"THE MOBILE" (SWEDEN)
In figure 1 you can see a mobile in perfect balance. The mobile have five weights 1 kg, 2 kg ... 5 kg. The distance between two marks is 1 m. You can check the balance through this calculation
-3·3 + -1·5 + 2·(1+2+4)=0
-2·1 + -1·2 +
1·4=0
When you get a mobile problem you will get the structure of the mobile from a character string. The mobile in figure 1 is described in this way
(-3,-1,2(-2,-1,1))
You have to calculate such weights so the mobile is in perfect balance and give the answer as another character string. From figure 1 with the five weights the answer is
(3,5,(1,2,4))
You will now write a program reading a description of a mobile from an input file, calculate the weights and writing the answer to an output file.
Input data (file MOBILE.IN)
(-3(-1(-1(-1,1,2),3),2),3(-2,1,2),6(-2,3))
Output data (file MOBILE.OUT)
((((8,6,1),5),10),(9,4,7),(3,2))
Input data (file MOBILE.IN)
(-8,-4(-5,-3,-1,1),-2(-1,1,3),2(-1(-3,-2,1(-2,1,3)),1,3),6)
Output data (file MOBILE.OUT)
(10,(1,2,4,15),(14,5,3),((6,8,(16,11,7)),9,13),12)