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def __len__(self) -> int:
return self.nodes | graphs |
def add_node(self, node: T) -> None:
# Add a node in the graph if it is not in the graph
if node not in self.connections:
self.connections[node] = {}
self.nodes += 1 | graphs |
def add_edge(self, node1: T, node2: T, weight: int) -> None:
# Add an edge between 2 nodes in the graph
self.add_node(node1)
self.add_node(node2)
self.connections[node1][node2] = weight
self.connections[node2][node1] = weight | graphs |
def find_parent(i):
if i != parent[i]:
parent[i] = find_parent(parent[i])
return parent[i] | graphs |
def __init__(self, graph, sources, sinks):
self.source_index = None
self.sink_index = None
self.graph = graph
self._normalize_graph(sources, sinks)
self.vertices_count = len(graph)
self.maximum_flow_algorithm = None | graphs |
def _normalize_graph(self, sources, sinks):
if sources is int:
sources = [sources]
if sinks is int:
sinks = [sinks]
if len(sources) == 0 or len(sinks) == 0:
return
self.source_index = sources[0]
self.sink_index = sinks[0]
# make fake vertex if there are more
# than one source or sink
if len(sources) > 1 or len(sinks) > 1:
max_input_flow = 0
for i in sources:
max_input_flow += sum(self.graph[i])
size = len(self.graph) + 1
for room in self.graph:
room.insert(0, 0)
self.graph.insert(0, [0] * size)
for i in sources:
self.graph[0][i + 1] = max_input_flow
self.source_index = 0
size = len(self.graph) + 1
for room in self.graph:
room.append(0)
self.graph.append([0] * size)
for i in sinks:
self.graph[i + 1][size - 1] = max_input_flow
self.sink_index = size - 1 | graphs |
def find_maximum_flow(self):
if self.maximum_flow_algorithm is None:
raise Exception("You need to set maximum flow algorithm before.")
if self.source_index is None or self.sink_index is None:
return 0
self.maximum_flow_algorithm.execute()
return self.maximum_flow_algorithm.getMaximumFlow() | graphs |
def set_maximum_flow_algorithm(self, algorithm):
self.maximum_flow_algorithm = algorithm(self) | graphs |
def __init__(self, flow_network):
self.flow_network = flow_network
self.verticies_count = flow_network.verticesCount
self.source_index = flow_network.sourceIndex
self.sink_index = flow_network.sinkIndex
# it's just a reference, so you shouldn't change
# it in your algorithms, use deep copy before doing that
self.graph = flow_network.graph
self.executed = False | graphs |
def execute(self):
if not self.executed:
self._algorithm()
self.executed = True | graphs |
def _algorithm(self):
pass | graphs |
def __init__(self, flow_network):
super().__init__(flow_network)
# use this to save your result
self.maximum_flow = -1 | graphs |
def get_maximum_flow(self):
if not self.executed:
raise Exception("You should execute algorithm before using its result!")
return self.maximum_flow | graphs |
def __init__(self, flow_network):
super().__init__(flow_network)
self.preflow = [[0] * self.verticies_count for i in range(self.verticies_count)]
self.heights = [0] * self.verticies_count
self.excesses = [0] * self.verticies_count | graphs |
def _algorithm(self):
self.heights[self.source_index] = self.verticies_count
# push some substance to graph
for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index]):
self.preflow[self.source_index][nextvertex_index] += bandwidth
self.preflow[nextvertex_index][self.source_index] -= bandwidth
self.excesses[nextvertex_index] += bandwidth
# Relabel-to-front selection rule
vertices_list = [
i
for i in range(self.verticies_count)
if i != self.source_index and i != self.sink_index
]
# move through list
i = 0
while i < len(vertices_list):
vertex_index = vertices_list[i]
previous_height = self.heights[vertex_index]
self.process_vertex(vertex_index)
if self.heights[vertex_index] > previous_height:
# if it was relabeled, swap elements
# and start from 0 index
vertices_list.insert(0, vertices_list.pop(i))
i = 0
else:
i += 1
self.maximum_flow = sum(self.preflow[self.source_index]) | graphs |
def process_vertex(self, vertex_index):
while self.excesses[vertex_index] > 0:
for neighbour_index in range(self.verticies_count):
# if it's neighbour and current vertex is higher
if (
