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Resistance Is Not Futile ACM Problem
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#!/usr/bin/env python3 | |
import math | |
from pprint import pprint | |
from collections import deque | |
#resistors = [10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82] | |
resistors = [82, 68, 56, 47, 39, 33, 27, 22, 18, 15, 12, 10] | |
decades = {} | |
# generate and cache decade lists on demand | |
def decade(d): | |
if d not in decades: | |
decades[d] = list(map(lambda x: x * 10 ** (d-1), resistors)) | |
return decades[d] | |
# finds the largest resistor that is within tolerance | |
# returns None if no resistor is found | |
def find_largest_resistor(rsum, rmax): | |
if rsum <= rmax: | |
dmax = int(math.log10(rmax-rsum)) | |
for d in range(dmax, 0, -1): | |
for i, r in enumerate(decade(d)): | |
if r + rsum <= rmax: | |
return r | |
# returns the next resistor smaller than r, or None | |
def next_smaller(r): | |
d = int(math.log10(r)) | |
i = decade(d).index(r) | |
i += 1 | |
if i >= len(resistors): | |
i = 0 | |
d -= 1 | |
if d >= 1: | |
return decade(d)[i] | |
# returns a list-of-lists containing resistors | |
# whose sums are between rmin and rmax | |
def find_resistor_lists(rmin, rmax): | |
rlists = [] | |
qlists = deque() | |
maxlen = float('inf') | |
nearest = find_largest_resistor(0, rmax) | |
if nearest is not None: | |
qlists.append([nearest]) | |
while qlists: | |
if rlists: | |
maxlen = len(min(rlists, key=len)) | |
cur = qlists.popleft() | |
lasti = -1 | |
nextlist = cur[0:lasti] | |
nextsum = sum(nextlist) | |
if len(nextlist) < maxlen: | |
r = next_smaller(cur[lasti]) | |
if r is not None: | |
qlists.append(nextlist + [r]) | |
rlist = cur | |
rsum = sum(rlist) | |
if rmin <= rsum <= rmax: | |
rlists.append(rlist[:]) | |
elif rsum < rmin and len(rlist) < maxlen: | |
nearest = find_largest_resistor(rsum, rmax) | |
if nearest is not None: | |
if nearest > rlist[-1]: | |
nearest = rlist[-1] | |
qlists.append(rlist + [nearest]) | |
return rlists | |
# Returns the single list that best fits the solution definition | |
def break_ties(rlists, r): | |
def helper(rlists, f): | |
smallest = float('inf') | |
smallests = [] | |
for rlist in rlists: | |
value = f(rlist) | |
if value < smallest: | |
smallest = value | |
smallests = [rlist] | |
elif value == smallest: | |
smallests.append(rlist) | |
return smallests | |
shortests = helper(rlists, len) # just in case | |
if len(shortests) > 1: | |
nearests = helper(shortests, lambda lst: perror(sum(lst), r)) | |
if len(nearests) > 1: | |
#return min(nearests, key=sum) | |
mns = helper(nearests, sum) | |
if len(mns) > 1: | |
return min(mns) | |
else: | |
return mns[0] | |
else: | |
return nearests[0] | |
else: | |
return shortests[0] | |
def main(v, i): | |
r = resistance(v, i) | |
if r < 10: | |
return 'Impossible' | |
else: | |
rmin = ( r ) / ( 1 / 100 + 1 ) | |
rmax = ( r ) / ( -1 / 100 + 1 ) | |
lists = find_resistor_lists(rmin, rmax) | |
if lists == []: | |
return 'Impossible' | |
final_list = break_ties(lists, r) | |
return final_list, lists, rmin, rmax | |
# percent error between target and value | |
def perror(value, target): | |
return abs(target - value) * 100 / value | |
def resistance(v, i): | |
return v / i | |
# formats output for debugging | |
def run_sample(v, i): | |
result = main(v, i) | |
if len(result) == 4: | |
final_list, lists, rmin, rmax = result | |
pprint(final_list) | |
pprint((rmax, rmin)) | |
pprint(list(map((lambda x: (x, sum(x))), lists))) | |
else: | |
print(result) | |
print() | |
if __name__ == '__main__': | |
# uncomment to read from stdin | |
## v, i = input().split() | |
## v, i = int(v), int(i) | |
## result = main(v, i) | |
## if len(result) == 4: | |
## print(' '.join(result[0])) | |
## else: | |
## print(result) | |
# included test cases | |
print('sample 1') | |
run_sample(50000, 5) | |
print('sample 2') | |
run_sample(44558, 10) | |
print('sample 3') | |
run_sample(1, 1) | |
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Oh I see. If you can make it to one of the MW 4:30 meetings you should, I think you should meet Anthony, he's running the ACM teams this year. Cheers