Create 530.py

530.py

@@ -0,0 +1,58 @@
+import math
+import sys
+
+class Problem():
+    def __init__(self):
+        self.hyperbola_point_count_cache = { 1 : 1 }
+        self.hyperbola_coprime_point_count_cache = { 1 : 1 }
+
+    def solve(self):
+        for n in [10**15]:
+            print(n, '=>', self.get(n))
+
+    def get(self, n):
+        total_count = 0
+        m = math.floor(math.sqrt(n))
+        r = math.floor(math.sqrt(m))
+        g_bound = math.floor(math.sqrt(n // (r + 1)))
+        for d in range(1, r + 1):
+            coprime_point_count = self.__get_hyperbola_coprime_point_count(d)
+            g_upper = self.__get_triangular_number(math.floor(math.sqrt(n // d)))
+            g_lower = self.__get_triangular_number(math.floor(math.sqrt(n // (d + 1))))
+            total_count += (g_upper - g_lower) * coprime_point_count
+        print('d =>', total_count)
+        for g in range(1, g_bound + 1):
+            coprime_point_count = self.__get_hyperbola_coprime_point_count(n // g**2)
+            total_count += g * coprime_point_count
+            print('g =>', g, n // g**2, coprime_point_count, total_count)
+        return total_count
+
+    def __get_hyperbola_point_count(self, n):
+        if n not in self.hyperbola_point_count_cache:
+            total_count = 0
+            m = math.floor(math.sqrt(n))
+            for k in range(1, n // (m + 1) + 1):
+                total_count += n // k
+            for d in range(1, m + 1):
+                total_count += d * (n // d - n // (d + 1))
+            self.hyperbola_point_count_cache[n] = total_count
+        return self.hyperbola_point_count_cache[n]
+
+    def __get_hyperbola_coprime_point_count(self, n):
+        if n not in self.hyperbola_coprime_point_count_cache:
+            total_count = self.__get_hyperbola_point_count(n)
+            m = math.floor(math.sqrt(n))
+            for g in range(2, m + 1):
+                total_count -= self.__get_hyperbola_coprime_point_count(n // g**2)
+            self.hyperbola_coprime_point_count_cache[n] = total_count
+        return self.hyperbola_coprime_point_count_cache[n]
+
+    def __get_triangular_number(self, n):
+        return (n * (n + 1)) // 2
+
+def main():
+    problem = Problem()
+    problem.solve()
+
+if __name__ == '__main__':
+    sys.exit(main())