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**About Computer Science: Algorithms, Theory, and Machines** **Course**

This course is for people who know the basics of Java programming and want to learn more about computer science as a whole. It’s the second half of our book Computer Science: An Interdisciplinary Approach (the first half is covered in our Coursera course Computer Science: Programming with a Purpose, to be released in the fall of 2018). Our goal is to take the mystery out of computing and make more people aware of the field of computer science’s strong intellectual foundations and long history.

First, we talk about old algorithms and scientific ways to measure how well they work in the context of new applications. Next, we talk about classic theoretical models that help us answer fundamental questions about computation, like whether something can be computed, whether it is universal, or whether it can’t be computed at all. We end with machine architecture, which includes machine-language programming and how it relates to Java programming (including a full CPU design built from the ground up).

The course focuses on how application programming, the theory of computation, and real computers work together. It also looks at the history and development of the field, including how Boole, Shannon, Turing, von Neumann, and others have helped.

All of this course’s features can be used for free. No certificate will be given at the end.

**Course Apply Link – Computer Science: Algorithms, Theory, and Machines**

**Computer Science: Algorithms, Theory, and Machines** **Quiz Answers**

### Week 01

**Sorting and Searching**

Q1. Which of the following results from using a blacklist filter (check all that apply)?

- Denies service to known untrustworthy clients
**Denies service to unknown clients****Allows service to trusted clients**- Allows service to unknown clients

Q2. Suppose that an array of strings contains [â€śblueberryâ€ť, â€śchocolateâ€ť, â€ścoconutâ€ť, â€ścoffeeâ€ť, â€śmintâ€ť, â€śstrawberryâ€ť, â€śvanillaâ€ť]. How many compares are used for a unsuccessful search for â€śpistachioâ€ť with binary search?

- 2
**3**- 4
- 5
- 6

Q3. Which of the following running times for a program sorting N 10-character strings is consistent with the hypothesis that the program is using *insertion sort*? Mark all that apply.

- 1 second for N = 10,000, 4 seconds for N = 20,000, 256 seconds for N = 160,000
**1 second for N = 1,000,000, 4 seconds for N = 2,000,000, 8 seconds for N = 4,000,000****1 second for N = 10,000, 4 seconds for N = 20,000, 64 seconds for N = 80,000**- 1 second for N = 1,000,000, 4 seconds for N = 2,000,000, 16 seconds for N = 4,000,000
**1 second for N = 10,000, 2 seconds for N = 20,000, 16 seconds for N = 160,000**

Q4. Which of the following best describes the order of growth of the worst-case running time of sequential search?

- logarithmic
- linear
- linearithmic
**quadratic**

### Week 02

**Stacks and Queues**

Q1. Suppose that you start with an empty stack and interpret a letter to mean *push* and â€“ to mean *pop*. Mark the sequences below that leave e at the *bottom* of the stack.

- a â€“ b c â€“ â€“ d â€“ e f g â€“ h
- a â€“ b c â€“ d â€“ e â€“ f g â€“ h
**a â€“ b â€“ c â€“ d â€“ e f g â€“ h****a b c d â€“ â€“ â€“ â€“ e f g â€“ h**- a â€“ b c â€“ â€“ d â€“ e f g h â€“

Q2. Which of the following is the primary reason to use generics when implementing stacks and queues?

- More space-efficient than using primitive types
- Makes it possible to have stacks and queues holding objects of mixed types
**Eliminates need to have multiple implementations for different types**- More time-efficient than using primitive types
- Makes it possible to meet the performance specifications

Q3. When does a data type not implement the Stack API? Mark all that apply.

- When the operation of removing an arbitrary item is supported
**When the space required cannot be bounded by a constant times the number of items in the stack at all time**- When the only operations that modify the stack are to insert an item and to remove the most recently inserted item
**When the order of growth of the time required to insert an item is logarithmic****When the maximum size of the stack needs to be specified ahead of time**- When the only operations that modify the stack are to insert an item and to remove the least recently inserted item

Q4. For which of the following expressions is the maximum stack size the largest when evaluated with the Postfix client given in lecture?

