Solving Project Euler Problem 9: Special Pythagorean Triplet

 Problem

"A Pythagorean triplet is a set of three natural numbers, a < b < c, for which: a² + b² = c²

For example, 3² + 4² = 5² or 9 + 16 = 25. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc."

Solution

A Pythagorean triplet is a set of three positive integers (a, b, c) that satisfy the Pythagorean Theorem: a² + b² = c². In other words, the square of the length of the hypotenuse (the side opposite the right angle) in a right-angled triangle is equal to the sum of the squares of the other two sides. For example, the triplet (3, 4, 5) is a Pythagorean triplet because 3² + 4² = 5². 

 

1.      The special_pythagorean function takes one argument, n, which is the desired sum of a + b + c.

2.      We use a nested loop structure to iterate through all possible values of a and b within the specified range.

3.      Inside the nested loops, we calculate the value of c by subtracting a and b from n (1000).

4.      We check if the current values of a, b, and c form a Pythagorean triplet by verifying if

           a² + b² = c².

5.      If a Pythagorean triplet is found, we break out of the loops and return the values of a, b, and c.

6.      Finally, we calculate the product abc and print the result.

 

Solving Project Euler Problems provides a great opportunity to practice coding and algorithmic thinking.