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Questions and Answers
When computing $x^n$ using only basic arithmetic operations ($+, -, *, /$), what is the primary consideration for handling both positive and negative values of $n$?
When computing $x^n$ using only basic arithmetic operations ($+, -, *, /$), what is the primary consideration for handling both positive and negative values of $n$?
- Using a loop that iterates from 1 to $|n|$ and multiplying by $x$ if $n$ is positive or dividing by $x$ if $n$ is negative. (correct)
- Checking if n is a multiple of 2, because this would require different handling.
- Using a single loop that always divides by $x$, adjusting the start and end iteration values.
- Employing a conditional statement that either multiplies by $x$ for positive values of $n$ or does nothing if n is negative.
In the problem of calculating $x^n$, what is the correct initial value for the result variable r before entering the loop?
In the problem of calculating $x^n$, what is the correct initial value for the result variable r before entering the loop?
- 0, regardless of the value of n
- 1, if n is not zero
- 1, regardless of the value of n (correct)
- x, the value that is being raised to the power of n
For an integer funds, what is the overall strategy when determining the smallest number of bills ($10, $5, $1) needed?
For an integer funds, what is the overall strategy when determining the smallest number of bills ($10, $5, $1) needed?
- Use a series of modulus operations to determine the remainder at each step in $10, $5, $1.
- Divide `funds` by 1, 5, and 10, respectively, then add the results.
- Repeatedly subtract the largest possible denomination (10, then 5, then 1) from the remaining fund until the remainder is zero. (correct)
- Use a single modulus operation to determine the number of $10, $5, and $1 bills
If an algorithm for $x^n$ computes $x^{-n}$ using division (i.e. $1 / x^n$), what critical check needs to be performed before proceeding with the calculation?
If an algorithm for $x^n$ computes $x^{-n}$ using division (i.e. $1 / x^n$), what critical check needs to be performed before proceeding with the calculation?
When decomposing an amount of money into the smallest number of bills, why are we checking larger denominations ($10) before smaller ones ($5, $1)?
When decomposing an amount of money into the smallest number of bills, why are we checking larger denominations ($10) before smaller ones ($5, $1)?
What is the purpose of fflush(stdout) in this program?
What is the purpose of fflush(stdout) in this program?
What data type is used for the variable 'funds' in this program?
What data type is used for the variable 'funds' in this program?
How does the program calculate the number of $10 bills?
How does the program calculate the number of $10 bills?
What will the variable 'tmp' hold after the line 'tmp = funds;' is executed?
What will the variable 'tmp' hold after the line 'tmp = funds;' is executed?
Which line of code is responsible for displaying the output to the user?
Which line of code is responsible for displaying the output to the user?
Which type of data representation is used for an integer in the CPU?
Which type of data representation is used for an integer in the CPU?
What is the correct format to declare an integer variable in C?
What is the correct format to declare an integer variable in C?
Which of the following statements is true regarding variable naming in C?
Which of the following statements is true regarding variable naming in C?
Which of the following is NOT a valid floating-point representation?
Which of the following is NOT a valid floating-point representation?
What happens when you declare a variable with an assignment statement?
What happens when you declare a variable with an assignment statement?
Which of the following is a correct example of declaring a character variable?
Which of the following is a correct example of declaring a character variable?
When using a flowchart to represent algorithms, which programming structure would you likely use?
When using a flowchart to represent algorithms, which programming structure would you likely use?
What is the effect of the statement 'int numBoxes = 20;'?
What is the effect of the statement 'int numBoxes = 20;'?
What character is represented by the notation used in printf for a linefeed?
What character is represented by the notation used in printf for a linefeed?
What is the purpose of the ampersand in the scanf function?
What is the purpose of the ampersand in the scanf function?
Which conversion code is used to print an integer in hexadecimal notation?
Which conversion code is used to print an integer in hexadecimal notation?
What will happen when the program reaches the scanf function?
What will happen when the program reaches the scanf function?
What does the printf function do in relation to strings?
What does the printf function do in relation to strings?
What should not be included in the string used with scanf?
What should not be included in the string used with scanf?
In the statement printf("%d dollars: %d 10s, %d 5s, %d 1s\n", funds, tens, fives, ones); what does each %d signify?
In the statement printf("%d dollars: %d 10s, %d 5s, %d 1s\n", funds, tens, fives, ones); what does each %d signify?
What is a key aspect of the scanf function?
What is a key aspect of the scanf function?
What is the primary method indicated for determining the number of tens from a total dollar amount?
What is the primary method indicated for determining the number of tens from a total dollar amount?
How does the algorithm determine the number of fives in the dollar count?
How does the algorithm determine the number of fives in the dollar count?
What assumption is necessary when designing an algorithm to find the square root of an integer x?
What assumption is necessary when designing an algorithm to find the square root of an integer x?
What operation is necessary to determine the value of 'ones' after counting tens and fives?
What operation is necessary to determine the value of 'ones' after counting tens and fives?
Which of the following methods for finding the square root may take a long time for large values of x?
Which of the following methods for finding the square root may take a long time for large values of x?
What is an important step in problem-solving as suggested by the summary?
What is an important step in problem-solving as suggested by the summary?
What can be inferred about the variable 'tmp' in the algorithms designed?
What can be inferred about the variable 'tmp' in the algorithms designed?
