Create suspensionBridges.vn.py

Author: Vic-Nas

kattis/Suspension Bridges/suspensionBridges.vn.py

@@ -0,0 +1,31 @@
+from math import cosh, ceil, log2
+d, s = map(int, input().split())
+
+# > 0.1 will fail :( 
+# (Math says it)
+tol = 10 ** -4
+
+def f(epsilon):
+    # epsilon = a / (a + s) | in 0, 1
+    return cosh(d*(1-epsilon)/(2*s*epsilon))-1/epsilon # Equation 1
+    
+def l(epsilon):
+    return 2*s*((1+epsilon)/(1-epsilon))**0.5 # Equation 2
+
+left, right = 0, 1
+# Fancy math. On peut juste iterer 50 fois
+# d_l/d_epsilon pour savoir tol_epsilon(tol_l)
+tol_epsilon = (tol ** 3) / (2 * s)
+iterations = ceil(log2(1/tol_epsilon - 2))
+# Btw, for bs la taille de l'intervalle est (born_sup - born_inf) / step
+# step = 1 pour les entiers.
+
+for _ in range(iterations):
+    epsilon = (left + right) / 2
+    fl = f(epsilon)
+    if fl > 0:
+        left = epsilon + tol_epsilon
+    else:
+        right = epsilon - tol_epsilon
+
+print(l(epsilon))