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Determine the types of some objects. Consider the following calls to the makelist function from page \(96:\) \(11=\) makelist \((0,100,1)\) \(12=\) makelist \((0,100,1.0)\) \(13=\) makelist \((-1,1,0.1)\) \(14=\) makelist \((10,20,20)\) \(15=\) makelist \(([1,2],[3,4],[5])\) \(16=\) makelist \(((1,-1,1)\), ('myfile. dat', 'yourfile. dat')) \(17=\) makelist('myfile.dat', 'yourfile.dat', 'herfile.dat') Determine in each case what type of objects that become elements in the returned list and what the contents of value is after one pass in the loop. Hint: Simulate the program by hand and check out in an interactive session what type of objects that result from the arithmetics. It is only necessary to simulate one pass of the loop to answer the questions. Some of the calls will lead to infinite loops if you really execute the makelist calls on a computer. This exercise demonstrates that we can write a function and have in mind certain types of arguments, here typically int and float objects. However, the function can be used with other (originally unintended) arguments, such as lists and strings in the present case, leading to strange and irrelevant behavior (the problem here lies in the boolean expression value \(<=\) stop which is meaningless for some of the arguments).

Short Answer

Expert verified
Different `makelist` calls return lists with int, float, and list types or incorrect endless iterations if types mismatch, as seen in steps.

Step by step solution

01

Understanding the makelist Function

The `makelist` function generates a list of values starting at a 'start' value, increasing each time by a 'step' value, and stops when it surpasses the 'stop' value. The crucial point here is that the step must be a compatible operation with the start and stop values to decide reasonable iteration.
02

Evaluate each makelist Call

To determine the type of objects and know what happens with each call, we examine one iteration of the loop that processes `(start, stop, step)` or similar arguments.
03

Determine Object Types for Each Call

1. **Makelist(11)**: `makelist(0, 100, 1)` considers integers. First iteration: 0, a valid int; continues with 1, 2,... 2. **Makelist(12)**: `makelist(0, 100, 1.0)` also for int, but `step` is a float. Thus, float type added: 0.0. 3. **Makelist(13)**: `makelist(-1, 1, 0.1)` involves floats: starts with -1.0, infers arithmetic is float, adds -0.9. 4. **Makelist(14)**: `makelist(10, 20, 20)`: single iteration means an empty list. Overlaps with stop, hence no list created. 5. **Makelist(15)**: `makelist([1,2],[3,4],[5])`. List iterators, operation involves addition of lists. Output begins as [[1,2]] after adding step. 6. **Makelist(16)**: `makelist((1,-1,1), ('myfile.dat', 'yourfile.dat'))`. Tuple iteration – when lists or tuples form the element, this starts iterating into type misunderstandings. 7. **Makelist(17)**: `makelist('myfile.dat', 'yourfile.dat', 'herfile.dat')`. Strings that should iterate form strings; character concatenation doesn't check boundary appropriately. Each past step call together creates unending iterations.
04

Simulation Result Analysis

Remarkably, some calls imply potential endless processes if naively run due to incorrect logical expressions which lead fallacies; on account of infinite loop threats, manual step processing is safer for insight like how `makelist(15)` yields incremental lists.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Object Types
In Python programming, understanding object types is crucial as they dictate how data is stored and manipulated. Python has several basic object types such as integers, floats, and strings, each serving distinct purposes. Recognizing these types helps you anticipate the behavior of functions like those seen in the `makelist` calls.

Object types determine how operations are carried out on them. For instance, arithmetic operations on integers differ from those on floats due to their precision and storage capacities. Knowing what type of object you are dealing with not only helps avoid errors but also allows you to exploit the unique features of each type. In the case of `makelist(11)` where integers are used, Python performs integer arithmetic, whereas `makelist(12)` involves float operations due to a float step, altering the output to 0.0, 1.0, etc.

Always ensure that operations within your functions are compatible with the object types being used, or you might face erroneous results or even runtime errors.
Function Arguments
Function arguments in Python are the inputs you provide to a function, determining its behavior and outcome. When creating functions, being aware of expected argument types and structures is essential.

In the `makelist` function, the arguments are anticipated to be numbers such as integers or floats. Arguably, supplying different data types like lists or strings can cause unexpected behavior. For example, providing lists as in `makelist(15)` initiates list addition operations, potentially leading to outcomes the function's creator did not foresee.

Good practice is to validate arguments within your functions to ensure they fall within an anticipated data form or to implement exceptions that gracefully handle incorrect input without causing crashes. Similarly, documenting your functions to specify the required argument types shields users from inadvertent errors.
Infinite Loops
Infinite loops are programming states where the loop continues indefinitely without terminating. This typically arises if the loop control conditions are never met, as seen in some `makelist` calls.

For example, the call `makelist(17)` with string arguments runs the risk of not satisfying stop conditions, leading to a potential infinite loop. This happens because the loop's end condition, such as value `<=` stop, might not logically complete for strings or lists when concatenated or combined.

To counter infinite loops, ensure your loop conditions are well-structured and account for all possible argument types. Adding break conditions or checks can help exit a loop safely. It can be helpful to test functions under various scenarios to identify potential infinite loops before deploying code in a live environment.
Data Types in Python
Python's flexibility with data types allows for a diverse programming approach but also requires careful management. Understanding data types in Python—from integers to more complex lists or tuples—is foundational for effective programming.