How is the numBoxes variable being changed in the expression numBoxes = 30?
How is the numBoxes variable being changed in the expression numBoxes = 30?
What does the variable 's' represent in the process of finding the square root of x?
What does the variable 's' represent in the process of finding the square root of x?
What does the operator % represent in arithmetic operations?
What does the operator % represent in arithmetic operations?
What will be the result of the operation a * b if int a = 9 and int b = 5?
What will be the result of the operation a * b if int a = 9 and int b = 5?
In the expression a - b, how is the subtraction operation executed based on the values of a and b?
In the expression a - b, how is the subtraction operation executed based on the values of a and b?
What is the role of parentheses in the expression ((a*b)+(c/3))-1?
What is the role of parentheses in the expression ((a*b)+(c/3))-1?
If tmp initially has the value of funds, which statement accurately describes tens ← tmp / 10?
If tmp initially has the value of funds, which statement accurately describes tens ← tmp / 10?
What would be the result of the division a / b with int a = 9 and int b = 5?
What would be the result of the division a / b with int a = 9 and int b = 5?
Which of the following statements describes the expression tmp = tmp - tens * 10?
Which of the following statements describes the expression tmp = tmp - tens * 10?
Flashcards
Power Calculation Algorithm
Power Calculation Algorithm
An algorithm that calculates the result of raising a base number (x) to a power (n) using only basic arithmetic operations (addition, subtraction, multiplication, and division). This algorithm is designed to handle both positive and negative exponents.
Base (x)
Base (x)
The input variable representing the base number in the power calculation algorithm.
Exponent (n)
Exponent (n)
The input variable representing the exponent in the power calculation algorithm. It determines how many times the base number is multiplied by itself.
Result (r)
Result (r)
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Assumption: Non-Negative Exponent
Assumption: Non-Negative Exponent
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High-Level Design
High-Level Design
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Code-Like Design
Code-Like Design
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Repeated Subtraction (Square Root)
Repeated Subtraction (Square Root)
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Square Calculation (Square Root)
Square Calculation (Square Root)
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Integer Division
Integer Division
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Problem Understanding
Problem Understanding
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Data Transformation
Data Transformation
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Problem Solution Design
Problem Solution Design
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Sequential Structure
Sequential Structure
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Conditional Structure
Conditional Structure
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Iterative Structure
Iterative Structure
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Integer
Integer
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Floating-Point Number
Floating-Point Number
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Character
Character
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Variable
Variable
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Declaring a Variable
Declaring a Variable
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printf()
printf()
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scanf()
scanf()
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Statements
Statements
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Temporary Variable
Temporary Variable
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funds
funds
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Assignment Operator (=)
Assignment Operator (=)
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Declaration
Declaration
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Expression
Expression
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Operator
Operator
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Precedence
Precedence
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Literal
Literal
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Simple Sequential Program
Simple Sequential Program
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Literal String
Literal String
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\n
\n
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Conversion code: %d
Conversion code: %d
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Ampersand (&)
Ampersand (&)
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Conversion codes in scanf()
Conversion codes in scanf()
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Standard output stream
Standard output stream
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Study Notes
Problem Solving Strategies
- Understand the problem completely
- Identify the given and needed data
- Clarify any uncertainties or state assumptions
- Analyze how the given data is transformed
- Consider the operations that can be performed
- Determine the operations leading to the desired outcome
- Employ programming structures like sequential, conditional, and iterative
- Draw a flowchart or create pseudocode
Integer Exponentiation
- Given two integers, x and n, calculate x raised to the power of n
- Use only basic arithmetic (+, -, *, /)
- Assume n is non-negative (n≥0)
Calculating the Minimum Number of Bills
- Given an integer representing a monetary amount (funds)
- Determine the fewest number of $10, $5, and $1 bills needed
- Employ integer division to simplify calculations.
Finding the Square Root of a Perfect Square
- Given an integer (x) that is a perfect square
- Compute the positive square root
- Compute successive squares until you match the target value of x
Data Types in C
- Integer: A whole number. C representation in memory will depend on the compiler but often includes positive and negative values.
- Floating-Point: A number with a decimal point. C representation will often use the IEEE floating-point standard.
- Text: Character data. It's stored in binary and often uses the ASCII standard.
Literals
- Numeric literals like '123' or '0xABC'
- String literals like "Hello world"
Variable Declaration
- Declaring a variable in C involves specifying its type and name.
- Example structure (type, name):
int numBoxes;
Variable Initialization
- Assign a value to a variable when it is declared.
- Example structure:
int numBoxes = 20;
Variable Assignment
- Change a variable's value in C
- Example structure:
numBoxes = 30;
Expressions in C
- Combine variables, literals, and operators to evaluate a value
- Example operators (+, -, *, /, % and others depend on the language)
- Example expression:
totalWeight + numBoxes * 20
Arithmetic Operators (integers)
- +, -, *, / (integer division): discards the fractional part
- % (modulo): calculates the remainder of division
- unary -: changes the sign of a number
Operator Precedence
- Order of operations in C follows standard mathematical conventions
- Parentheses override any order of operations.
Output to the Console
- Use
printfto display information to the user. - Use placeholders (like
%dfor integers or%sfor strings) followed by the variable names.
Input from the Console
- Use
scanfto obtain input from the user - Specify data type using conversion codes like
%d
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