- 1 1 1 1 + * 1 1 + 1 *
- 1 1 + 1 1 + * 1 1 * +
**1 1 1 1 1 1 + + * + ***- 1 1 + 1 1 + * 1 + 1 +
- 1 1 1 + 1 + * 1 + 1 *

### Week 03

**Symbol Tables**

Q1. Which of the following are reasons to have ordered keys in a symbol-table API?

- They make it simpler to support iteration
**They arise naturally in many applications****Implementations can take advantage of ordering to gain efficiency****They allow for useful extensions to the API**- They make it possible to support multiple types of data

Q2. Of the following, which is the most important reason not to use a linked list for a symbol-table implementation?

- Doesnâ€™t support ordered keys
**Not scalable because search is too slow**- Uses too much space
- None of the above
- Not scalable because insertion is too slow

Q3. In the BST built from the keys â€śis this an easy questionâ€ť which key is in the root of the left subtree of the root?

- question
**an**- is
- this
- easy

Q4. Of the following, which is most likely to be closest to the height of a red-black tree with 1 million nodes?

**10**- 100
- 1000
- 10000
- 100000

### Week 04

**Theory of Computing**

Q1. Which of the following strings matches the RE a*bb(ab|ba)* ?

**aaaaaabbababababbaab**- abbababbabaabbaabbaabbabba
- bbbb
- bbabbabaabaaab
- aaabbaaa

Q2. Consider a two-state DFA with a binary alphabet having the following transitions: Stay in state 0 if the input is 0 and stay in state 1 if the input is 1, otherwise switch to the other state. If state 0 is the accept state, which of the following does this DFA accept?

- Bitstrings with at least one 0
**Bitstrings with an equal number of occurrences of 01 and 10**- Bitstrings that end in 0
- Bitstrings with more 0s than 1s
- Bitstrings with an equal number of occurrences of 0 and 1

Q3. Which of the following strings matches the generalized RE [$_A-Za-z][$_A-Za-z0-9]* ? Mark all that apply.

**23abcxyz**- 123456
- $
**$ABABab$**- abcxyz23

Q4. Which of the following statements are true? Mark all that apply.

**Every DFA can be simulated by some NFA**- Every NFA can be simulated by some DFA
**All formal languages are regular**- Every formal language can be recognized by some NFA
- NFAs and REs are equivalent

### Week 05

**Turing Machines**

Q1. Which of the following properties are common to both Turing machines are and DFAs? Mark all that apply.

- No limit on number of steps
**Simple model of computation****Finite number of states****Can read from or write onto the tape****State transitions are determined by current state and input symbol**- Input on tape is a finite string with symbols from a finite alphabet

Q2.Which of the following models of computation are universal? Mark all that apply.

**Java**- Conwayâ€™s Game of Life
**NFAs****your mobile phone****Turing machines****regular expressions**

Q3. Which of the following best characterizes the following statement: â€ś*There exists a mathematical function that can be computed in Java, but cannot be computed on a Turing machine.*â€ś

**1 point**

**known to be false**- known to be true
- truth or falsity not known
- if true would prove the Churchâ€“Turing thesis
- if true would falsify the Churchâ€“Turing thesis

Q4. Which of the following problems is undecidable?

- Do two given programs always print the same value?
- Is every variable in a given program initialized before it is used?
- Is every statement in a given program executed at least once?
- Does a given program contain a computer virus?
**All of the above**

### Week 06

**Intractability**

Q1. Assume that checking a box below corresponds to setting the variable to 1 and leaving it unchecked corresponds to setting it to 0. Give settings that solve the integer programming problem for the equations v+w+x â‰Ą 1, w+x+y â‰Ą 2, x+y+z â‰Ą 3, v+x+z â‰Ą 2, and v+w+x+y+z â‰¤ 3.

- v
**w****x****y**- z

Q2. Assume that P = NP. Mark all correct options for FACTOR.

**is computable**- is in NP
**is NP-complete****is intractable**- is in P

Q3. Let A and B be two decision problems. Suppose we know that A polynomial-time reduces to B. Which of the following can we infer? Mark all that apply.