Each data type has its unique properties and methods. For instance, integer types support basic arithmetic operations, whereas lists allow for iteration and concatenation. This diversity empowers developers to select the most appropriate type for a task, enhancing code efficiency and clarity.

However, mixing data types without consideration can lead to errors or unintended outcomes. In the `makelist` function, mixing integers and floats changes the arithmetic performed, demonstrated in `makelist(13)`. Recognizing these subtleties, Python encourages strong typing practices where the expected type of each variable or return can be declared or checked, mitigating type-related bugs.

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Most popular questions from this chapter

Make a table for approximations of \(\cos x\). The function \(\cos (x)\) can be approximated by the sum $$ C(x ; n)=\sum_{j=0}^{n} c_{j} $$ where $$ c_{j}=-c_{j-1} \frac{x^{2}}{2 j(2 j-1)}, \quad j=1,2, \ldots, n $$ and \(c_{0}=1\). Make a Python function for computing \(C(x ; n)\). (Hint: Represent \(c_{j}\) by a variable term, make updates term = -term*... inside a for loop, and accumulate the term variable in a variable for the sum.) Also make a function for writing out a table of the errors in the approximation \(C(x ; n)\) of \(\cos (x)\) for some \(x\) and \(n\) values given as arguments to the function. Let the \(x\) values run downward in the rowsand the \(n\) values to the right in the columns. For example, a table for \(x=4 \pi, 6 \pi, 8 \pi, 10 \pi\) and \(n=5,25,50,100,200\) can look like \(\begin{array}{rccccc}\mathrm{x} & 5 & 25 & 50 & 100 & 200 \\ 12.5664 & 1.61 \mathrm{e}+04 & 1.87 \mathrm{e}-11 & 1.74 \mathrm{e}-12 & 1.74 \mathrm{e}-12 & 1.74 \mathrm{e}-12 \\ 18.8496 & 1.22 \mathrm{e}+06 & 2.28 \mathrm{e}-02 & 7.12 \mathrm{e}-11 & 7.12 \mathrm{e}-11 & 7.12 \mathrm{e}-11 \\ 25.1327 & 2.41 \mathrm{e}+07 & 6.58 \mathrm{e}+04 & -4.87 \mathrm{e}-07 & -4.87 \mathrm{e}-07 & -4.87 \mathrm{e}-07 \\ 31.4159 & 2.36 \mathrm{e}+08 & 6.52 \mathrm{e}+09 & 1.65 \mathrm{e}-04 & 1.65 \mathrm{e}-04 & 1.65 \mathrm{e}-04\end{array}\) Observe how the error increases with \(x\) and decreases with \(n .\) Name of program file: cossum.py.

Resolve a problem with a function. Consider the following interactive session: Why do we not get any output when calling \(f(5)\) and \(f(10) ?\) (Hint: Save the \(\mathrm{f}\) value in a variable \(\mathrm{r}\) and write print \(\mathrm{r}\).)

Find the max/min elements in a list. Given a list a, the max function in Python's standard library computes the largest element in a: max(a). Similarly, min(a) returns the smallest element in a. The purpose of this exercise is to write your own max and min function. Use the following technique: Initialize a variable max_elem by the first element in the list, then visit all the remaining elements (a [1:]), compare each element to max_elem, and if greater, make max_elem refer to that element. Use a similar technique to compute the minimum element. Collect the two pieces of code in functions. Name of program file: maxmin_list. py.

Compute the length of a path. Some object is moving along a path in the plane. At \(n\) points of time we have recorded the corresponding \((x, y)\) positions of the object: \(\left(x_{0}, y_{0}\right),\left(x_{1}, y_{2}\right), \ldots,\left(x_{n-1}, y_{n-1}\right) .\) The total length \(L\) of the path from \(\left(x_{0}, y_{0}\right)\) to \(\left(x_{n-1}, y_{n-1}\right)\) is the sum of all the individual line segments \(\left(\left(x_{i-1}, y_{i-1}\right)\right.\) to \(\left.\left(x_{i}, y_{i}\right), i=1, \ldots, n-1\right)\) : $$ L=\sum_{i=1}^{n-1} \sqrt{\left(x_{i}-x_{i-1}\right)^{2}+\left(y_{i}-y_{i-1}\right)^{2}} $$ Make a function pathlength \((x, y)\) for computing \(L\) according to the formula. The arguments \(\mathrm{x}\) and \(\mathrm{y}\) hold all the \(x_{0}, \ldots, x_{n-1}\) and \(y_{0}, \ldots, y_{n-1}\) coordinates, respectively. Test the function on a triangular path with the four points \((1,1),(2,1),(1,2)\), and \((1,1) .\) Name of program file: pathlength.py.

Compute the area of an arbitrary triangle. An arbitrary triangle can be described by the coordinates of its three vertices: \(\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right)\), numbered in a counterclockwise direction. The area of the triangle is given by the formula $$ A=\frac{1}{2}\left|x_{2} y_{3}-x_{3} y_{2}-x_{1} y_{3}+x_{3} y_{1}+x_{1} y_{2}-x_{2} y_{1}\right| $$ Write a function area(vertices) that returns the area of a triangle whose vertices are specified by the argument vertices, which is a nested list of the vertex coordinates. For example, vertices can be \([[0,0],[1,0],[0,2]]\) if the three corners of the triangle have coordinates \((0,0),(1,0)\), and \((0,2)\). Test the area function on a triangle with known area. Name of program file: area_triangle.py.

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