Problem Statement: Pythagorean triplets
You are given a range of integers [start, end]. Your task is to find all Pythagorean triplets (a, b, c) within this range where start <= a <= b <= c <= end. A Pythagorean triplet is a set of three positive integers (a, b, c) such that a^2 + b^2 = c^2.
Write a Python program that takes two integers start and end as input and outputs the count of Pythagorean triplets along with the list of those triplets, using list comprehension.
Write a Python function with the following signature to solve this problem:
def pythagorean_triplets(start: int, end: int) -> list:
"""
Finds all Pythagorean triplets within the range [start, end].
Args:
- start (int): The start of the range.
- end (int): The end of the range.
Returns:
- list: A list containing tuples of Pythagorean triplets.
"""
Input:
The input consists of a single line containing two integers separated by space: start and end (1 <= start <= end <= 1000).
Output:
The output should consist of two parts:
The first line should contain a single integer representing the count of Pythagorean triplets within the range [start, end].
The subsequent lines should contain the Pythagorean triplets separated by space.
Sample Input:
3 10
Sample Output:
2
(3, 4, 5)
(6, 8, 10)
Explanation:
For the given input range [3, 10], there are two Pythagorean triplets:
(3, 4, 5): 3^2 + 4^2 = 5^2
(6, 8, 10): 6^2 + 8^2 = 10^2
Note: The output format represents the count of Pythagorean triplets followed by each triplet in a separate line. Use list comprehension to solve this problem.
Test Cases
1 30
11
(3, 4, 5)
(5, 12, 13)
(6, 8, 10)
(7, 24, 25)
(8, 15, 17)
(9, 12, 15)
(10, 24, 26)
(12, 16, 20)
(15, 20, 25)
(18, 24, 30)
(20, 21, 29)
7 18
2
(8, 15, 17)
(9, 12, 15)
SOLUTION:
def pythagorean_triplets(start, end):
return [(a, b, c) for a in range(start, end + 1)
for b in range(a, end + 1)
for c in range(b, end + 1)
if a ** 2 + b ** 2 == c ** 2]
val = input()
s, e = map(int, val.split())
result = pythagorean_triplets(s, e)
print(len(result))
for i in result:
print(i)
Insights:
- The function generates Pythagorean triplets within the range [start, end], where start and end are inclusive.
- It uses list comprehension to generate all possible combinations of a, b, and c within the given range.
- The list comprehension involves three nested loops iterating over a, b, and c, respectively. This generates all combinations of values for the triplets.
- The ranges of b and c are restricted to start from the current value of a. This ensures that b and c are greater than or equal to a. It applies a condition within the list comprehension to check if the current combination (a, b, c) satisfies the Pythagorean theorem a^2 + b^2 = c^2.
- For each valid combination satisfying the Pythagorean theorem, a tuple (a, b, c) is constructed and added to the resulting list.
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