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def get_mid(p1: tuple[float, float], p2: tuple[float, float]) -> tuple[float, float]:
return (p1[0] + p2[0]) / 2, (p1[1] + p2[1]) / 2 | fractals |
def triangle(
vertex1: tuple[float, float],
vertex2: tuple[float, float],
vertex3: tuple[float, float],
depth: int,
) -> None:
my_pen.up()
my_pen.goto(vertex1[0], vertex1[1])
my_pen.down()
my_pen.goto(vertex2[0], vertex2[1])
my_pen.goto(vertex3[0], vertex3[1])
my_pen.goto(vertex1[0], vertex1[1])
if depth == 0:
return
triangle(vertex1, get_mid(vertex1, vertex2), get_mid(vertex1, vertex3), depth - 1)
triangle(vertex2, get_mid(vertex1, vertex2), get_mid(vertex2, vertex3), depth - 1)
triangle(vertex3, get_mid(vertex3, vertex2), get_mid(vertex1, vertex3), depth - 1) | fractals |
def get_distance(x: float, y: float, max_step: int) -> float:
a = x
b = y
for step in range(max_step): # noqa: B007
a_new = a * a - b * b + x
b = 2 * a * b + y
a = a_new
# divergence happens for all complex number with an absolute value
# greater than 4
if a * a + b * b > 4:
break
return step / (max_step - 1) | fractals |
def get_black_and_white_rgb(distance: float) -> tuple:
if distance == 1:
return (0, 0, 0)
else:
return (255, 255, 255) | fractals |
def get_color_coded_rgb(distance: float) -> tuple:
if distance == 1:
return (0, 0, 0)
else:
return tuple(round(i * 255) for i in colorsys.hsv_to_rgb(distance, 1, 1)) | fractals |
def get_image(
image_width: int = 800,
image_height: int = 600,
figure_center_x: float = -0.6,
figure_center_y: float = 0,
figure_width: float = 3.2,
max_step: int = 50,
use_distance_color_coding: bool = True,
) -> Image.Image:
img = Image.new("RGB", (image_width, image_height))
pixels = img.load()
# loop through the image-coordinates
for image_x in range(image_width):
for image_y in range(image_height):
# determine the figure-coordinates based on the image-coordinates
figure_height = figure_width / image_width * image_height
figure_x = figure_center_x + (image_x / image_width - 0.5) * figure_width
figure_y = figure_center_y + (image_y / image_height - 0.5) * figure_height
distance = get_distance(figure_x, figure_y, max_step)
# color the corresponding pixel based on the selected coloring-function
if use_distance_color_coding:
pixels[image_x, image_y] = get_color_coded_rgb(distance)
else:
pixels[image_x, image_y] = get_black_and_white_rgb(distance)
return img | fractals |
def iterate(initial_vectors: list[numpy.ndarray], steps: int) -> list[numpy.ndarray]:
vectors = initial_vectors
for _ in range(steps):
vectors = iteration_step(vectors)
return vectors | fractals |
def iteration_step(vectors: list[numpy.ndarray]) -> list[numpy.ndarray]:
new_vectors = []
for i, start_vector in enumerate(vectors[:-1]):
end_vector = vectors[i + 1]
new_vectors.append(start_vector)
difference_vector = end_vector - start_vector
new_vectors.append(start_vector + difference_vector / 3)
new_vectors.append(
start_vector + difference_vector / 3 + rotate(difference_vector / 3, 60)
)
new_vectors.append(start_vector + difference_vector * 2 / 3)
new_vectors.append(vectors[-1])
return new_vectors | fractals |
def rotate(vector: numpy.ndarray, angle_in_degrees: float) -> numpy.ndarray:
theta = numpy.radians(angle_in_degrees)
c, s = numpy.cos(theta), numpy.sin(theta)
rotation_matrix = numpy.array(((c, -s), (s, c)))
return numpy.dot(rotation_matrix, vector) | fractals |
def plot(vectors: list[numpy.ndarray]) -> None:
# avoid stretched display of graph
axes = plt.gca()
axes.set_aspect("equal")
# matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
# y-coordinates as inputs, which are constructed from the vector-list using
# zip()
x_coordinates, y_coordinates = zip(*vectors)
plt.plot(x_coordinates, y_coordinates)
plt.show() | fractals |
def minimum_squares_to_represent_a_number(number: int) -> int:
if number != int(number):
raise ValueError("the value of input must be a natural number")
if number < 0:
raise ValueError("the value of input must not be a negative number")
if number == 0:
return 1
answers = [-1] * (number + 1)
answers[0] = 0
for i in range(1, number + 1):
answer = sys.maxsize
root = int(math.sqrt(i))
for j in range(1, root + 1):
current_answer = 1 + answers[i - (j**2)]
answer = min(answer, current_answer)
answers[i] = answer
return answers[number] | dynamic_programming |
def fizz_buzz(number: int, iterations: int) -> str:
if not isinstance(iterations, int):
raise ValueError("iterations must be defined as integers")
if not isinstance(number, int) or not number >= 1:
raise ValueError(
)
if not iterations >= 1:
raise ValueError("Iterations must be done more than 0 times to play FizzBuzz")
out = ""
while number <= iterations:
if number % 3 == 0:
out += "Fizz"
if number % 5 == 0:
out += "Buzz"
if 0 not in (number % 3, number % 5):
out += str(number)
# print(out)
number += 1
out += " "
return out | dynamic_programming |
def combination_util(arr, n, r, index, data, i):
if index == r:
for j in range(r):
print(data[j], end=" ")
print(" ")
return
# When no more elements are there to put in data[]
if i >= n:
return
# current is included, put next at next location
data[index] = arr[i]
combination_util(arr, n, r, index + 1, data, i + 1)
# current is excluded, replace it with
# next (Note that i+1 is passed, but
# index is not changed)
combination_util(arr, n, r, index, data, i + 1)
# The main function that prints all combinations
# of size r in arr[] of size n. This function
# mainly uses combinationUtil() | dynamic_programming |
def print_combination(arr, n, r):
# A temporary array to store all combination one by one
data = [0] * r
# Print all combination using temporary array 'data[]'
combination_util(arr, n, r, 0, data, 0) | dynamic_programming |
def dynamic_programming(index: int) -> int:
if index > 365:
return 0
if index not in days_set:
return dynamic_programming(index + 1)
return min(
costs[0] + dynamic_programming(index + 1),
costs[1] + dynamic_programming(index + 7),
costs[2] + dynamic_programming(index + 30),
) | dynamic_programming |
def naive_cut_rod_recursive(n: int, prices: list):
_enforce_args(n, prices)
if n == 0:
return 0
max_revue = float("-inf")
for i in range(1, n + 1):
max_revue = max(
max_revue, prices[i - 1] + naive_cut_rod_recursive(n - i, prices)
)
return max_revue | dynamic_programming |
def top_down_cut_rod(n: int, prices: list):
_enforce_args(n, prices)
max_rev = [float("-inf") for _ in range(n + 1)]
return _top_down_cut_rod_recursive(n, prices, max_rev) | dynamic_programming |
def _top_down_cut_rod_recursive(n: int, prices: list, max_rev: list):
if max_rev[n] >= 0:
return max_rev[n]
elif n == 0:
return 0
else:
max_revenue = float("-inf")
for i in range(1, n + 1):
max_revenue = max(
max_revenue,
prices[i - 1] + _top_down_cut_rod_recursive(n - i, prices, max_rev),
)
max_rev[n] = max_revenue
return max_rev[n] | dynamic_programming |
def bottom_up_cut_rod(n: int, prices: list):
_enforce_args(n, prices)
# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
# length 0.
max_rev = [float("-inf") for _ in range(n + 1)]
max_rev[0] = 0
for i in range(1, n + 1):
max_revenue_i = max_rev[i]
for j in range(1, i + 1):
max_revenue_i = max(max_revenue_i, prices[j - 1] + max_rev[i - j])
max_rev[i] = max_revenue_i
return max_rev[n] | dynamic_programming |
def _enforce_args(n: int, prices: list):
if n < 0:
raise ValueError(f"n must be greater than or equal to 0. Got n = {n}")
if n > len(prices):
raise ValueError(
"Each integral piece of rod must have a corresponding "
f"price. Got n = {n} but length of prices = {len(prices)}"
) | dynamic_programming |
def main():
prices = [6, 10, 12, 15, 20, 23]
n = len(prices)
# the best revenue comes from cutting the rod into 6 pieces, each
# of length 1 resulting in a revenue of 6 * 6 = 36.
expected_max_revenue = 36
max_rev_top_down = top_down_cut_rod(n, prices)
max_rev_bottom_up = bottom_up_cut_rod(n, prices)
max_rev_naive = naive_cut_rod_recursive(n, prices)
assert expected_max_revenue == max_rev_top_down
assert max_rev_top_down == max_rev_bottom_up
assert max_rev_bottom_up == max_rev_naive | dynamic_programming |
def find_max_sub_array(a, low, high):
if low == high:
return low, high, a[low]
else:
mid = (low + high) // 2
left_low, left_high, left_sum = find_max_sub_array(a, low, mid)
right_low, right_high, right_sum = find_max_sub_array(a, mid + 1, high)
cross_left, cross_right, cross_sum = find_max_cross_sum(a, low, mid, high)
if left_sum >= right_sum and left_sum >= cross_sum:
return left_low, left_high, left_sum
elif right_sum >= left_sum and right_sum >= cross_sum:
return right_low, right_high, right_sum
else:
return cross_left, cross_right, cross_sum | dynamic_programming |
def find_max_cross_sum(a, low, mid, high):
left_sum, max_left = -999999999, -1
right_sum, max_right = -999999999, -1
summ = 0
for i in range(mid, low - 1, -1):
summ += a[i]
if summ > left_sum:
left_sum = summ
max_left = i
summ = 0
for i in range(mid + 1, high + 1):
summ += a[i]
if summ > right_sum:
right_sum = summ
max_right = i
return max_left, max_right, (left_sum + right_sum) | dynamic_programming |
def max_sub_array(nums: list[int]) -> int:
best = 0
current = 0
for i in nums:
current += i
current = max(current, 0)
best = max(best, current)
return best | dynamic_programming |
def all_construct(target: str, word_bank: list[str] | None = None) -> list[list[str]]:
word_bank = word_bank or []
# create a table
table_size: int = len(target) + 1
table: list[list[list[str]]] = []
for _ in range(table_size):
table.append([])
# seed value
table[0] = [[]] # because empty string has empty combination
# iterate through the indices
for i in range(table_size):
# condition
if table[i] != []:
for word in word_bank:
# slice condition
if target[i : i + len(word)] == word:
new_combinations: list[list[str]] = [
[word, *way] for way in table[i]
]
# adds the word to every combination the current position holds
# now,push that combination to the table[i+len(word)]
table[i + len(word)] += new_combinations
# combinations are in reverse order so reverse for better output
for combination in table[len(target)]:
combination.reverse()
return table[len(target)] | dynamic_programming |
def fibonacci(n: int) -> int:
if n < 0:
raise ValueError("Negative arguments are not supported")
return _fib(n)[0] | dynamic_programming |
def _fib(n: int) -> tuple[int, int]:
if n == 0: # (F(0), F(1))
return (0, 1)
# F(2n) = F(n)[2F(n+1) − F(n)]
# F(2n+1) = F(n+1)^2+F(n)^2
a, b = _fib(n // 2)
c = a * (b * 2 - a)
d = a * a + b * b
return (d, c + d) if n % 2 else (c, d) | dynamic_programming |
def min_distance(index1: int, index2: int) -> int:
# if first word index is overflow - delete all from the second word
if index1 >= len_word1:
return len_word2 - index2
# if second word index is overflow - delete all from the first word
if index2 >= len_word2:
return len_word1 - index1
diff = int(word1[index1] != word2[index2]) # current letters not identical
return min(
1 + min_distance(index1 + 1, index2),
1 + min_distance(index1, index2 + 1),
diff + min_distance(index1 + 1, index2 + 1),
) | dynamic_programming |
def abbr(a: str, b: str) -> bool:
n = len(a)
m = len(b)
dp = [[False for _ in range(m + 1)] for _ in range(n + 1)]
dp[0][0] = True
for i in range(n):
for j in range(m + 1):
if dp[i][j]:
if j < m and a[i].upper() == b[j]:
dp[i + 1][j + 1] = True
if a[i].islower():
dp[i + 1][j] = True
return dp[n][m] | dynamic_programming |
def max_subarray_sum(nums: list) -> int:
if not nums:
return 0
n = len(nums)
res, s, s_pre = nums[0], nums[0], nums[0]
for i in range(1, n):
s = max(nums[i], s_pre + nums[i])
s_pre = s
res = max(res, s)
return res | dynamic_programming |
def longest_common_subsequence(x: str, y: str):
# find the length of strings
assert x is not None
assert y is not None
m = len(x)
n = len(y)
# declaring the array for storing the dp values
l = [[0] * (n + 1) for _ in range(m + 1)] # noqa: E741
for i in range(1, m + 1):
for j in range(1, n + 1):
match = 1 if x[i - 1] == y[j - 1] else 0
l[i][j] = max(l[i - 1][j], l[i][j - 1], l[i - 1][j - 1] + match)
seq = ""
i, j = m, n
while i > 0 and j > 0:
match = 1 if x[i - 1] == y[j - 1] else 0
if l[i][j] == l[i - 1][j - 1] + match:
if match == 1:
seq = x[i - 1] + seq
i -= 1
j -= 1
elif l[i][j] == l[i - 1][j]:
i -= 1
else:
j -= 1
return l[m][n], seq | dynamic_programming |
def longest_common_substring(text1: str, text2: str) -> str:
if not (isinstance(text1, str) and isinstance(text2, str)):
raise ValueError("longest_common_substring() takes two strings for inputs")
text1_length = len(text1)
text2_length = len(text2)
dp = [[0] * (text2_length + 1) for _ in range(text1_length + 1)]
ans_index = 0
ans_length = 0
for i in range(1, text1_length + 1):
for j in range(1, text2_length + 1):
if text1[i - 1] == text2[j - 1]:
dp[i][j] = 1 + dp[i - 1][j - 1]
if dp[i][j] > ans_length:
ans_index = i
ans_length = dp[i][j]
return text1[ans_index - ans_length : ans_index] | dynamic_programming |
def mf_knapsack(i, wt, val, j):
global f # a global dp table for knapsack
if f[i][j] < 0:
if j < wt[i - 1]:
val = mf_knapsack(i - 1, wt, val, j)
else:
val = max(
mf_knapsack(i - 1, wt, val, j),
mf_knapsack(i - 1, wt, val, j - wt[i - 1]) + val[i - 1],
)
f[i][j] = val
return f[i][j] | dynamic_programming |
def knapsack(w, wt, val, n):
dp = [[0] * (w + 1) for _ in range(n + 1)]
for i in range(1, n + 1):
for w_ in range(1, w + 1):
if wt[i - 1] <= w_:
dp[i][w_] = max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]], dp[i - 1][w_])
else:
dp[i][w_] = dp[i - 1][w_]
return dp[n][w_], dp | dynamic_programming |
def knapsack_with_example_solution(w: int, wt: list, val: list):
if not (isinstance(wt, (list, tuple)) and isinstance(val, (list, tuple))):
raise ValueError(
"Both the weights and values vectors must be either lists or tuples"
)
num_items = len(wt)
if num_items != len(val):
raise ValueError(
"The number of weights must be the "
"same as the number of values.\nBut "
f"got {num_items} weights and {len(val)} values"
)
for i in range(num_items):
if not isinstance(wt[i], int):
raise TypeError(
"All weights must be integers but "
f"got weight of type {type(wt[i])} at index {i}"
)
optimal_val, dp_table = knapsack(w, wt, val, num_items)
example_optional_set: set = set()
_construct_solution(dp_table, wt, num_items, w, example_optional_set)
