University of Central Florida COP 3502: Computer Science 1

Transcription

1 University of Central Florida COP 3502: Computer Science 1 Student Academic Resource Center presents... Computer Science 1 Study Union Review Written by: Soliman Alnaizy Fall 2018

2 Contents 1 TRIES Runtimes Sample Code Behold The Majesty of Tries HEAPS Runtimes (again) Heap Properties Heap Algorithms Heap Representation HeapSort More run times (Our favorite, yaaay!) Understanding HeapSort HASHTABLES even more run TiMeS Explaining hashtables to your grandmother Applying our hashtable knowledge MATHY STUFF Base Conversion Bits & Binary Logical Operators Base facts Bitmasks BACKTRACKING Understanding backtracking CS2 teaser JUST IN CASE 14 1

3 1 TRIES 1.1 Runtimes Table 1 Function Best Average Worst Insertion Searching Deletion *Use this space to write down the reasoning behind some of the run times listed above* 1.2 Sample Code Write out a typical TrieNode struct in C: In no more than 10 lines, write a function that takes the root of a trie and inserts a string into it: 2

4 1.3 Behold The Majesty of Tries In the trie given below... Figure 1: A majestic trie that I spent way too much time on to make What is wrong with this trie? How many words are represented in the trie? What are they? Delete the following strings from the trie above: ape banana i What would the trie look like after completing all deletions? Cross out the nodes on Figure 1 that will be deleted. What does the 1 at the root of the trie represent? 3

5 2 HEAPS 2.1 Runtimes (again) Table 2 Function Best Average Worst Insertion Searching Deletion percolateup percolatedown *Use this space to write down the reasoning behind some of the run times listed above* 2.2 Heap Properties What is the structural property of a Heap? What is the ordering property of a Heap? What are the different types of heaps? How are they different? 4

6 2.3 Heap Algorithms Describe how the following algorithms work when it comes to heaps: Insertion Deletion Search 5

7 2.4 Heap Representation Insert the following numbers into a minheap. Draw out the heap after inserting each number: 45, 23, 84, 31, 59, 2, 64, 15 Draw a heap that contains at least 16 nodes that will cause an O(1) deletion: Draw the array representation of the Heap that you just drew: 6

8 2.5 HeapSort More run times (Our favorite, yaaay!) Table 3 Function Best Average Worst Heapify HeapSort Understanding HeapSort What s the difference between Heapify and HeapSort? Describe Heapify: Describe HeapSort: What would the following array look like after going through a Heapify function?

9 3 HASHTABLES 3.1 even more run TiMeS Table 4 Function Best Average Worst Insertion Searching Deletion *Use this space to write down the reasoning behind some of the run times listed above* 3.2 Explaining hashtables to your grandmother Briefly describe what are hash tables: What are the properties of a good hash function? What are the properties of a good hashtable? What are the properties of a good hashtable? What are the main issues with hashtables and what different techniques do we use to resolve them? 8

10 3.3 Applying our hashtable knowledge Given the hash function: hash(x) = 3x + x 2 Insert the following numbers into a hashtable using the different collision resolution techniques discussed earlier: *Space for some arithmetic in case you need it* 34, 12, 77, 25, 64, 19, 0, 7 1. Linear Probing 2. Quadratic Probing 3. Separate Chaining 9

11 4 MATHY STUFF 4.1 Base Conversion Preform the following conversions: 1. (4245) 6 to base (917) 10 to base 7 3. ( ) 2 to base 8 4. (A2D) 16 to base 4 5. (45B) 13 to base 9 10

12 4.2 Bits & Binary What system do we use to represent numbers in binary? Why don t we use other systems? In two s complement, what do the following numbers represent in decimal? ( ) 2 = ( ) 2 = ( ) 2 = ( ) 2 = ( ) 2 = ( ) 2 = ( ) 2 = ( ) 2 = Represent the following decimal numbers in two s compliment using 8 bits: 20 = 45 = -1 = 127 = -55 = -128 = -90 = 11

13 4.3 Logical Operators What s the ouput of the following program? #include <stdio.h> int main (void) { int c = 5; } printf("%d", c << 2); printf("%d", c); printf("%d", 92 >> 3); printf("%d", c = c << 31); printf("%d", c = (~c) + 1); printf("%d", ~c); printf("%d", 0xfe1); printf("%d", 011); printf("%d", 92 & 78); printf("%d", 92 78); printf("%d", 92 ^ 78); printf("%d", ~( ))); printf("%d", ~3); 4.4 Base facts 1. How many unique numbers can be represented with an unsigned int? 2. How many unique numbers can be represented with a signed int? 3. What is the largest number that can be represented with a unsigned int? 4. What is the smallest number that can be represented with a unsigned int? 5. Why is there a difference between question 1 and question 3? 12

14 6. What is the largest number that can be represented with a signed int? 7. What is the smallest number that can be represented with a signed int? 8. What is the largest negative number that can be represented with a signed int? 9. How many unique numbers can be represented using n bits in base b? 10. What is the highest number we can represent using n bits in base b? 4.5 Bitmasks The functions below take int *attributes and int bit as parameters. Fill out missing lines of code: int switch bit on(int *attribute, int bit) { } int switch bit off(int *attribute, int bit) { } int toggle bit(int *attribute, int bit) { } 13

15 5 BACKTRACKING 5.1 Understanding backtracking In 10 words or less, give a very brief description of backtracking. What is the recipe for a typical backtracking algorithm? Why is backtracking so powerful? What are some examples of backtracking that you might have seen up until now? What are the downsides of backtracking? Why might a programmer want to steer away from writing up a backtracking solution to a problem? 5.2 CS2 teaser What are the different types of backtracking? 6 JUST IN CASE Solve the recurrence relation of MergeSort :) The End 14