Add new solution for the euler project problem 9 - precompute the squ…

…ares.

project_euler/problem_009/sol4.py

@@ -0,0 +1,51 @@
+"""
+Project Euler Problem 9: https://projecteuler.net/problem=9
+
+Special Pythagorean triplet
+
+A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
+
+    a^2 + b^2 = c^2
+
+For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
+
+There exists exactly one Pythagorean triplet for which a + b + c = 1000.
+Find the product a*b*c.
+
+References:
+    - https://en.wikipedia.org/wiki/Pythagorean_triple
+"""
+
+
+def get_squares(n: int) -> list[int]:
+    res = [0] * n
+    for i in range(n):
+        res[i] = i * i
+    return res
+
+
+def solution(n: int = 1000) -> int:
+    """
+    Precomputing squares and checking if a*a + b*b is the square by set look-up.
+
+    >>> solution(12)
+    60
+    >>> solution(36)
+    1620
+    """
+
+    squares = get_squares(n)
+    squares_set = set(squares)
+    for i in range(1, n):
+        for j in range(i, n):
+            if (
+                squares[i] + squares[j] in squares_set
+                and squares[n - i - j] == squares[i] + squares[j]
+            ):
+                return i * j * (n - i - j)
+
+    return -1
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")