def compute(): # Each die has (10 choose 6) arrangements, so we have at most 44100 arrangements to check ans = sum(1 for i in range(1 << 10) for j in range(i, 1 << 10) # Ensure i <= j to force the dice to be orderless # If both have Hamming weight of 6 if eulerlib.popcount(i) == eulerlib.popcount(j) == 6 and is_arrangement_valid(i, j)) return str(ans)
def compute():
# Each die has (10 choose 6) arrangements, so we have at most 44100 arrangements to check
ans = sum(1 for i in range(1 << 10) for j in range(
i, 1 << 10) # Ensure i <= j to force the dice to be orderless
# If both have Hamming weight of 6
if eulerlib.popcount(i) == eulerlib.popcount(j) == 6
and is_arrangement_valid(i, j))
return str(ans)
def sam_transitions_minus_max_transitions(n):
samtrans = 0
maxtrans = 0
segmentstate = 0
while True:
newstate = number_to_segments(n)
if newstate == segmentstate:
break
maxtrans += eulerlib.popcount(newstate ^ segmentstate)
segmentstate = newstate
samtrans += 2 * eulerlib.popcount(newstate)
n = digit_sum(n)
maxtrans += eulerlib.popcount(segmentstate)
return samtrans - maxtrans
def sam_transitions_minus_max_transitions(n): samtrans = 0 maxtrans = 0 segmentstate = 0 while True: newstate = number_to_segments(n) if newstate == segmentstate: break maxtrans += eulerlib.popcount(newstate ^ segmentstate) segmentstate = newstate samtrans += 2 * eulerlib.popcount(newstate) n = digit_sum(n) maxtrans += eulerlib.popcount(segmentstate) return samtrans - maxtrans
def list_all_states():
result = set()
# Try all 2^11 ways for which cells (or ant) hold a seed
for i in range(2**11):
if eulerlib.popcount(i) != 5:
continue # Invalid state if not 5 things hold a seed
# For all 5*5 possible ant positions
for y in range(5):
for x in range(5):
seed = [((i >> j) & 1) != 0 for j in range(11)]
result.add(State(False, x, y, seed))
result.add(State.DONE_STATE)
return result
def list_all_states(): result = set() # Try all 2^11 ways for which cells (or ant) hold a seed for i in range(2**11): if eulerlib.popcount(i) != 5: continue # Invalid state if not 5 things hold a seed # For all 5*5 possible ant positions for y in range(5): for x in range(5): seed = [((i >> j) & 1) != 0 for j in range(11)] result.add(State(False, x, y, seed)) result.add(State.DONE_STATE) return result
def find_maximum_sum(startrow, setofcols): if startrow == ROWS: assert eulerlib.popcount(setofcols) == COLUMNS - ROWS return 0 if maxsum[startrow][setofcols] is None: result = 0 col = 0 bit = 1 while True: if bit > setofcols: break if setofcols & bit != 0: result = max(MATRIX[startrow][col] + find_maximum_sum(startrow + 1, setofcols ^ bit), result) col += 1 bit <<= 1 maxsum[startrow][setofcols] = result return maxsum[startrow][setofcols]
def find_maximum_sum(startrow, setofcols):
if startrow == ROWS:
assert eulerlib.popcount(setofcols) == COLUMNS - ROWS
return 0
if maxsum[startrow][setofcols] is None:
result = 0
col = 0
bit = 1
while True:
if bit > setofcols:
break
if setofcols & bit != 0:
result = max(
MATRIX[startrow][col] +
find_maximum_sum(startrow + 1, setofcols ^ bit),
result)
col += 1
bit <<= 1
maxsum[startrow][setofcols] = result
return maxsum[startrow][setofcols]
def find_minimum_length(currentsphereindex, setofspheres):
if setofspheres & (1 << currentsphereindex) == 0:
raise ValueError()
# Memoization
if minlength[currentsphereindex][setofspheres] is None:
if eulerlib.popcount(setofspheres) == 1:
result = sphereradii[currentsphereindex] # This sphere is rightmost
else:
result = float("inf")
newsetofspheres = setofspheres ^ (1 << currentsphereindex)
for i in range(NUM_SPHERES): # i is the index of the next sphere
if newsetofspheres & (1 << i) == 0:
continue
# The sqrt() here is what makes the entire computation not guaranteed to be accurate
temp = math.sqrt((sphereradii[i] + sphereradii[currentsphereindex] - 50000) * 200000)
temp += find_minimum_length(i, newsetofspheres)
result = min(temp, result)
minlength[currentsphereindex][setofspheres] = result
return minlength[currentsphereindex][setofspheres]
def find_minimum_length(currentsphereindex, setofspheres):
if setofspheres & (1 << currentsphereindex) == 0:
raise ValueError()
# Memoization
if minlength[currentsphereindex][setofspheres] is None:
if eulerlib.popcount(setofspheres) == 1:
result = sphereradii[currentsphereindex] # This sphere is rightmost
else:
result = float("inf")
newsetofspheres = setofspheres ^ (1 << currentsphereindex)
for i in range(NUM_SPHERES): # i is the index of the next sphere
if newsetofspheres & (1 << i) == 0:
continue
# The sqrt() here is what makes the entire computation not guaranteed to be accurate
temp = math.sqrt((sphereradii[i] + sphereradii[currentsphereindex] - 50000) * 200000)
temp += find_minimum_length(i, newsetofspheres)
result = min(temp, result)
minlength[currentsphereindex][setofspheres] = result
return minlength[currentsphereindex][setofspheres]