Solve more problems road to 200.

2024-05-04 09:24:18 -04:00
parent 5ce2c5bcbf
commit a07f34075b
6 changed files with 182 additions and 1 deletions
--- a/python/e195.py
+++ b/python/e195.py
@@ -0,0 +1,50 @@
+import math
+
+
+def inradius(a, b, c):
+    s = (a + b + c) / 2
+    area = (s * (s - a) * (s - b) * (s - c))
+    inradius = area / s**2
+    return inradius
+
+
+def euler_195():
+    count = 0
+    limit = 1053779
+    limit2 = limit * limit
+    for m in range(0, limit2):
+        for n in range(1, m // 2 + 1):
+            if math.gcd(m, n) == 1:
+                # Generator function from wiki for 60 degree eisenstein
+                # triangles.
+                a = m**2 - m*n + n**2
+                b = 2*m*n - n**2
+                c = m**2 - n**2
+                gcd = math.gcd(a, b, c)
+                a, b, c = a // gcd, b // gcd, c // gcd
+
+                # if gcd == 3 and inradius(a, b, c) > limit2:
+                #     break
+                if inradius(a / 3, b / 3, c / 3) > limit2:
+                    if n == 1:
+                        return count
+                    break
+
+                if a == b and b == c:
+                    continue
+
+                k = 1
+                while True:
+                    ir = inradius(a*k, b*k, c*k)
+                    if ir > limit2:
+                        break
+                    count += 1
+                    k += 1
+
+    return count
+
+
+if __name__ == "__main__":
+    solution = euler_195()
+    print("e195.py: " + str(solution))
+    assert solution == 75085391