def countdown(N,T):
# M is a map: (bitmask of used input numbers -> (expression value -> expression text))
M=[{} for i in range(1<<len(N))]
# initialize M with single-number expressions
for i in range(len(N)):
M[1<<i][1.0*N[i]] = "%d" % N[i]
# allowed operators
ops = (("+",lambda x,y:x+y),("-",lambda x,y:x-y),("*",lambda x,y:x*y),("/",lambda x,y:x/y))
# enumerate all expressions
n=0
while 1:
# test to see if we're done (last iteration didn't change anything)
c=0
for x in M: c +=len(x)
if c==n: break
n=c
# loop over all values we have so far, indexed by bitmask of used input numbers
for i in range(len(M)):
for j in range(len(M)):
if i & j: continue # skip if both expressions used the same input number
for (x,s) in M[i].items():
for (y,t) in M[j].items():
if y: # avoid /0 (and +0,-0,*0 while we're at it)
for (o,f) in ops:
M[i|j][f(x,y)]="(%s %s %s)"%(s,o,t)
# pick best expression
L=[]
for t in M:
for(x,e) in t.items():
L+=[(abs(x-T),e)]
L.sort();return L[0][1]
print countdown([1,2,3],10)