self.graph[vertex_index][neighbour_index]
- self.preflow[vertex_index][neighbour_index]
> 0
and self.heights[vertex_index] > self.heights[neighbour_index]
):
self.push(vertex_index, neighbour_index)
self.relabel(vertex_index) | graphs |
def push(self, from_index, to_index):
preflow_delta = min(
self.excesses[from_index],
self.graph[from_index][to_index] - self.preflow[from_index][to_index],
)
self.preflow[from_index][to_index] += preflow_delta
self.preflow[to_index][from_index] -= preflow_delta
self.excesses[from_index] -= preflow_delta
self.excesses[to_index] += preflow_delta | graphs |
def relabel(self, vertex_index):
min_height = None
for to_index in range(self.verticies_count):
if (
self.graph[vertex_index][to_index]
- self.preflow[vertex_index][to_index]
> 0
) and (min_height is None or self.heights[to_index] < min_height):
min_height = self.heights[to_index]
if min_height is not None:
self.heights[vertex_index] = min_height + 1 | graphs |
def __init__(self, graph: dict[str, list[str]], source_vertex: str) -> None:
self.graph = graph
# mapping node to its parent in resulting breadth first tree
self.parent: dict[str, str | None] = {}
self.source_vertex = source_vertex | graphs |
def breath_first_search(self) -> None:
visited = {self.source_vertex}
self.parent[self.source_vertex] = None
queue = [self.source_vertex] # first in first out queue
while queue:
vertex = queue.pop(0)
for adjacent_vertex in self.graph[vertex]:
if adjacent_vertex not in visited:
visited.add(adjacent_vertex)
self.parent[adjacent_vertex] = vertex
queue.append(adjacent_vertex) | graphs |
def shortest_path(self, target_vertex: str) -> str:
if target_vertex == self.source_vertex:
return self.source_vertex
target_vertex_parent = self.parent.get(target_vertex)
if target_vertex_parent is None:
raise ValueError(
f"No path from vertex: {self.source_vertex} to vertex: {target_vertex}"
)
return self.shortest_path(target_vertex_parent) + f"->{target_vertex}" | graphs |
def __init__(self):
self.cur_size = 0
self.array = []
self.pos = {} # To store the pos of node in array | graphs |
def is_empty(self):
return self.cur_size == 0 | graphs |
def min_heapify(self, idx):
lc = self.left(idx)
rc = self.right(idx)
if lc < self.cur_size and self.array(lc)[0] < self.array(idx)[0]:
smallest = lc
else:
smallest = idx
if rc < self.cur_size and self.array(rc)[0] < self.array(smallest)[0]:
smallest = rc
if smallest != idx:
self.swap(idx, smallest)
self.min_heapify(smallest) | graphs |
def insert(self, tup):
# Inserts a node into the Priority Queue
self.pos[tup[1]] = self.cur_size
self.cur_size += 1
self.array.append((sys.maxsize, tup[1]))
self.decrease_key((sys.maxsize, tup[1]), tup[0]) | graphs |
def extract_min(self):
# Removes and returns the min element at top of priority queue
min_node = self.array[0][1]
self.array[0] = self.array[self.cur_size - 1]
self.cur_size -= 1
self.min_heapify(1)
del self.pos[min_node]
return min_node | graphs |
def left(self, i):
# returns the index of left child
return 2 * i + 1 | graphs |
def right(self, i):
# returns the index of right child
return 2 * i + 2 | graphs |
def par(self, i):
# returns the index of parent
return math.floor(i / 2) | graphs |
def swap(self, i, j):
# swaps array elements at indices i and j
# update the pos{}
self.pos[self.array[i][1]] = j
self.pos[self.array[j][1]] = i
temp = self.array[i]
self.array[i] = self.array[j]
self.array[j] = temp | graphs |
def decrease_key(self, tup, new_d):
idx = self.pos[tup[1]]
# assuming the new_d is atmost old_d
self.array[idx] = (new_d, tup[1])
while idx > 0 and self.array[self.par(idx)][0] > self.array[idx][0]:
self.swap(idx, self.par(idx))
idx = self.par(idx) | graphs |
def __init__(self, num):
self.adjList = {} # To store graph: u -> (v,w)
self.num_nodes = num # Number of nodes in graph
# To store the distance from source vertex
self.dist = [0] * self.num_nodes
self.par = [-1] * self.num_nodes # To store the path | graphs |
def add_edge(self, u, v, w):
# Edge going from node u to v and v to u with weight w
# u (w)-> v, v (w) -> u
# Check if u already in graph
if u in self.adjList:
self.adjList[u].append((v, w))
else:
self.adjList[u] = [(v, w)]
