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kinda_usual solution in Uncategorized category for How Much Gold by ciel
from fractions import Fraction
import random
def gauss(a):
if not a or len(a)==0: return None
n=len(a)
for i in range(n):
while a[0][0]!=1 or a[i][i]==0: random.shuffle(a)
for j in range(n):
if i!=j:
r = Fraction(a[j][i],1) / a[i][i]
for k in range(i,n+1): a[j][k] = a[j][k] - a[i][k]*r
for i in range(n):
x=Fraction(a[i][i],1)
for j in range(len(a[i])):
a[i][j] /= x
return a
def checkio(matrix):
lst={'gold':0,'tin':1,'iron':2,'copper':3}
m=[[1,1,1,1,1]]
for k,v in matrix.items():
a=[0,0,0,0,v]
for e in k.split('-'): a[lst[e]]=1
m.append(a)
return gauss(m)[0][4]
#These "asserts" using only for self-checking and not necessary for auto-testing
if __name__ == '__main__':
checkio({
'gold-tin': Fraction(1, 2),
'gold-iron': Fraction(1, 3),
'gold-copper': Fraction(1, 4),
}) == Fraction(1, 24)
checkio({
'tin-iron': Fraction(1, 2),
'iron-copper': Fraction(1, 2),
'copper-tin': Fraction(1, 2),
}) == Fraction(1, 4)
March 14, 2014
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