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/Lasso/problem-of-apollonius.lasso
+++ b/Task/Problem-of-Apollonius/Lasso/problem-of-apollonius.lasso
@ -0,0 +1,59 @@
+define solveApollonius(c1, c2, c3, s1, s2, s3) => {
+	local(
+		x1 = decimal(#c1->get(1)),
+		y1 = decimal(#c1->get(2)),
+		r1 = decimal(#c1->get(3))
+	)
+	local(
+		x2 = decimal(#c2->get(1)),
+		y2 = decimal(#c2->get(2)),
+		r2 = decimal(#c2->get(3))
+	)
+	local(
+		x3 = decimal(#c3->get(1)),
+		y3 = decimal(#c3->get(2)),
+		r3 = decimal(#c3->get(3))
+	)
+    local(
+    	v11 = 2*#x2 - 2*#x1,
+    	v12 = 2*#y2 - 2*#y1,
+    	v13 = #x1*#x1 - #x2*#x2 + #y1*#y1 - #y2*#y2 - #r1*#r1 + #r2*#r2,
+    	v14 = 2*#s2*#r2 - 2*#s1*#r1,
+    	
+		v21 = 2*#x3 - 2*#x2,
+		v22 = 2*#y3 - 2*#y2,
+		v23 = #x2*#x2 - #x3*#x3 + #y2*#y2 - #y3*#y3 - #r2*#r2 + #r3*#r3,
+		v24 = 2*#s3*#r3 - 2*#s2*#r2,
+		
+		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*#x1 + 2*#P*#Q - 2*#Q*#y1 + 2*#s1*#r1,
+		c = #x1*#x1 + #M*#M - 2*#M*#x1 + #P*#P + #y1*#y1 - 2*#P*#y1 - #r1*#r1
+
+	)
+	
+	// Find a root of a quadratic equation. This requires the circle centers not to be e.g. colinear
+	local(
+		D = #b*#b-4*#a*#c,
+		rs = (-#b - #D->sqrt)/(2*#a),
+		
+		xs = #M+#N*#rs,
+		ys = #P+#Q*#rs
+	)
+	return (:#xs, #ys, #rs)
+}
+// Tests:
+solveApollonius((:0, 0, 1), (:4, 0, 1), (:2, 4, 2), 1,1,1)
+solveApollonius((:0, 0, 1), (:4, 0, 1), (:2, 4, 2), -1,-1,-1)