# Assuming undirected graph
if v in self.adjList:
self.adjList[v].append((u, w))
else:
self.adjList[v] = [(u, w)] | graphs |
def show_graph(self):
# u -> v(w)
for u in self.adjList:
print(u, "->", " -> ".join(str(f"{v}({w})") for v, w in self.adjList[u])) | graphs |
def dijkstra(self, src):
# Flush old junk values in par[]
self.par = [-1] * self.num_nodes
# src is the source node
self.dist[src] = 0
q = PriorityQueue()
q.insert((0, src)) # (dist from src, node)
for u in self.adjList:
if u != src:
self.dist[u] = sys.maxsize # Infinity
self.par[u] = -1
while not q.is_empty():
u = q.extract_min() # Returns node with the min dist from source
# Update the distance of all the neighbours of u and
# if their prev dist was INFINITY then push them in Q
for v, w in self.adjList[u]:
new_dist = self.dist[u] + w
if self.dist[v] > new_dist:
if self.dist[v] == sys.maxsize:
q.insert((new_dist, v))
else:
q.decrease_key((self.dist[v], v), new_dist)
self.dist[v] = new_dist
self.par[v] = u
# Show the shortest distances from src
self.show_distances(src) | graphs |
def show_distances(self, src):
print(f"Distance from node: {src}")
for u in range(self.num_nodes):
print(f"Node {u} has distance: {self.dist[u]}") | graphs |
def show_path(self, src, dest):
# To show the shortest path from src to dest
# WARNING: Use it *after* calling dijkstra
path = []
cost = 0
temp = dest
# Backtracking from dest to src
while self.par[temp] != -1:
path.append(temp)
if temp != src:
for v, w in self.adjList[temp]:
if v == self.par[temp]:
cost += w
break
temp = self.par[temp]
path.append(src)
path.reverse()
print(f"----Path to reach {dest} from {src}----")
for u in path:
print(f"{u}", end=" ")
if u != dest:
print("-> ", end="")
print("\nTotal cost of path: ", cost) | graphs |
def topological_sort(graph):
indegree = [0] * len(graph)
queue = []
topo = []
cnt = 0
for values in graph.values():
for i in values:
indegree[i] += 1
for i in range(len(indegree)):
if indegree[i] == 0:
queue.append(i)
while queue:
vertex = queue.pop(0)
cnt += 1
topo.append(vertex)
for x in graph[vertex]:
indegree[x] -= 1
if indegree[x] == 0:
queue.append(x)
if cnt != len(graph):
print("Cycle exists")
else:
print(topo) | graphs |
def __init__(self, directed: bool = True) -> None:
self.adj_list: dict[T, list[T]] = {} # dictionary of lists
self.directed = directed | graphs |
def add_edge(
self, source_vertex: T, destination_vertex: T
) -> GraphAdjacencyList[T]:
if not self.directed: # For undirected graphs
# if both source vertex and destination vertex are both present in the
# adjacency list, add destination vertex to source vertex list of adjacent
# vertices and add source vertex to destination vertex list of adjacent
# vertices.
if source_vertex in self.adj_list and destination_vertex in self.adj_list:
self.adj_list[source_vertex].append(destination_vertex)
self.adj_list[destination_vertex].append(source_vertex)
# if only source vertex is present in adjacency list, add destination vertex
# to source vertex list of adjacent vertices, then create a new vertex with
# destination vertex as key and assign a list containing the source vertex
# as it's first adjacent vertex.
elif source_vertex in self.adj_list:
self.adj_list[source_vertex].append(destination_vertex)
self.adj_list[destination_vertex] = [source_vertex]
# if only destination vertex is present in adjacency list, add source vertex
# to destination vertex list of adjacent vertices, then create a new vertex
# with source vertex as key and assign a list containing the source vertex
# as it's first adjacent vertex.
elif destination_vertex in self.adj_list:
self.adj_list[destination_vertex].append(source_vertex)
self.adj_list[source_vertex] = [destination_vertex]
# if both source vertex and destination vertex are not present in adjacency
# list, create a new vertex with source vertex as key and assign a list
# containing the destination vertex as it's first adjacent vertex also
# create a new vertex with destination vertex as key and assign a list
# containing the source vertex as it's first adjacent vertex.
else:
self.adj_list[source_vertex] = [destination_vertex]
self.adj_list[destination_vertex] = [source_vertex]
