def solve(data):
grid = data
base = grid
for j in range(1, 5):
appendix = base + j
appendix[appendix > 9] -= 9
grid = np.concatenate((grid, appendix), axis = 0)
base = grid
for i in range(1, 5):
appendix = base + i
appendix[appendix > 9] -= 9
grid = np.concatenate((grid, appendix), axis = 1)
h, w = np.shape(grid)
graph = Graph()
for j in range(0, h):
for a, b in pairwise(range(0, w)):
graph.add_edge(j * h + a, j * h + b, grid[j][b])
graph.add_edge(j * h + b, j * h + a, grid[j][a])
for i in range(0, w):
for a, b in pairwise(range(0, h)):
graph.add_edge(a * h + i, b * h + i, grid[b][i])
graph.add_edge(b * h + i, a * h + i, grid[a][i])
return find_path(graph, 0, h * w - 1).total_cost
def insert(start, ruleSet, steps):
occurences = Counter()
pairOccurences = Counter()
for x in start:
occurences[x] += 1
pairs = pairwise(start)
for pair in pairs:
pairOccurences[pair] += 1
newPairOccurences = deepcopy(pairOccurences)
for _ in range(steps):
pairOccurences = deepcopy(newPairOccurences)
for (x, y), quantity in pairOccurences.items():
if quantity == 0:
continue
newElement = ruleSet[(x, y)]
occurences[newElement] += quantity
newPairOccurences[(x, newElement)] += quantity
newPairOccurences[(newElement, y)] += quantity
newPairOccurences[(x, y)] -= quantity
return occurences
def parts1and2(template, repl, num):
pairs = Counter(pairwise(template))
for _ in range(num):
pairs = _round2(pairs, repl)
counts = _count_elements(template[0], template[-1], pairs)
return max(counts.values()) - min(counts.values())
def insert(polymer, transformations):
inserted_polymer = []
for p in pairwise(polymer):
inserted_polymer += transform(p, transformations)
inserted_polymer.append(polymer[-1])
return "".join(inserted_polymer)
def transform(scid, point):
path = paths[(0, scid)]
for v, w in reversed(list(itertools.pairwise(path))):
po = lor(point)[oris[(v, w)]]
origin = pos[(v, w)]
point = tuple(ac + bc for ac, bc in zip(origin, po))
return point
def magnitude(self):
levels = self.levels
numbers = self.numbers
for level_curr in range(max(levels), 0, -1):
numbers_new = []
levels_new = []
paired = False
for inds in itertools.pairwise(range(len(numbers))):
i, j = inds
if levels[i] == levels[j] == level_curr:
if paired:
paired = False
else:
res = 3 * numbers[i] + 2 * numbers[j]
numbers_new.append(res)
levels_new.append(levels[i] - 1)
paired = True
else:
if not paired:
numbers_new.append(numbers[i])
levels_new.append(levels[i])
else:
paired = False
if j == len(numbers) - 1:
numbers_new.append(numbers[j])
levels_new.append(levels[j])
numbers = numbers_new
levels = levels_new
return numbers[0]
def start_pair_insertion_process(template: List[str], rules: Dict[str,
str]) -> int:
recipe: DefaultDict[str, int] = defaultdict(int)
polymer_counter = Counter("".join(template))
for polymer_pair in pairwise(template):
if "".join(polymer_pair) in recipe:
recipe["".join(polymer_pair)] += 1
else:
recipe["".join(polymer_pair)] = recipe.get("".join(polymer_pair),
1)
for _ in range(NUMBER_OF_STEPS):
pairs = {}
for pair, result in rules.items():
if pair in recipe and recipe[pair] > 0:
pairs.update({pair: result})
new_pairs: DefaultDict[str, int] = defaultdict(int)
for pair, result in pairs.items():
polymer_counter[result] += recipe[pair]
first_pair = pair[0] + result
second_pair = result + pair[1]
new_pairs[first_pair] += recipe[pair]
new_pairs[second_pair] += recipe[pair]
recipe[pair] = 0
for pair, value in new_pairs.items():
recipe[pair] = value
most_commons = polymer_counter.most_common(len(polymer_counter))
return most_commons[0][1] - most_commons[-1][1]
def generate_polymer(rules: Rules, template: str, steps: int = 40) -> int:
"""
Solves part 2.
Consider a rule AB -> C. If a polymer has 10 pairs AB, 10 new AC and CB
pairs are created, and the 10 AB pairs are "broken".
The resulting 10 C elements are added to the polymer.