return optimal_val, example_optional_set | dynamic_programming |
def _construct_solution(dp: list, wt: list, i: int, j: int, optimal_set: set):
# for the current item i at a maximum weight j to be part of an optimal subset,
# the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
# where i - 1 means considering only the previous items at the given maximum weight
if i > 0 and j > 0:
if dp[i - 1][j] == dp[i][j]:
_construct_solution(dp, wt, i - 1, j, optimal_set)
else:
optimal_set.add(i)
_construct_solution(dp, wt, i - 1, j - wt[i - 1], optimal_set) | dynamic_programming |
def catalan_numbers(upper_limit: int) -> "list[int]":
if upper_limit < 0:
raise ValueError("Limit for the Catalan sequence must be ≥ 0")
catalan_list = [0] * (upper_limit + 1)
# Base case: C(0) = C(1) = 1
catalan_list[0] = 1
if upper_limit > 0:
catalan_list[1] = 1
# Recurrence relation: C(i) = sum(C(j).C(i-j-1)), from j = 0 to i
for i in range(2, upper_limit + 1):
for j in range(i):
catalan_list[i] += catalan_list[j] * catalan_list[i - j - 1]
return catalan_list | dynamic_programming |
def minimum_cost_path(matrix: list[list[int]]) -> int:
# preprocessing the first row
for i in range(1, len(matrix[0])):
matrix[0][i] += matrix[0][i - 1]
# preprocessing the first column
for i in range(1, len(matrix)):
matrix[i][0] += matrix[i - 1][0]
# updating the path cost for current position
for i in range(1, len(matrix)):
for j in range(1, len(matrix[0])):
matrix[i][j] += min(matrix[i - 1][j], matrix[i][j - 1])
return matrix[-1][-1] | dynamic_programming |
def dp_count(s, n):
if n < 0:
return 0
# table[i] represents the number of ways to get to amount i
table = [0] * (n + 1)
# There is exactly 1 way to get to zero(You pick no coins).
table[0] = 1
# Pick all coins one by one and update table[] values
# after the index greater than or equal to the value of the
# picked coin
for coin_val in s:
for j in range(coin_val, n + 1):
table[j] += table[j - coin_val]
return table[n] | dynamic_programming |
def matrix_chain_order(array):
n = len(array)
matrix = [[0 for x in range(n)] for x in range(n)]
sol = [[0 for x in range(n)] for x in range(n)]
for chain_length in range(2, n):
for a in range(1, n - chain_length + 1):
b = a + chain_length - 1
matrix[a][b] = sys.maxsize
for c in range(a, b):
cost = (
matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
)
if cost < matrix[a][b]:
matrix[a][b] = cost
sol[a][b] = c
return matrix, sol | dynamic_programming |
def print_optiomal_solution(optimal_solution, i, j):
if i == j:
print("A" + str(i), end=" ")
else:
print("(", end=" ")
print_optiomal_solution(optimal_solution, i, optimal_solution[i][j])
print_optiomal_solution(optimal_solution, optimal_solution[i][j] + 1, j)
print(")", end=" ") | dynamic_programming |
def main():
array = [30, 35, 15, 5, 10, 20, 25]
n = len(array)
# Size of matrix created from above array will be
# 30*35 35*15 15*5 5*10 10*20 20*25
matrix, optimal_solution = matrix_chain_order(array)
print("No. of Operation required: " + str(matrix[1][n - 1]))
print_optiomal_solution(optimal_solution, 1, n - 1) | dynamic_programming |
def count_of_possible_combinations(target: int) -> int:
if target < 0:
return 0
if target == 0:
return 1
return sum(count_of_possible_combinations(target - item) for item in array) | dynamic_programming |
def count_of_possible_combinations_with_dp_array(
target: int, dp_array: list[int] | dynamic_programming |
def combination_sum_iv_bottom_up(n: int, array: list[int], target: int) -> int:
dp_array = [0] * (target + 1)
dp_array[0] = 1
for i in range(1, target + 1):
for j in range(n):
if i - array[j] >= 0:
dp_array[i] += dp_array[i - array[j]]
return dp_array[target] | dynamic_programming |