- A and B cannot both be NP-complete
**If A is NP-complete then so is B**- If B is NP-complete and A is in NP then A is NP-complete
- If B is in P, then A is in P
**If A is in P, then B is in P****If A is NP-complete and B is in NP then B is NP-complete****If B is NP-complete then so is A**

Q4. Which of the following can we infer from the fact that a problem is NP-complete, if we assume that P â‰ NP? Mark all that apply.

- No algorithm exists that solves arbitrary instances of the problem
- No algorithm exists that
*efficiently*solves arbitrary instances of the problem **There exists an algorithm that efficiently solves arbitrary instances of the problem, but no one has been able to find it****The problem is not in P****All algorithms that are guaranteed to solve the problem run in polynomial time for some family of inputs****All algorithms that are guaranteed to solve the problem run in exponential time for all families of inputs**

### Week 07

**A Computing Machine**

Q1. Which of the following is the 4-digit hexadecimal twoâ€™s complement representation of the decimal number â€“16?

- 0010
- 0011
**FFF0**- FFF1
- FF16

Q2. Which of the following are components of a machineâ€™s state (value at the beginning of each instruction cycle determines what happens next)? Mark all that apply.

- IR
**ALU****PC****Memory**- Registers

Q3. Suppose that R[2] contains a small integer x. Which of the following describes the value in R[2] after the instruction 5222 is executed?

- 0
- x
*x* **2Ă—2***x*- 2^x2
*x* - x2^x
*x*2*x*

Q4. Suppose that the following sequence of instructions is loaded into memory locations 10-16: 10: 7C0A 11: 7101 12: 7201 13: 1222 14: 2CC1 15: DC13 16: 0000 and you set the PC to 10 and press RUN. Give the decimal number represented by the contents of R[2] when the machine halts.

### Week 08

**von Neumann Machines**

Q1. Suppose that the following sequence of instructions is loaded into memory locations 10-14: 10: 8113 11: 2111 12: 9113 13: 8113 14: 0000 and you set the PC to 10 and press RUN. What is the contents of R[1] when the machine halts?

- FFFF
**8113**- 0000
- 9113
- 2111

Q2. Which of the following are programs that process programs? Mark all that apply.

- ALU
**Java Virtual Machine****Assembler****Compiler**- Interpreter

Q3. Which of the following are (approximately) true of your cellphone, as compared to von Neumannâ€™s EDVAC? Mark all that apply.

- thousands of times faster
**thousands of times more memory****millions of times smaller****millions of times faster****thousands of times smaller**- millions of times more memory

Q4. Which of the following are true about virtual machines? Mark all that apply.

- They allow software to be prepared for a new computer before it is built.
- They are faster and have more memory than real machines.
**They allow for backwards capability.****They are generally too expensive to be useful in modern computing.****They cannot be implemented on von Neumann machines.**

### Week 09

**Combinational Circuits**

Q1. How many different Boolean functions of 4 variables are there?

- 4
- 16
- 64
**1024**- 65536

Q2. Suppose that one input of a NAND gate is set to x and the other is set to 1. Which function of x does it compute?

- 0
- 1
- x
- xâ€™
**x+1**

Q3. By checking a box for 1 and leaving it unchecked for 0, give the truth table column that defines the EVEN PARITY Boolean function of 3 variables.

- 0 0 0
- 0 0 1
**0 1 0****0 1 1****1 0 0****1 0 1****1 1 0**- 1 1 1

Q4. Which of the following circuits have 4 outputs? Mark all that apply.

- 2-bit majority
**4-bit decoder****2-bit decoder**- 4-bit adder
**4-bit ALU**

### Week 10

**CPU**

Q1. Which of the following modules are found in a memory? Mark all that apply.

**odd parity**- majority
**flipâ€“flop****multiplexer**- decoder

Q2. Which of the following are *not* combinational circuits? Mark all that apply.

**CLOCK****ALU**- CONTROL
**MEMORY**- INCREMENTER

Q3. Which of the following decodes instructions?

- ALU
- CLOCK
**CONTROL**- MEMORY
- PC

Q4. How many flipâ€“flops are in the TOY-8 CPU?

- 128
- 132
- 136
**148**- 149

**Conclusion**

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