"""
counts = Counter(template)
pairs = Counter(pairwise(template))
step = 0
while step < steps:
for (left, right), count in Counter(pairs).items():
result = rules[left, right]
# These pairs are created in one step
pairs[left, result] += count
pairs[result, right] += count
# The original pair is broken in one step
pairs[left, right] -= count
# Add to current count of the new element
counts[result] += count
step += 1
least_common, *_, most_common = sorted(counts.items(), key=itemgetter(1))
return most_common[1] - least_common[1]
def alienOrder(self, words: List[str]) -> str:
graph, s = defaultdict(list), set()
for w in words:
s = s.union(set(w))
d = [0] * 26
# pairwise(x) Return an iterator of overlapping pairs taken from the input iterator. ABCD -> AB BC CD
for a, b in pairwise(words):
for ca, cb in zip(a, b):
# 说明ca排在cb之前 拓扑可以变为 ca->cb ca出度+1 cb入度+1
if ca != cb:
graph[ca].append(cb)
d[ord(cb) - ord('a')] += 1
break
# 长度不同
else:
# abc > ab 这种不符合规则 ab abc 这种无法比较字母的字典序
if len(a) > len(b):
return ""
start = [k for k in s if d[ord(k) - ord('a')] == 0]
# 拓扑遍历 依次获取入度为0的点
for ch in start:
for nxt in graph[ch]:
d[v := ord(nxt) - ord('a')] -= 1
if not d[v]:
start.append(nxt)
return "".join(start) if len(start) == len(s) else ""
def part2(a):
return len([
i for i in range(*a)
if any(len(list(a[1])) == 2
for a in groupby(str(i))) and all(a <= b
for a, b in pairwise(str(i)))
])
def can_multiply(*matrices):
"""Does m0 @ m1 @ ... @ mn make sense?"""
for a, b in itertools.pairwise(matrices):
n, m = a.shape
k, l = b.shape
if m != k:
return False
return True
def build_graph(input_data: list[list[int]]) -> nx.Graph:
size = len(input_data)
graph = nx.DiGraph()
for i, line in enumerate(input_data):
for j, risk in enumerate(line):
graph.add_node((i, j), risk=risk)
for i1, i2 in pairwise(range(size)):
for j in range(size):
graph.add_edge((i1, j), (i2, j), risk=graph.nodes[i2, j]["risk"])
graph.add_edge((i2, j), (i1, j), risk=graph.nodes[i1, j]["risk"])
for i in range(size):
for j1, j2 in pairwise(range(size)):
graph.add_edge((i, j1), (i, j2), risk=graph.nodes[i, j2]["risk"])
graph.add_edge((i, j2), (i, j1), risk=graph.nodes[i, j1]["risk"])
return graph, size
def apply_pair_insertion(template, rules, *, steps):
pairs = Counter(map("".join, pairwise(template)))
for _ in range(steps):
counts = pairs.items()
pairs = Counter()
for pair, count in counts:
for new_pair in rules[pair]:
pairs[new_pair] += count
return pairs
def __init__(self, iterable):
prev = None
for prev_token, token in pairwise(iterable):
if prev is None:
self.head = Node(token=prev_token)
prev = self.head
v = Node(token=token)
prev.next = v
prev = v
def __call__(self, segment):
"""Add links between segment nodes to those previously collected."""
try:
nodes = [segment.downstream._nodes[-1]]
except AttributeError:
nodes = [segment._nodes[0]]
nodes.extend(segment._nodes[1:])
for head, tail in pairwise(nodes):
self._links.append((head, tail))
def part1(inp):
current = inp[0]
for _ in range(10):
s = ""
for a, b in pairwise(current):
s += a + inp[1][a + b]
current = s + current[-1]
v = sorted(Counter(current).values())
return v[-1] - v[0]
def process_fact(self):
_, fact = self.request.encoded_text.split("bbot:-")
if "-is-" in fact:
unknown_subject, description = fact.split("-is-")
elif "-are-" in fact:
unknown_subject, description = fact.split("-are-")
else:
return "yo"
subject = None
adjective = None
for word in unknown_subject.split("-"):
subject = Subject.objects.filter(name=word).first()
if subject:
unknown_subject = None
self.request.bot.unknown_subject = None
if not subject:
for word_one, word_two in pairwise(unknown_subject.split("-")):
possible_subject = f"{word_one}-{word_two}"
subject = Subject.objects.filter(name=possible_subject).first()
if subject:
unknown_subject = None
self.request.bot.unknown_subject = None
# We have a known subject
for word in description.split("-"):
possible_adjective = Phrase.objects.filter(
text=word, kind="ADJECTIVE").first()
if possible_adjective:
# we have a known adjective
adjective = possible_adjective
for word_one, word_two in pairwise(description.split("-")):
possible_adjective = f"{word_one}-{word_two}"
adjective = Phrase.objects.filter(text=possible_adjective,
kind="ADJECTIVE").first()
self.request.bot.save()
return self.follow_up(subject=subject,
adjective=adjective,
unknown_subject=unknown_subject,
unknown_adjective=description)
def magnitude(num):
num = num[:]
while len(num) > 1:
for i, ((n, d), (nn, dd)) in enumerate(pairwise(num)):
if d == dd:
num[i] = [3*n+2*nn, d-1]
del num[i+1]
break
assert num[0][1] == 0
return num[0][0]
def process(rules, polymer, remaining_steps):
if remaining_steps == 0:
return polymer
new_polymer = ""