def min_steps_to_one(number: int) -> int:
if number <= 0:
raise ValueError(f"n must be greater than 0. Got n = {number}")
table = [number + 1] * (number + 1)
# starting position
table[1] = 0
for i in range(1, number):
table[i + 1] = min(table[i + 1], table[i] + 1)
# check if out of bounds
if i * 2 <= number:
table[i * 2] = min(table[i * 2], table[i] + 1)
# check if out of bounds
if i * 3 <= number:
table[i * 3] = min(table[i * 3], table[i] + 1)
return table[number] | dynamic_programming |
def __init__(self, arr):
# we need a list not a string, so do something to change the type
self.array = arr.split(",") | dynamic_programming |
def solve_sub_array(self):
rear = [int(self.array[0])] * len(self.array)
sum_value = [int(self.array[0])] * len(self.array)
for i in range(1, len(self.array)):
sum_value[i] = max(
int(self.array[i]) + sum_value[i - 1], int(self.array[i])
)
rear[i] = max(sum_value[i], rear[i - 1])
return rear[len(self.array) - 1] | dynamic_programming |
def longest_subsequence(array: list[int]) -> list[int]: # This function is recursive
array_length = len(array)
# If the array contains only one element, we return it (it's the stop condition of
# recursion)
if array_length <= 1:
return array
# Else
pivot = array[0]
is_found = False
i = 1
longest_subseq: list[int] = []
while not is_found and i < array_length:
if array[i] < pivot:
is_found = True
temp_array = [element for element in array[i:] if element >= array[i]]
temp_array = longest_subsequence(temp_array)
if len(temp_array) > len(longest_subseq):
longest_subseq = temp_array
else:
i += 1
temp_array = [element for element in array[1:] if element >= pivot]
temp_array = [pivot, *longest_subsequence(temp_array)]
if len(temp_array) > len(longest_subseq):
return temp_array
else:
return longest_subseq | dynamic_programming |
def __init__(self, task_performed, total):
self.total_tasks = total # total no of tasks (N)
# DP table will have a dimension of (2^M)*N
# initially all values are set to -1
self.dp = [
[-1 for i in range(total + 1)] for j in range(2 ** len(task_performed))
]
self.task = defaultdict(list) # stores the list of persons for each task
# final_mask is used to check if all persons are included by setting all bits
# to 1
self.final_mask = (1 << len(task_performed)) - 1 | dynamic_programming |
def count_ways_until(self, mask, task_no):
# if mask == self.finalmask all persons are distributed tasks, return 1
if mask == self.final_mask:
return 1
# if not everyone gets the task and no more tasks are available, return 0
if task_no > self.total_tasks:
return 0
# if case already considered
if self.dp[mask][task_no] != -1:
return self.dp[mask][task_no]
# Number of ways when we don't this task in the arrangement
total_ways_util = self.count_ways_until(mask, task_no + 1)
# now assign the tasks one by one to all possible persons and recursively
# assign for the remaining tasks.
if task_no in self.task:
for p in self.task[task_no]:
# if p is already given a task
if mask & (1 << p):
continue
# assign this task to p and change the mask value. And recursively
# assign tasks with the new mask value.
total_ways_util += self.count_ways_until(mask | (1 << p), task_no + 1)
# save the value.
self.dp[mask][task_no] = total_ways_util
return self.dp[mask][task_no] | dynamic_programming |
def count_no_of_ways(self, task_performed):
# Store the list of persons for each task
for i in range(len(task_performed)):
for j in task_performed[i]:
self.task[j].append(i)
# call the function to fill the DP table, final answer is stored in dp[0][1]
return self.count_ways_until(0, 1) | dynamic_programming |
def factorial(num: int) -> int:
if num < 0:
raise ValueError("Number should not be negative.")