else: # For directed graphs
# if both source vertex and destination vertex are present in adjacency
# list, add destination vertex to source vertex list of adjacent vertices.
if source_vertex in self.adj_list and destination_vertex in self.adj_list:
self.adj_list[source_vertex].append(destination_vertex)
# if only source vertex is present in adjacency list, add destination
# vertex to source vertex list of adjacent vertices and create a new vertex
# with destination vertex as key, which has no adjacent vertex
elif source_vertex in self.adj_list:
self.adj_list[source_vertex].append(destination_vertex)
self.adj_list[destination_vertex] = []
# if only destination vertex is present in adjacency list, create a new
# vertex with source vertex as key and assign a list containing destination
# vertex as first adjacent vertex
elif destination_vertex in self.adj_list:
self.adj_list[source_vertex] = [destination_vertex]
# if both source vertex and destination vertex are not present in adjacency
# list, create a new vertex with source vertex as key and a list containing
# destination vertex as it's first adjacent vertex. Then create a new vertex
# with destination vertex as key, which has no adjacent vertex
else:
self.adj_list[source_vertex] = [destination_vertex]
self.adj_list[destination_vertex] = []
return self | graphs |
def __init__(self, vertex):
self.vertex = vertex
self.graph = [[0] * vertex for i in range(vertex)] | graphs |
def add_edge(self, u, v):
self.graph[u - 1][v - 1] = 1
self.graph[v - 1][u - 1] = 1 | graphs |
def show(self):
for i in self.graph:
for j in i:
print(j, end=" ")
print(" ") | graphs |
def longest_distance(graph):
indegree = [0] * len(graph)
queue = []
long_dist = [1] * len(graph)
for values in graph.values():
for i in values:
indegree[i] += 1
for i in range(len(indegree)):
if indegree[i] == 0:
queue.append(i)
while queue:
vertex = queue.pop(0)
for x in graph[vertex]:
indegree[x] -= 1
if long_dist[vertex] + 1 > long_dist[x]:
long_dist[x] = long_dist[vertex] + 1
if indegree[x] == 0:
queue.append(x)
print(max(long_dist)) | graphs |
def _print_dist(dist, v):
print("\nThe shortest path matrix using Floyd Warshall algorithm\n")
for i in range(v):
for j in range(v):
if dist[i][j] != float("inf"):
print(int(dist[i][j]), end="\t")
else:
print("INF", end="\t")
print() | graphs |
def floyd_warshall(graph, v):
dist = [[float("inf") for _ in range(v)] for _ in range(v)]
for i in range(v):
for j in range(v):
dist[i][j] = graph[i][j]
# check vertex k against all other vertices (i, j)
for k in range(v):
# looping through rows of graph array
for i in range(v):
# looping through columns of graph array
for j in range(v):
if (
dist[i][k] != float("inf")
and dist[k][j] != float("inf")
and dist[i][k] + dist[k][j] < dist[i][j]
):
dist[i][j] = dist[i][k] + dist[k][j]
_print_dist(dist, v)
return dist, v | graphs |
def __init__(self, vertices: int) -> None:
self.vertices = vertices
self.graph = [[0] * vertices for _ in range(vertices)] | graphs |
def print_solution(self, distances_from_source: list[int]) -> None:
print("Vertex \t Distance from Source")
for vertex in range(self.vertices):
print(vertex, "\t\t", distances_from_source[vertex]) | graphs |
def minimum_distance(
self, distances_from_source: list[int], visited: list[bool]
) -> int:
# Initialize minimum distance for next node
minimum = 1e7
min_index = 0
# Search not nearest vertex not in the shortest path tree
for vertex in range(self.vertices):
if distances_from_source[vertex] < minimum and visited[vertex] is False:
minimum = distances_from_source[vertex]
min_index = vertex
return min_index | graphs |
def dijkstra(self, source: int) -> None:
distances = [int(1e7)] * self.vertices # distances from the source
distances[source] = 0
visited = [False] * self.vertices
