Question

Go through the code below by hand, statement by statement, and calculate the numbers that will be printed. n = 3 for i in range(-1, n): if i != 0: print i for i in range(1, 13, 2*n): for j in range(n): print i, j for i in range(1, n+1): for j in range(i): if j: print i, j for i in range(1, 13, 2*n): for j in range(0, i, 2): for k in range(2, j, 1): b = i > j > k if b: print i, j, k You may use a debugger, see Appendix F.1, to step through the code to see what happens.

Short answer

The printed numbers are: -1, 1, 2, (1,0), (1,1), (1,2), (7,0), (7,1), (7,2), (2,1), (3,1), (3,2), (7,4,2), (7,4,3).

Step-by-step solution

Initialize Variables

First, we define the variable \( n \) and set it to \( 3 \). This variable will be used to control loops and calculate step sizes.

First Loop Iteration

The first loop iterates over the range from \(-1\) to \( n \), which results in values \(-1, 0, 1, 2\). The print condition is for \( i eq 0 \). Therefore, the numbers \(-1, 1, 2\) will be printed.

Second Loop Iteration

The second for-loop iterates over \( i \) in the range from \( 1 \) to \( 13 \) with a step of \( 2n \), or \( 6 \). This results in values \( (1, 7, 13) \). In each iteration, a nested loop over \( j \) runs for \( n \) times (0 to 2).This results in the print statements:- \( (1, 0), (1, 1), (1, 2) \)- \( (7, 0), (7, 1), (7, 2) \)(Note: it doesn't execute for \( i = 13 \) because it's beyond the range).

Third Loop Iteration

This loop iterates over \( i \) from \( 1 \) to \( n+1 \) (i.e., \( i = 1, 2, 3 \)) and the nested loop runs from 0 to \( i-1 \). A condition \( j eq 0 \) is checked before printing, to ensure \( j \) is not zero.The result will be:- For \( i = 2, j = 1 \) print \( (2, 1) \)- For \( i = 3, j = 1 \) and \( j = 2 \) printing \( (3, 1), (3, 2) \).

Fourth Loop Iteration

The fourth loop uses \( i \) with the same step of 6. It iterates \( j \) from 0 to \( i \) in steps of 2, and inside that, it checks for a condition involving \( k \) over its range. The condition \( i > j > k \) must be true to print. - For \( i = 1 \), no \( j \) value will fit.- For \( i = 7 \), valid \( j = 4 \) allows for \( k = 2, 3 \). - Results are: \( (7, 4, 2), (7, 4, 3) \).

Key concepts

Python for Loops

In Python, 'for loops' are essential for iterating over a sequence of numbers or items in a list. In the given exercise, the `for` loop is utilized in multiple scenarios to iterate over ranges dictated by conditions. The initial loop in the exercise, `for i in range(-1, n):`, generates numbers from -1 to just below 3. This range includes -1, 0, 1, and 2. However, due to the condition `if i != 0:`, the loop skips the print statement when `i` is 0 and prints -1, 1, and 2 instead.
This understanding of iterating with a loop over a range is foundational when it comes to looping in Python. The key syntax here is `range(start, stop)`, where `start` is inclusive, and `stop` is exclusive. By default, a step value is `1`, but programmers can specify different step values if needed. Additional loops in the exercise exploit different ranges and conditions to explore these programmable capabilities of Python.

Conditional Statements

Conditional statements are crucial in controlling the flow of a program. In Python, common conditional statements include `if`, `elif`, and `else`. These statements help to determine which blocks of code execute based on certain conditions. In the exercise, we see the conditional `if j:` used, which checks if `j` is a truthy value (not zero). This condition filters out integers where `j` equals zero, thus preventing zero from being printed alongside `i` and `k` values.
Another example is `if i != 0:`, which ensures that the print occurs only when `i` is not zero. This prompt filtering allows specific numbers or sequences to be processed or ignored, enhancing program logic. Understanding how these conditions affect the flow can be pivotal in constructing functional and efficient loops.

Nested Loops

Nested loops, which involve placing one loop inside another, are often used to navigate through multi-dimensional data structures like matrices or grids. In this exercise, nested loops are employed several times. One example is the loop `for j in range(n):` inside another `for i in range(1, 13, 2*n):`. Here, for each iteration of `i`, the inner loop fully iterates through its range for `j`, demonstrating how nested loops can create multiple layers of iteration.
This construct is powerful as it allows comprehensive exploration of all combinations of the loop variables. However, it also necessitates mindful design to prevent excessive computation or infinite loops. The use of nested loops is clear in extracting combinations of `i, j, k` in the final set of loops. Developers must ensure that each loop has a valid endpoint and that the operations inside are efficient.

Code Step-Through

A code step-through technique is invaluable in understanding program behavior and debugging. By stepping through each line, developers can observe changes in variable states and ensure logic flows as expected. In this exercise, manually or through a debugger, stepping through each line fosters understanding of how loops and conditions interact, ensuring comprehension of the underlying logic. Appendix F.1 suggests using a debugger, which can visually highlight which part of the code is currently active, making the learning and debugging process interactive.
By methodically assessing each iteration's state, developers can verify expected outcomes against actual variable states, spot errors, and optimize logic. Practicing code step-through, particularly with complex nested structures and multiple conditions, becomes essential in mastering precise and bug-free coding.