return 1 if num in (0, 1) else num * factorial(num - 1) | dynamic_programming |
def is_sum_subset(arr: list[int], required_sum: int) -> bool:
# a subset value says 1 if that subset sum can be formed else 0
# initially no subsets can be formed hence False/0
arr_len = len(arr)
subset = [[False] * (required_sum + 1) for _ in range(arr_len + 1)]
# for each arr value, a sum of zero(0) can be formed by not taking any element
# hence True/1
for i in range(arr_len + 1):
subset[i][0] = True
# sum is not zero and set is empty then false
for i in range(1, required_sum + 1):
subset[0][i] = False
for i in range(1, arr_len + 1):
for j in range(1, required_sum + 1):
if arr[i - 1] > j:
subset[i][j] = subset[i - 1][j]
if arr[i - 1] <= j:
subset[i][j] = subset[i - 1][j] or subset[i - 1][j - arr[i - 1]]
return subset[arr_len][required_sum] | dynamic_programming |
def __init__(self):
self.word1 = ""
self.word2 = ""
self.dp = [] | dynamic_programming |
def __min_dist_top_down_dp(self, m: int, n: int) -> int:
if m == -1:
return n + 1
elif n == -1:
return m + 1
elif self.dp[m][n] > -1:
return self.dp[m][n]
else:
if self.word1[m] == self.word2[n]:
self.dp[m][n] = self.__min_dist_top_down_dp(m - 1, n - 1)
else:
insert = self.__min_dist_top_down_dp(m, n - 1)
delete = self.__min_dist_top_down_dp(m - 1, n)
replace = self.__min_dist_top_down_dp(m - 1, n - 1)
self.dp[m][n] = 1 + min(insert, delete, replace)
return self.dp[m][n] | dynamic_programming |
def min_dist_top_down(self, word1: str, word2: str) -> int:
self.word1 = word1
self.word2 = word2
self.dp = [[-1 for _ in range(len(word2))] for _ in range(len(word1))]
return self.__min_dist_top_down_dp(len(word1) - 1, len(word2) - 1) | dynamic_programming |
def min_dist_bottom_up(self, word1: str, word2: str) -> int:
self.word1 = word1
self.word2 = word2
m = len(word1)
n = len(word2)
self.dp = [[0 for _ in range(n + 1)] for _ in range(m + 1)]
for i in range(m + 1):
for j in range(n + 1):
if i == 0: # first string is empty
self.dp[i][j] = j
elif j == 0: # second string is empty
self.dp[i][j] = i
elif word1[i - 1] == word2[j - 1]: # last characters are equal
self.dp[i][j] = self.dp[i - 1][j - 1]
else:
insert = self.dp[i][j - 1]
delete = self.dp[i - 1][j]
replace = self.dp[i - 1][j - 1]
self.dp[i][j] = 1 + min(insert, delete, replace)
return self.dp[m][n] | dynamic_programming |
def __init__(self, n=0): # a graph with Node 0,1,...,N-1
self.n = n
self.w = [
[math.inf for j in range(0, n)] for i in range(0, n)
] # adjacency matrix for weight
self.dp = [
[math.inf for j in range(0, n)] for i in range(0, n)
] # dp[i][j] stores minimum distance from i to j | dynamic_programming |
def add_edge(self, u, v, w):
self.dp[u][v] = w | dynamic_programming |
def floyd_warshall(self):
for k in range(0, self.n):
for i in range(0, self.n):
for j in range(0, self.n):
self.dp[i][j] = min(self.dp[i][j], self.dp[i][k] + self.dp[k][j]) | dynamic_programming |
def show_min(self, u, v):
return self.dp[u][v] | dynamic_programming |
def list_of_submasks(mask: int) -> list[int]:
assert (
isinstance(mask, int) and mask > 0
), f"mask needs to be positive integer, your input {mask}"
all_submasks = []
submask = mask
while submask:
all_submasks.append(submask)
submask = (submask - 1) & mask
return all_submasks | dynamic_programming |