for _ in range(self.vertices):
u = self.minimum_distance(distances, visited)
visited[u] = True
# Update dist value of the adjacent vertices
# of the picked vertex only if the current
# distance is greater than new distance and
# the vertex in not in the shortest path tree
for v in range(self.vertices):
if (
self.graph[u][v] > 0
and visited[v] is False
and distances[v] > distances[u] + self.graph[u][v]
):
distances[v] = distances[u] + self.graph[u][v]
self.print_solution(distances) | graphs |
def __init__(self, data: T) -> None:
self.data = data
self.parent = self
self.rank = 0 | graphs |
def __init__(self) -> None:
# map from node name to the node object
self.map: dict[T, DisjointSetTreeNode[T]] = {} | graphs |
def make_set(self, data: T) -> None:
# create a new set with x as its member
self.map[data] = DisjointSetTreeNode(data) | graphs |
def find_set(self, data: T) -> DisjointSetTreeNode[T]:
# find the set x belongs to (with path-compression)
elem_ref = self.map[data]
if elem_ref != elem_ref.parent:
elem_ref.parent = self.find_set(elem_ref.parent.data)
return elem_ref.parent | graphs |
def link(
self, node1: DisjointSetTreeNode[T], node2: DisjointSetTreeNode[T]
) -> None:
# helper function for union operation
if node1.rank > node2.rank:
node2.parent = node1
else:
node1.parent = node2
if node1.rank == node2.rank:
node2.rank += 1 | graphs |
def union(self, data1: T, data2: T) -> None:
# merge 2 disjoint sets
self.link(self.find_set(data1), self.find_set(data2)) | graphs |
def __init__(self) -> None:
# connections: map from the node to the neighbouring nodes (with weights)
self.connections: dict[T, dict[T, int]] = {} | graphs |
def add_node(self, node: T) -> None:
# add a node ONLY if its not present in the graph
if node not in self.connections:
self.connections[node] = {} | graphs |
def add_edge(self, node1: T, node2: T, weight: int) -> None:
# add an edge with the given weight
self.add_node(node1)
self.add_node(node2)
self.connections[node1][node2] = weight
self.connections[node2][node1] = weight | graphs |
def format_ruleset(ruleset: int) -> list[int]:
return [int(c) for c in f"{ruleset:08}"[:8]] | cellular_automata |
def new_generation(cells: list[list[int]], rule: list[int], time: int) -> list[int]:
population = len(cells[0]) # 31
next_generation = []
for i in range(population):
# Get the neighbors of each cell
# Handle neighbours outside bounds by using 0 as their value
left_neighbor = 0 if i == 0 else cells[time][i - 1]
right_neighbor = 0 if i == population - 1 else cells[time][i + 1]
# Define a new cell and add it to the new generation
situation = 7 - int(f"{left_neighbor}{cells[time][i]}{right_neighbor}", 2)
next_generation.append(rule[situation])
return next_generation | cellular_automata |
def generate_image(cells: list[list[int]]) -> Image.Image:
# Create the output image
img = Image.new("RGB", (len(cells[0]), len(cells)))
pixels = img.load()
# Generates image
for w in range(img.width):
for h in range(img.height):
color = 255 - int(255 * cells[h][w])
pixels[w, h] = (color, color, color)
return img | cellular_automata |
def new_generation(cells: list[list[int]]) -> list[list[int]]:
next_generation = []
for i in range(len(cells)):
next_generation_row = []
for j in range(len(cells[i])):
# Get the number of live neighbours
neighbour_count = 0
if i > 0 and j > 0:
neighbour_count += cells[i - 1][j - 1]
if i > 0:
neighbour_count += cells[i - 1][j]
if i > 0 and j < len(cells[i]) - 1:
neighbour_count += cells[i - 1][j + 1]
if j > 0:
neighbour_count += cells[i][j - 1]
if j < len(cells[i]) - 1:
neighbour_count += cells[i][j + 1]
if i < len(cells) - 1 and j > 0:
neighbour_count += cells[i + 1][j - 1]
if i < len(cells) - 1:
neighbour_count += cells[i + 1][j]
if i < len(cells) - 1 and j < len(cells[i]) - 1:
neighbour_count += cells[i + 1][j + 1]
