison to find 14 by fibonacci search?
X 5 Y 4 Z 3 [ 2
(15) There is a sequence, 15, 21, 25, 31, 49, 51, 69, 70, 74, 85, 87. What is the number of key comparison to find 85 by binary search?
X 5 Y 4 Z 3 [ 2
(16) What is the sum of the costs in the minimal spanning tree reduced from the following graph by Prim's algorithm?
X 132 Y 88 Z 97 [ 79 ２ ７ １ ７ Ａ Ｂ Ｄ Ｆ Ｇ ３ ２ １ ９ １ ５ ３ ０ ４ ０ Ｃ Ｅ １ ８ ８ ３ ３ ７ 請依據下列 C++程式，回答第(17)題至第(21)題： #include "stdafx.h" #include "Example01.h" #include "Example01Doc.h" #include "Example01View.h" IMPLEMENT_DYNCREATE(CExample01View, CView) BEGIN_MESSAGE_MAP(CExample01View, CView) ON_COMMAND(ID_FILE_PRINT, CView::OnFilePrint) ON_COMMAND(ID_FILE_PRINT_DIRECT, CView::OnFilePrint) ON_COMMAND(ID_FILE_PRINT_PREVIEW, CView::OnFilePrintPreview) END_MESSAGE_MAP() CExamlpe01View::CExample01View( ) { } CExample01View::~CExample01View( ) { }
void CExample01View::OnDraw(CDC* pDC) { CExampleDoc* pDoc = GetDocument();
pDC->TextOut(325, 200, "Hello World"); }
BOOL CExample01View::OnPreparePrinting(CPrintInfo* pInfo) { return DoPreparePrinting(pInfo); }
void CExample01View::OnBeginPrinting(CDC* pDC, CPrintInfo* pInfo) { } void CExample01View::OnEndPrinting(CDC* pDC, CPrintInfo* pInfo) { } (17) 請問這段程式的主要目的是什麼？ X宣告一個物件 Y建構一個列印程式 Z執行一個完整的視窗程式 [定義一個類別的成員函式 (18) 請問下列那一個函式是建構程式碼？ X IMPLEMENT_DYNCREATE( ) Y CExample01View( ) Z ~CExample01View( ) [ OnBeginPrinting( ) (19) 請問這個程式會對幾種事件做反應？ X 3 Y 2 Z 1 [ 0 (20) 請問下列何者是 cs 的類別？ X CView Y CExample01View Z CREATESTRUCT [ CExample01Doc (21) 請問執行這個程式後，其所顯示的視窗會出現下列那一個情況？ X顯示 Hello World Y顯示一個對話方塊 Z顯示一個列印訊息 [除非使用者按其按鈕，否則沒有任何顯示
請依據下列 C++程式，回答第(22)題至第(25)題： #include "stdafx.h"
#include <iostream> using namespace std;
int _tmain(int argc, _TCHAR* argv[]) { float x = 1.23E+30; float y = x + 1; cout<<"y - x ="<<y - x<<"\n"; return 0; } (22) 請問執行這段程式後，所顯示的結果是什麼？ X y – x =1 Y y – x =0 Z y – x =1\n [ overflow (23) 請問執行這段程式後，y 的數值為何？ X 1.23E+31 Y 2.23E+30 Z 1.23E+30 [ 2.23E+31 (24) 請問 #include <iostream> 的目的為何？ X使用 cout Y使用 std Z使用 _TCHAR [使用 _tmain (25)請問下列何者是 cout 的類別？ X C++ Y String Z char [ iostream
請依據下列敘述，回答第(26)題至第(29)題：
設某一程式的 input size 為 n ，running time 為T n ，且定義三種集合如下： ( )
1 2 0
1 2
( ( )) { ( ) : there exist postive constants , , and
such that 0 ( ) ( ) ( ), for all }
g n f n c c n c g n f n c g n n n Θ = ≤ ≤ ≤ ≥ 0 0 0
( ( )) { ( ) : there exist postive constants , and such that 0 ( ) ( ), for all }
O g n f n c n f n cg n n n = ≤ ≤ ≥ 0 0
( ( )) { ( ) : there exist postive constants , and such that 0 ( ) ( ), for all }
g n f n c n cg n f n n n Ω = ≤ ≤ ≥ (26) 設 ( ) 9 ( ) 3 n T n = T n + 下列何者為T n 最精確之範圍？ ( ) nΘ(n2) o O n( 2) pΘ( logn 2n) qO n( 2log2n) (27) 設 ( ) (2 ) 1 3 n T = T n + 下列何者為T n 最精確之範圍？ n ( )
nΘ( )n oΘ(log2n) pΘ( logn 2 ) qΘ(3log2n)
(28)設 ( ) 3 ( ) log2 4 n T n n = + T n 下列何者為T n 最精確之範圍？ ( )
nO n( 2) oΘ(n2log2n) pΘ( logn 2n) qΩ( logn 2n)
(29)下列敘述何者為真？ n Any comparison sort runs in Ω( logn 2n)
o Any comparison sort runs in O n( log2n)
p Any comparison sort can be optimized to run in O n( ) q Any comparison sort can be optimized to run in Θ( logn 2n)
(30)下列為 Merge Sort 之 pseudo code，其中 A[p,…,r] 為欲排序之陣列(array), Merge(X,Y)表將 X, Y 二陣列合併成一陣列，[ ] 為高斯符號。 Merge-Sort(A, p, r) if p<r then q = [(p+r)/2] X=Merge-Sort(A,p,q) Y=Merge-Sort(A,q+1,r) Merge(X,Y)
此 Merge Sort 之 worst-case running timeT n 最精確範圍為下列何者？ ( ) nΘ(n2) oΩ(n2) pO n( 2log2n) qΘ( logn 2n)
貳、簡答題（每題 12.5 分，共 25 分）
(1)請用 c 或 c++ 設計一函數使其具有類似 basic mid$ 函數之功能。 例如：
str=”Something happened yesterday” mid$(str,11,6)=>happen
