Assignment Description:

Your program should accept an integer and calculate, then print all the Pythagorean Triples as demonstrated in the sample run.

Grading Rubric:

- If your program does not compile, you lose 50% of the grade.
- Once compiled, each requirement will weigh equally for grading. Not meeting a requirement may result in losing 10−20% of your grade, depending on the total number of requirements.
- Post-midterm note: If your program enters an infinite loop or has runtime errors, you will lose 25% of your grade.

Requirements:

1. Your output should match the examples in the sample run and analyze your triples search with a histogram printed at the bottom of each sample run.
2. If the number in any category exceeds 80, the histogram should print a message rather than 80 or more stars for that category.
3. Triples are printed as (x, y, z) where \( z^2 = x^2 + y^2 \).
4. The list is printed as follows:
- Category 1: If \( z = y + 1 \), then print (x, y, z) after a tab (e.g., \t).
- Category 2: If \( y = x + 1 \), then print (x, y, z) after two tabs (e.g., \t\t).
5. Your horizontal histogram should display the number of stars corresponding to the total number of triples, each category separately, and the combined number for both categories.

Prompt for Input:

Enter a positive integer: 55

Question

21-12-2023
Computers and Technology

High School

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Assignment Description:

Your program should accept an integer and calculate, then print all the Pythagorean Triples as demonstrated in the sample run.

Grading Rubric:

- If your program does not compile, you lose 50% of the grade.
- Once compiled, each requirement will weigh equally for grading. Not meeting a requirement may result in losing 10−20% of your grade, depending on the total number of requirements.
- Post-midterm note: If your program enters an infinite loop or has runtime errors, you will lose 25% of your grade.

Requirements:

1. Your output should match the examples in the sample run and analyze your triples search with a histogram printed at the bottom of each sample run.
2. If the number in any category exceeds 80, the histogram should print a message rather than 80 or more stars for that category.
3. Triples are printed as (x, y, z) where \( z^2 = x^2 + y^2 \).
4. The list is printed as follows:
- Category 1: If \( z = y + 1 \), then print (x, y, z) after a tab (e.g., \t).
- Category 2: If \( y = x + 1 \), then print (x, y, z) after two tabs (e.g., \t\t).
5. Your horizontal histogram should display the number of stars corresponding to the total number of triples, each category separately, and the combined number for both categories.

Prompt for Input:

Enter a positive integer: 55

Answer :

Final answer:

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. A Pythagorean Triple is a set of three positive integers that satisfy this equation. The program needs to accept an integer and calculate and print all the Pythagorean Triples for that integer.

Explanation:

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In other words, if a and b are the lengths of the two shorter sides of a right triangle, and c is the length of the hypotenuse, then a^2 + b^2 = c^2. The program you need to write should accept an integer, and then calculate and print all the Pythagorean Triples for that integer.

A Pythagorean Triple is a set of three positive integers (a, b, c) that satisfy the equation a^2 + b^2 = c^2. These triples represent the lengths of the sides of right-angled triangles. For example, the triple (3, 4, 5) is a Pythagorean Triple because 3^2 + 4^2 = 5^2.

When printing the Pythagorean Triples, you need to follow specific formatting rules. If z = y + 1, the triple (x, y, z) should be printed after one tab. If y = x + 1, the triple (x, y, z) should be printed after two tabs.

Learn more about Pythagorean Theorem here:

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Answer :

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