# Rules of the game of life (excerpt from Wikipedia):
# 1. Any live cell with two or three live neighbours survives.
# 2. Any dead cell with three live neighbours becomes a live cell.
# 3. All other live cells die in the next generation.
# Similarly, all other dead cells stay dead.
alive = cells[i][j] == 1
if (
(alive and 2 <= neighbour_count <= 3)
or not alive
and neighbour_count == 3
):
next_generation_row.append(1)
else:
next_generation_row.append(0)
next_generation.append(next_generation_row)
return next_generation | cellular_automata |
def generate_images(cells: list[list[int]], frames: int) -> list[Image.Image]:
images = []
for _ in range(frames):
# Create output image
img = Image.new("RGB", (len(cells[0]), len(cells)))
pixels = img.load()
# Save cells to image
for x in range(len(cells)):
for y in range(len(cells[0])):
colour = 255 - cells[y][x] * 255
pixels[x, y] = (colour, colour, colour)
# Save image
images.append(img)
cells = new_generation(cells)
return images | cellular_automata |
def create_canvas(size: int) -> list[list[bool]]:
canvas = [[False for i in range(size)] for j in range(size)]
return canvas | cellular_automata |
def seed(canvas: list[list[bool]]) -> None:
for i, row in enumerate(canvas):
for j, _ in enumerate(row):
canvas[i][j] = bool(random.getrandbits(1)) | cellular_automata |
def run(canvas: list[list[bool]]) -> list[list[bool]]:
current_canvas = np.array(canvas)
next_gen_canvas = np.array(create_canvas(current_canvas.shape[0]))
for r, row in enumerate(current_canvas):
for c, pt in enumerate(row):
next_gen_canvas[r][c] = __judge_point(
pt, current_canvas[r - 1 : r + 2, c - 1 : c + 2]
)
current_canvas = next_gen_canvas
del next_gen_canvas # cleaning memory as we move on.
return_canvas: list[list[bool]] = current_canvas.tolist()
return return_canvas | cellular_automata |
def __judge_point(pt: bool, neighbours: list[list[bool]]) -> bool:
dead = 0
alive = 0
# finding dead or alive neighbours count.
for i in neighbours:
for status in i:
if status:
alive += 1
else:
dead += 1
# handling duplicate entry for focus pt.
if pt:
alive -= 1
else:
dead -= 1
# running the rules of game here.
state = pt
if pt:
if alive < 2:
state = False
elif alive == 2 or alive == 3:
state = True
elif alive > 3:
state = False
else:
if alive == 3:
state = True
return state | cellular_automata |
def construct_highway(
number_of_cells: int,
frequency: int,
initial_speed: int,
random_frequency: bool = False,
random_speed: bool = False,
max_speed: int = 5,
) -> list:
highway = [[-1] * number_of_cells] # Create a highway without any car
i = 0
initial_speed = max(initial_speed, 0)
while i < number_of_cells:
highway[0][i] = (
randint(0, max_speed) if random_speed else initial_speed
) # Place the cars
i += (
randint(1, max_speed * 2) if random_frequency else frequency
) # Arbitrary number, may need tuning
return highway | cellular_automata |
def get_distance(highway_now: list, car_index: int) -> int:
distance = 0
cells = highway_now[car_index + 1 :]
for cell in range(len(cells)): # May need a better name for this
if cells[cell] != -1: # If the cell is not empty then
return distance # we have the distance we wanted
distance += 1
# Here if the car is near the end of the highway
return distance + get_distance(highway_now, -1) | cellular_automata |
def update(highway_now: list, probability: float, max_speed: int) -> list:
number_of_cells = len(highway_now)
# Beforce calculations, the highway is empty
next_highway = [-1] * number_of_cells
for car_index in range(number_of_cells):
if highway_now[car_index] != -1:
# Add 1 to the current speed of the car and cap the speed
next_highway[car_index] = min(highway_now[car_index] + 1, max_speed)
# Number of empty cell before the next car
dn = get_distance(highway_now, car_index) - 1
# We can't have the car causing an accident
next_highway[car_index] = min(next_highway[car_index], dn)
if random() < probability:
# Randomly, a driver will slow down
next_highway[car_index] = max(next_highway[car_index] - 1, 0)
return next_highway | cellular_automata |
def simulate(
highway: list, number_of_update: int, probability: float, max_speed: int
) -> list:
number_of_cells = len(highway[0])
for i in range(number_of_update):
next_speeds_calculated = update(highway[i], probability, max_speed)
real_next_speeds = [-1] * number_of_cells
for car_index in range(number_of_cells):
speed = next_speeds_calculated[car_index]
if speed != -1:
# Change the position based on the speed (with % to create the loop)
index = (car_index + speed) % number_of_cells
# Commit the change of position
real_next_speeds[index] = speed
highway.append(real_next_speeds)
return highway | cellular_automata |
def newtons_second_law_of_motion(mass: float, acceleration: float) -> float:
force = float()
try:
force = mass * acceleration
except Exception:
return -0.0
return force | physics |
def shear_stress(
stress: float,
tangential_force: float,
area: float,
) -> tuple[str, float]:
if (stress, tangential_force, area).count(0) != 1:
raise ValueError("You cannot supply more or less than 2 values")
elif stress < 0:
raise ValueError("Stress cannot be negative")
elif tangential_force < 0:
raise ValueError("Tangential Force cannot be negative")
elif area < 0:
raise ValueError("Area cannot be negative")
elif stress == 0:
return (
"stress",
tangential_force / area,
)
elif tangential_force == 0:
return (
"tangential_force",
stress * area,
)
else:
return (
"area",
tangential_force / stress,
) | physics |
def malus_law(initial_intensity: float, angle: float) -> float:
if initial_intensity < 0:
raise ValueError("The value of intensity cannot be negative")
# handling of negative values of initial intensity
if angle < 0 or angle > 360:
raise ValueError("In Malus Law, the angle is in the range 0-360 degrees")
# handling of values out of allowed range
return initial_intensity * (math.cos(math.radians(angle)) ** 2) | physics |
def kinetic_energy(mass: float, velocity: float) -> float:
if mass < 0:
raise ValueError("The mass of a body cannot be negative")
return 0.5 * mass * abs(velocity) * abs(velocity) | physics |
def beta(velocity: float) -> float:
if velocity > c:
raise ValueError("Speed must not exceed light speed 299,792,458 [m/s]!")
