15 122: Principles of Imperative Computation. Practice Exam August 4, 2015

Transcription

1 15 122: Principles of Imperative Computation Practice Exam August 4, 2015

2 Practice Exam Page 2 of Fun with C. The following C programs have between 0 and 1 errors in them. If the function has no errors, state that this is the case and write what the function prints. (a) #include <stdio.h> #define double(x) ((x) + (x)) int i = 2; int j = 1; printf("%d\n", i=double(j*3)); printf("%d\n", i); (b) #include <stdio.h> int rot13(char *s) { int size = 1; while(*s++ = (*s + 13)) { size++; return s - size; printf("%s\n", rot13("abcd"))

3 Practice Exam Page 3 of 17 (c) #include <stdio.h> char *s = "yay 122 :)"; printf("%s\n", (char *)((int *) s + 2)); (d) #include <stdio.h> int a = 1; char *s = "abcdef"; while (a = 1) { if(*s > d ) a = 0; else ++s; printf("s is %s\n", s);

4 Practice Exam Page 4 of 17 (e) #include <stdio.h> char **alphabet; for(int i = 0; i < 26; i++) { *(alphabet + i) = xmalloc(sizeof(char) + 1); alphabet[i][0] = a + i; alphabet[i][1] = \0 ; printf("the first letter of the alphabet is %s\n", alphabet[0]); (f) #include <stdio.h> char *str = "yesterday"; char t[10]; while(*t++ = *str++); printf("t is %s\n", t);

5 Practice Exam Page 5 of 17 (g) #include <stdio.h> struct tree { char *data; struct tree *left; struct tree *right; void print_tree (struct tree t) { if (t == NULL) return; print_tree(t->left); printf("%s\n", t->data); print_tree(t->right); struct tree t; t->data = "new tree!" t->left = NULL; t->right = NULL; print_tree(t);

6 Practice Exam Page 6 of 17 (h) #include <stdio.h> #include <string.h> char *copy_string (char *str) { char copy[strlen(str)]; while(*copy++ = *str++); return copy; printf("copy of copy is %s\n", copy_string("copy"));

7 Practice Exam Page 7 of Memory. For each of the following code segments, state what is wrong with the code and how to correct it. You can look for errors such as unallocated or uninitialized memory, dereference of an invalid pointer, freeing of an invalid pointer, and etc. You may assume that all appropriate libraries have been included. (a) int allocate(int** array, int n) { array = (int**) xmalloc(n*sizeof(int*)); int** A; allocate(a, 10); free(a); (b) char* word = (char*) xmalloc(strlen("1337")*sizeof(char)); strcpy(word, "1337"); free(word);

8 Practice Exam Page 8 of 17 (c) int** p = (int**) xmalloc(sizeof(int*)); *p[0] = 42; free(p); (d) struct player { char* name; int score; ; typedef struct player player; player* noob = (player*) xmalloc(sizeof(player)); strcpy(noob->name, "Player"); noob->score = -1337; free(noob);

9 Practice Exam Page 9 of 17 (e) int free_array(char** array, int num_elts) { for (int i = 0; i < num_elts; i++) { free(array[i]); free(array); int n = 10; char** A = (char**) malloc(n*sizeof(char*)); char* word = (char*) malloc(100*sizeof(char)); strcpy(word, "You are just so cool."); for (int i = 0; i < n; i++) { A[i] = word; free_array(a, n);

10 Practice Exam Page 10 of Function Pointers. Some functions we studied such as bsearch perform operations only on an array of integers. In practice, we would want to develop more generic functions that can perform operations on arrays of arbitrary data. Therefore, in this problem we will sketch portions of such a generic function and write code to demonstrate how to use it. Assume we have the following generic function declaration typedef void* elem; elem findmax(elem array, int length, int type, int (*cmp)(elem x, elem y)) The function is supposed to take an array of arbitrary comparable data, the array length, a size type of each element (in bytes) and a function pointer, and then return a pointer to the maximum element of the array. (15) (a) Complete the function body of findmax(). Be sure to write pre condition as assertions. elem findmax(elem array,int length,int type,int (*cmp)(elem x,elem y)){ (5) (b) Suppose that the findmax function is to be used with an array of ints. Write the intcmp function used to compare two elements. intcmp returns 1,0,-1 based on comparison (behavior similar to standard compare functions) int intcmp(elem x, elem y) {

11 Practice Exam Page 11 of 17 (5) (c) Suppose that the function findmax is to be used with an array of strings. Write the strcmp function used to compare two string elements. intcmp returns 1,0,-1 based on comparison (behavior similar to standard compare functions) int strcmp(elem x, elem y) { (6) (d) Complete the following main function using intcmp and strcmp. Do a proper casting. int A[] = {23, 10, 12, 38, 9, 15; printf("the max is %d \n", ); char* B[] = {"victor", "guna", "frank", "tom"; printf("in a sorted (ascending) order %s would be the last\n", );

12 Practice Exam Page 12 of Perfect Trees. Recall the structure of a tree: typedef struct tree_node* tree; struct tree_node { elem data; tree left; tree right; The perfect binary tree is defined as a tree that has the maximum number of possible nodes for a given height (which is defined by the number of links - that is, a tree with only a root node has height 0). More formally, a perfect binary tree T with height h satisfies the following conditions: 1. An empty tree cannot be perfect. 2. If h = 0, then the left and right subtrees must be empty. 3. If h > 0, then both subtrees are perfect binary trees of height h 1. (10) (a) Implement the recursive function bool is perfect tree(tree T, int h), which returns true if and only if the tree T, of height h, is a perfect tree, according to the above definition. It returns false otherwise. You may assume that h is the correct height of the tree T. bool is_perfect_tree(tree T, int h) {

13 Practice Exam Page 13 of 17 (5) (b) What can you say about the complexity of search operation on a perfect binary tree? Hint: What can we assume if a tree is perfect?

14 Practice Exam Page 14 of Complexity. (6) (a) You have the method transform shown below that transforms a two-dimensional array of ints into a stack: stack transform(int *input, int rows, int cols) { stack stk = stack_new(); for(int i = 0; i < rows; i++) { for(int j = 0; j < cols; j++) { stack temp = stack_new(); push(*(input + i*cols + j), stk); while(!stack_empty(stk)) push(pop(stk), temp); stk = temp; return stk; Assuming that the input array has n rows and n columns, what is the worst-case runtime complexity in Big-O of the above method in terms of n? Explain your answer. (6) (b) Given Circle ALL upper bounds that apply. T (n) = n log n n log(log n) T (n) = O(n 2 ) T (n) = O(n log n) T (n) = O(n log(log n)) T (n) = O(n) T (n) = O(log n) T (n) = O(n 1/2 )

15 Practice Exam Page 15 of 17 Prove, using the formal definition of O (e.g., using n o and c) that f(n) = O(g(n)). (5) (c) f(n) = 3n 2 + 6n, g(n) = 1 2 n2

16 Practice Exam Page 16 of Splay Trees. Insert 30, 8, 29, 16, 86, 63, 20 (in the given order) into an initially empty splay tree. Draw the tree after each insertion.

17 Practice Exam Page 17 of Graphs. Consider a generic adjacency list directed graph implementation: typedef size_t vertex; typedef struct list_node* list; typedef struct graph_header* graph; struct list_node { vertex vert; list next; ; struct graph_header { size_t cap; // the table length and the number of vertices list* table; // array of adjacency lists ; Write a recursive function isconnected(graph G) that uses Depth First Traversal to check if the graph G is connected. The only functions you can use are is graph(g) and is vertex(g, v). bool isconnected(graph G)