COS 126 General Computer Science Fall Midterm 1

Transcription

1 COS 126 General Computer Science Fall 2001 Midterm 1 This test has 11 questions worth a total of 50 points. You have 120 minutes. The exam is closed book, except that you are allowed to use a one page cheatsheet. No calculators or other electronic devices are permitted. Give your answers and show your work in the space provided. Write out and sign the Honor Code pledge before turning in the test. I pledge my honor that I have not violated the Honor Code during this examination. Problem Score Problem Score Sub 1 Sub 2 Name: Login ID: Precept: 1 MF 10:00 Donna 2 MF 11:00 Donna 3 MF 1:30 Kevin 4 MF 2:30 Kevin Total 1

2 2 PRINCETON UNIVERSITY 0. Miscellaneous. (2 points) (a) Write your name and arizona login in the space provided on the front of the exam, and circle your precept number. (b) Write and sign the honor code on the front of the exam. 1. Number systems. (4 points) (a) Give the hexadecimal representation of the binary integer Circle your answer. (b) Give the decimal representation of the 16-bit 2 s complement binary number Circle your answer. (c) Give the hexadecimal representation of the decimal integer Circle your answer. (d) Evalute the following postfix expression. Circle your answer * * 2 +

3 COS 126 MIDTERM 1, FALL C Basics. (6 points) Consider the three C code fragments. hello I. i = 10; while (i > 4) { printf("%d ", 2*i); i--; printf("%d ", 2*i); II. for (i = 21; i >= 10; i--) { i--; printf("%d ", i); printf("%d ", i); III. i = 22; do { i = i - 2; printf("%d ", i); while (i >= 10); Which of the code fragments above print out the following? (a) I only. (b) I and II only. (d) I, II and III. (e) None. (c) I and III only.

4 4 PRINCETON UNIVERSITY 3. Arrays. (6 points) Consider the following C program. #include <stdio.h> #define N 16 int main(void) { int a[n], i, j, n; for (n = 1; n < N; n += n) { for (i = 0; i < N; i += n) a[i] = n; for (i = 1; i < N; i++) { for (j = 0; j < a[i]; j++) printf("*"); printf("\n"); return 0; The above program prints out 15 lines of output. hello I. Every line contains 2 n asterisks, for some integer n. II. Line i is identical to line 16 i. III. Every line i that is a power of 2 contains i asterisks. Which of the three statements are true. Circle the best answer. (a) I only. (b) I and II only. (d) I, II and III. (e) None. (c) I and III only.

5 COS 126 MIDTERM 1, FALL Data types. (4 points) Match up each of the following terms with the best matching example on the right. data type implementation of a first class data type interface for an abstract data type client that uses a first class data type (a) int (b) COMPLEX.h (c) STACK.h (d) rat.c (e) stackarray.c (f) e.c (g) postfix.c 5. Stack. (3 points) Suppose that an intermixed sequence of push and pop operations are performed. The pushes push the integers 0 through 9 in order; the pops print out the return value. Circle which one of the following sequences could not occur. (a) (b) (c) (d)

6 6 PRINCETON UNIVERSITY 6. Recursive graphics. (5 points) void recur(int depth, double x, double y, double size) { drawshadedsquare(x, y, size); recur(depth-1, x - size/2, y + size/2, size/2.1); recur(depth-1, x + size/2, y + size/2, size/2.1); recur(depth-1, x - size/2, y - size/2, size/2.1); recur(depth-1, x + size/2, y - size/2, size/2.1); if (depth <= 0) return; The function call recur(5, 256.0, 256.0, 256.0) is supposed to produce the recursive pattern above. The function drawshadedsquare() plots a gray square that is outlined in black: the square is centered at (x,y) and has side length s. If you draw several objects in the same location, the last one appears on top. All 6 numbered statements above are correct, except that they are not necessarily in the right order. hello I. Statement 6 is first. II. Statements 1 and 6 are first and second, but not necessarily in that order. III. Swapping statements 3 and 4 produces another correct ordering. Which of the three statements are true for every correct ordering? Circle the best answer. (a) I only. (b) I and II only. (d) I, II and III. (e) None. (c) I and III only.

7 COS 126 MIDTERM 1, FALL Quicksort. (6 points) Suppose that the standard (in-place) recursive quicksort is used to sort an array containing the following keys: O R A N G E B L A C K (a) Which one of the following is not the contents of the array during the first partitioning step? i. C A A B G E N L R O K ii. C A A B G E K L R O N iii. C A A B G E K N L R O iv. C A A N G E B L R O K v. C R A N G E B L A O K (b) What are the contents of the array after the partitioning function returns for the third time? i. A A B C E G K L N O R ii. A A B C E G K L R O N iii. C A A B E G K L N O R iv. C A A B E G K L R O N v. C A A B G E K L R O N

8 8 PRINCETON UNIVERSITY 8. TOY. (5 points) Suppose that you load the following into locations of X-TOY, set the PC to 10, and press Run. Give the contents of register A upon termination. Circle your answer. 10: 7C01 11: 720F 12: 7A00 13: 1AA2 14: 222C 15: D213 16: TOY. (3 points) What is the primary difference between instructions and integers in the X-TOY machine? Circle the correct answer. (a) First hex digit of instruction is an opcode; integers start with 0. (b) Integers are encoded in binary; instructions in hex. (c) There is no difference. (d) Instructions refer to registers; integers do not. (e) Registers can hold integers but not instructions.

9 COS 126 MIDTERM 1, FALL TOY INSTRUCTION SET INSTRUCTION FORMATS Format 1: opcode d s t (0-6, A-B) Format 2: opcode d addr (7-9, C-F) ARITHMETIC and LOGICAL operations 1: add R[d] <- R[s] + R[t] 2: subtract R[d] <- R[s] - R[t] 3: and R[d] <- R[s] & R[t] 4: xor R[d] <- R[s] ^ R[t] 5: shift left R[d] <- R[s] << R[t] 6: shift right R[d] <- R[s] >> R[t] TRANSFER between registers and memory 7: load address R[d] <- addr 8: load R[d] <- mem[addr] 9: store mem[addr] <- R[d] A: load indirect R[d] <- mem[r[t]] B: store indirect mem[r[t]] <- R[d] CONTROL 0: halt halt C: branch zero if (R[d] == 0) pc <- addr D: branch positive if (R[d] > 0) pc <- addr E: jump register pc <- R[d] F: jump and link R[d] <- pc; pc <- addr Register 0 always reads 0. Loads from mem[ff] come from stdin. Stores to mem[ff] go to stdout.

10 10. Recursion. (6 points) Consider the following pair of mutually recursive functions. void f(int n) { void g(int n) { if (n == 0) if (n == 0) return; return; g(n-1); f(n-1); printf("%d ", -n); printf("%d ", n); g(n-1); f(n-1); (a) What are the last 8 integers printed out when f(40) is called? Circle your answer. (b) As a function of n, how many function calls occur when calling f(n), including the original function call? Circle your answer. (c) Assume that calling a function pushes the local environment onto the stack, and returning from a function pops it. What is the maximum number of copies of the variable n on the stack at any one instant during the execution of f(40)? (d) In five words or less, what classic problem does the function f() solve? 10