elif velocity < 1:
# Usually the speed should be much higher than 1 (c order of magnitude)
raise ValueError("Speed must be greater than or equal to 1!")
return velocity / c | physics |
def gamma(velocity: float) -> float:
return 1 / sqrt(1 - beta(velocity) ** 2) | physics |
def transformation_matrix(velocity: float) -> np.ndarray:
return np.array(
[
[gamma(velocity), -gamma(velocity) * beta(velocity), 0, 0],
[-gamma(velocity) * beta(velocity), gamma(velocity), 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1],
]
) | physics |
def transform(velocity: float, event: np.ndarray | None = None) -> np.ndarray:
# Ensure event is not empty
if event is None:
event = np.array([ct, x, y, z]) # Symbolic four vector
else:
event[0] *= c # x0 is ct (speed of light * time)
return transformation_matrix(velocity) @ event | physics |
def archimedes_principle(
fluid_density: float, volume: float, gravity: float = g
) -> float:
if fluid_density <= 0:
raise ValueError("Impossible fluid density")
if volume < 0:
raise ValueError("Impossible Object volume")
if gravity <= 0:
raise ValueError("Impossible Gravity")
return fluid_density * gravity * volume | physics |
def casimir_force(force: float, area: float, distance: float) -> dict[str, float]:
if (force, area, distance).count(0) != 1:
raise ValueError("One and only one argument must be 0")
if force < 0:
raise ValueError("Magnitude of force can not be negative")
if distance < 0:
raise ValueError("Distance can not be negative")
if area < 0:
raise ValueError("Area can not be negative")
if force == 0:
force = (REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (
240 * (distance) ** 4
)
return {"force": force}
elif area == 0:
area = (240 * force * (distance) ** 4) / (
REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2
)
return {"area": area}
elif distance == 0:
distance = (
(REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (240 * force)
) ** (1 / 4)
return {"distance": distance}
raise ValueError("One and only one argument must be 0") | physics |
def check_args(init_velocity: float, angle: float) -> None:
# Ensure valid instance
if not isinstance(init_velocity, (int, float)):
raise TypeError("Invalid velocity. Should be a positive number.")
if not isinstance(angle, (int, float)):
raise TypeError("Invalid angle. Range is 1-90 degrees.")
# Ensure valid angle
if angle > 90 or angle < 1:
raise ValueError("Invalid angle. Range is 1-90 degrees.")
