Add tasks for all the new languages

2016-12-05 23:44:36 +01:00 · 2016-12-05 23:44:36 +01:00 · bba7bfd280
commit bba7bfd280
parent 9dc3c2bb62
13208 changed files with 134745 additions and 0 deletions
--- a/Task/Problem-of-Apollonius/Nim/problem-of-apollonius.nim
+++ b/Task/Problem-of-Apollonius/Nim/problem-of-apollonius.nim
@ -0,0 +1,48 @@
+import math
+
+type Circle = tuple[x, y, r: float]
+
+proc solveApollonius(c1, c2, c3: Circle; s1, s2, s3: float): Circle =
+  let
+    v11 = 2*c2.x - 2*c1.x
+    v12 = 2*c2.y - 2*c1.y
+    v13 = c1.x*c1.x - c2.x*c2.x + c1.y*c1.y - c2.y*c2.y - c1.r*c1.r + c2.r*c2.r
+    v14 = 2*s2*c2.r - 2*s1*c1.r
+
+    v21 = 2*c3.x - 2*c2.x
+    v22 = 2*c3.y - 2*c2.y
+    v23 = c2.x*c2.x - c3.x*c3.x + c2.y*c2.y - c3.y*c3.y - c2.r*c2.r + c3.r*c3.r
+    v24 = 2*s3*c3.r - 2*s2*c2.r
+
+    w12 = v12/v11
+    w13 = v13/v11
+    w14 = v14/v11
+
+    w22 = v22/v21-w12
+    w23 = v23/v21-w13
+    w24 = v24/v21-w14
+
+    p = -w23/w22
+    q = w24/w22
+    m = -w12*p-w13
+    n = w14 - w12*q
+
+    a = n*n + q*q - 1
+    b = 2*m*n - 2*n*c1.x + 2*p*q - 2*q*c1.y + 2*s1*c1.r
+    c = c1.x*c1.x + m*m - 2*m*c1.x + p*p + c1.y*c1.y - 2*p*c1.y - c1.r*c1.r
+
+    d = b*b-4*a*c
+    rs = (-b-sqrt(d))/(2*a)
+
+    xs = m+n*rs
+    ys = p+q*rs
+
+  return (xs, ys, rs)
+
+let
+  c1: Circle = (0.0, 0.0, 1.0)
+  c2: Circle = (4.0, 0.0, 1.0)
+  c3: Circle = (2.0, 4.0, 2.0)
+
+echo solveApollonius(c1, c2, c3, 1.0, 1.0, 1.0)
+echo solveApollonius(c1, c2, c3, -1.0, -1.0, -1.0)