for first_elem, second_elem in pairwise(polymer):
new_polymer += first_elem
new_polymer += rules[first_elem + second_elem]
new_polymer += polymer[-1]
return process(rules, new_polymer, remaining_steps - 1)
def run_polymerase(polymer: str, rules: dict[str, str], steps: int = 1) -> int:
pairs = dict(Counter(pairwise(polymer)).most_common())
for s in range(steps):
new_pairs = defaultdict(int)
for (l, r), total in pairs.items():
if i := rules.get(f"{l}{r}", ""):
new_pairs[f"{l}{i}"] += total
new_pairs[f"{i}{r}"] += total
else:
new_pairs[f"{l}{r}"] += total
pairs = new_pairs
def calc_route_fitness(route: np.array, weights: np.array) -> float:
edges = pairwise(route)
def get_weight(edge) -> float:
return weights[edge[0]][edge[1]]
def accumulator(s, edge):
return s + get_weight(edge)
fitness_result = reduce(accumulator, edges, 0)
return fitness_result
def alienOrder(self, words: List[str]) -> str:
graph = collections.defaultdict(list)
for s, t in itertools.pairwise(words):
for u, v in zip(s, t):
if u != v:
graph[u].append(v)
break
else:
if len(s) > len(t):
return ''
states = {}
order = []
def sanity(c):
if c[0] in ops:
return False
if c[5] in ops:
return False
for p in itertools.pairwise(c):
if p in op_doubles:
return False
else:
pass
return True
def difference_minmax_frequency(input=parse(), remaining_steps=40):
polymer, rules = input
frequencies = [
frequency(rules, first_elem, second_elem, remaining_steps)
for first_elem, second_elem in pairwise(polymer)
]
global_frequency = {polymer[-1]: 1}
for f in frequencies:
global_frequency = merge_frequency(global_frequency, f)
return max(global_frequency.values()) - min(global_frequency.values())
def evolve_polymer(polymer, rules, iterations):
for iteration in range(iterations):
new_polymer = [polymer[0]]
for pair in pairwise(polymer):
if pair in rules:
new_polymer.append(rules[pair])
new_polymer.append(pair[1])
polymer = "".join(new_polymer)
return polymer
def counts(*, rules: str, text: str, steps: int) -> dict:
translations = load_translations(rules)
if steps == 0:
return Counter(text)
counter = Counter({text[0]: 1})
for a, b in pairwise(text):
c = translations.get(a + b, '')
counter.update(counts(rules=rules, text=a + c + b, steps=steps - 1))
counter[a] -= 1
return counter
def grow_polymer(steps: int) -> int:
counter = Counter(map(lambda p: "".join(p), pairwise(polymer)))
for _ in range(steps):
new_counter = defaultdict[str, int](int)
for pair, count in counter.items():
new_counter[replace_rules[pair][0]] += count
new_counter[replace_rules[pair][1]] += count
counter = new_counter
letters = defaultdict[str, int](int)
for pair, count in counter.items():
letters[pair[0]] += count
letters[polymer[-1]] += 1 # last char never gets replaced
return max(letters.values()) - min(letters.values())
def part2():
steps = read_input()
x_divisions = set()
y_divisions = set()
z_divisions = set()
for step in steps:
x_divisions.add(step.xmin)
x_divisions.add(step.xmax + 1)
y_divisions.add(step.ymin)
y_divisions.add(step.ymax + 1)
z_divisions.add(step.zmin)
z_divisions.add(step.zmax + 1)
x_divisions = sorted(x_divisions)
y_divisions = sorted(y_divisions)
z_divisions = sorted(z_divisions)
shape = (len(x_divisions) - 1,
len(y_divisions) - 1,
len(z_divisions) - 1)
cuboids = np.zeros(shape, bool)
for step in steps:
value = (step.action == 'on')
cuboids[
x_divisions.index(step.xmin):x_divisions.index(step.xmax + 1),
y_divisions.index(step.ymin):y_divisions.index(step.ymax + 1),
z_divisions.index(step.zmin):z_divisions.index(step.zmax + 1)
] = value
x_weights = np.array([x2 - x1 for x1, x2 in pairwise(x_divisions)])
y_weights = np.array([y2 - y1 for y1, y2 in pairwise(y_divisions)])
z_weights = np.array([z2 - z1 for z1, z2 in pairwise(z_divisions)])
return np.einsum('xyz,x,y,z->', cuboids, x_weights, y_weights, z_weights)
def parse_input(input_file: TextIO) -> tuple[dict[str, int], dict[str, str]]:
polymer = next(input_file).strip()
next(input_file) # skip blank line
rules: dict[str, str] = {}
for line in input_file:
k, v = line.strip().split(" -> ")
rules[k] = v
polymer_counts: defaultdict[str, int] = defaultdict(int)
for element in polymer:
polymer_counts[element] += 1
for pair in pairwise(polymer):
polymer_counts["".join(pair)] += 1
return polymer_counts, rules
def get_polymer_element_frequencies(
polymer: str, rules: Rules, generations: int
) -> dict[tuple[str, str], int]:
counts = Counter(pairwise(polymer))
for _ in range(1, generations + 1):
new_count = defaultdict(lambda: 0)
for (a, b), count in counts.items():
insert = rules[a, b]
new_count[a, insert] += count
new_count[insert, b] += count
counts = new_count
return counts
def functional_ascending_impl(seq):
return all(l < r for l, r in pairwise(seq))