# Ensure valid velocity
if init_velocity < 0:
raise ValueError("Invalid velocity. Should be a positive number.") | physics |
def horizontal_distance(init_velocity: float, angle: float) -> float:
check_args(init_velocity, angle)
radians = angle_to_radians(2 * angle)
return round(init_velocity**2 * sin(radians) / g, 2) | physics |
def max_height(init_velocity: float, angle: float) -> float:
check_args(init_velocity, angle)
radians = angle_to_radians(angle)
return round(init_velocity**2 * sin(radians) ** 2 / (2 * g), 2) | physics |
def total_time(init_velocity: float, angle: float) -> float:
check_args(init_velocity, angle)
radians = angle_to_radians(angle)
return round(2 * init_velocity * sin(radians) / g, 2) | physics |
def test_motion() -> None:
v0, angle = 25, 20
assert horizontal_distance(v0, angle) == 40.97
assert max_height(v0, angle) == 3.73
assert total_time(v0, angle) == 1.74 | physics |
def gravitational_law(
force: float, mass_1: float, mass_2: float, distance: float
) -> dict[str, float]:
product_of_mass = mass_1 * mass_2
if (force, mass_1, mass_2, distance).count(0) != 1:
raise ValueError("One and only one argument must be 0")
if force < 0:
raise ValueError("Gravitational force can not be negative")
if distance < 0:
raise ValueError("Distance can not be negative")
if mass_1 < 0 or mass_2 < 0:
raise ValueError("Mass can not be negative")
if force == 0:
force = GRAVITATIONAL_CONSTANT * product_of_mass / (distance**2)
return {"force": force}
elif mass_1 == 0:
mass_1 = (force) * (distance**2) / (GRAVITATIONAL_CONSTANT * mass_2)
return {"mass_1": mass_1}
elif mass_2 == 0:
mass_2 = (force) * (distance**2) / (GRAVITATIONAL_CONSTANT * mass_1)
return {"mass_2": mass_2}
elif distance == 0:
distance = (GRAVITATIONAL_CONSTANT * product_of_mass / (force)) ** 0.5
return {"distance": distance}
raise ValueError("One and only one argument must be 0") | physics |
def rms_speed_of_molecule(temperature: float, molar_mass: float) -> float:
if temperature < 0:
raise Exception("Temperature cannot be less than 0 K")
if molar_mass <= 0:
raise Exception("Molar mass cannot be less than or equal to 0 kg/mol")
else:
return (3 * UNIVERSAL_GAS_CONSTANT * temperature / molar_mass) ** 0.5 | physics |
def hubble_parameter(
hubble_constant: float,
radiation_density: float,
matter_density: float,
dark_energy: float,
redshift: float,
) -> float:
parameters = [redshift, radiation_density, matter_density, dark_energy]
if any(p < 0 for p in parameters):
raise ValueError("All input parameters must be positive")
if any(p > 1 for p in parameters[1:4]):
raise ValueError("Relative densities cannot be greater than one")
else:
curvature = 1 - (matter_density + radiation_density + dark_energy)
e_2 = (
radiation_density * (redshift + 1) ** 4
+ matter_density * (redshift + 1) ** 3
+ curvature * (redshift + 1) ** 2
+ dark_energy
)
hubble = hubble_constant * e_2 ** (1 / 2)
return hubble | physics |
def centripetal(mass: float, velocity: float, radius: float) -> float:
if mass < 0:
raise ValueError("The mass of the body cannot be negative")
if radius <= 0:
raise ValueError("The radius is always a positive non zero integer")
return (mass * (velocity) ** 2) / radius | physics |
def pressure_of_gas_system(moles: float, kelvin: float, volume: float) -> float:
if moles < 0 or kelvin < 0 or volume < 0:
raise ValueError("Invalid inputs. Enter positive value.")
return moles * kelvin * UNIVERSAL_GAS_CONSTANT / volume | physics |
def volume_of_gas_system(moles: float, kelvin: float, pressure: float) -> float:
if moles < 0 or kelvin < 0 or pressure < 0:
raise ValueError("Invalid inputs. Enter positive value.")
return moles * kelvin * UNIVERSAL_GAS_CONSTANT / pressure | physics |
def potential_energy(mass: float, height: float) -> float:
# function will accept mass and height as parameters and return potential energy
if mass < 0:
# handling of negative values of mass
raise ValueError("The mass of a body cannot be negative")
if height < 0:
# handling of negative values of height
raise ValueError("The height above the ground cannot be negative")
return mass * g * height | physics |
def __init__(
self,
position_x: float,
position_y: float,
velocity_x: float,
velocity_y: float,
mass: float = 1.0,
size: float = 1.0,
color: str = "blue",
) -> None:
self.position_x = position_x
self.position_y = position_y
self.velocity_x = velocity_x
self.velocity_y = velocity_y
self.mass = mass
self.size = size
self.color = color | physics |
def position(self) -> tuple[float, float]:
return self.position_x, self.position_y | physics |
def velocity(self) -> tuple[float, float]:
return self.velocity_x, self.velocity_y | physics |
def update_velocity(
self, force_x: float, force_y: float, delta_time: float
) -> None:
self.velocity_x += force_x * delta_time
self.velocity_y += force_y * delta_time | physics |
def update_position(self, delta_time: float) -> None:
self.position_x += self.velocity_x * delta_time
self.position_y += self.velocity_y * delta_time | physics |
def __init__(
self,
bodies: list[Body],
gravitation_constant: float = 1.0,
time_factor: float = 1.0,
softening_factor: float = 0.0,
) -> None:
self.bodies = bodies
self.gravitation_constant = gravitation_constant
self.time_factor = time_factor
self.softening_factor = softening_factor | physics |