def climb_stairs(number_of_steps: int) -> int:
assert (
isinstance(number_of_steps, int) and number_of_steps > 0
), f"number_of_steps needs to be positive integer, your input {number_of_steps}"
if number_of_steps == 1:
return 1
previous, current = 1, 1
for _ in range(number_of_steps - 1):
current, previous = current + previous, current
return current | dynamic_programming |
def is_breakable(index: int) -> bool:
if index == len_string:
return True
trie_node = trie
for i in range(index, len_string):
trie_node = trie_node.get(string[i], None)
if trie_node is None:
return False
if trie_node.get(word_keeper_key, False) and is_breakable(i + 1):
return True
return False | dynamic_programming |
def partition(m: int) -> int:
memo: list[list[int]] = [[0 for _ in range(m)] for _ in range(m + 1)]
for i in range(m + 1):
memo[i][0] = 1
for n in range(m + 1):
for k in range(1, m):
memo[n][k] += memo[n][k - 1]
if n - k > 0:
memo[n][k] += memo[n - k - 1][k]
return memo[m][m - 1] | dynamic_programming |
def find_minimum_partitions(string: str) -> int:
length = len(string)
cut = [0] * length
is_palindromic = [[False for i in range(length)] for j in range(length)]
for i, c in enumerate(string):
mincut = i
for j in range(i + 1):
if c == string[j] and (i - j < 2 or is_palindromic[j + 1][i - 1]):
is_palindromic[j][i] = True
mincut = min(mincut, 0 if j == 0 else (cut[j - 1] + 1))
cut[i] = mincut
return cut[length - 1] | dynamic_programming |
def ceil_index(v, l, r, key): # noqa: E741
while r - l > 1:
m = (l + r) // 2
if v[m] >= key:
r = m
else:
l = m # noqa: E741
return r | dynamic_programming |
def longest_increasing_subsequence_length(v: list[int]) -> int:
if len(v) == 0:
return 0
tail = [0] * len(v)
length = 1
tail[0] = v[0]
for i in range(1, len(v)):
if v[i] < tail[0]:
tail[0] = v[i]
elif v[i] > tail[length - 1]:
tail[length] = v[i]
length += 1
else:
tail[ceil_index(tail, -1, length - 1, v[i])] = v[i]
return length | dynamic_programming |
def viterbi(
observations_space: list,
states_space: list,
initial_probabilities: dict,
transition_probabilities: dict,
emission_probabilities: dict,
) -> list:
_validation(
observations_space,
states_space,
initial_probabilities,
transition_probabilities,
emission_probabilities,
)
# Creates data structures and fill initial step
probabilities: dict = {}
pointers: dict = {}
for state in states_space:
observation = observations_space[0]
probabilities[(state, observation)] = (
initial_probabilities[state] * emission_probabilities[state][observation]
)
pointers[(state, observation)] = None
# Fills the data structure with the probabilities of
# different transitions and pointers to previous states
for o in range(1, len(observations_space)):
observation = observations_space[o]
prior_observation = observations_space[o - 1]
for state in states_space:
# Calculates the argmax for probability function
arg_max = ""
max_probability = -1
for k_state in states_space:
probability = (
probabilities[(k_state, prior_observation)]
* transition_probabilities[k_state][state]
* emission_probabilities[state][observation]
)
if probability > max_probability:
max_probability = probability
arg_max = k_state
# Update probabilities and pointers dicts
probabilities[(state, observation)] = (
probabilities[(arg_max, prior_observation)]
* transition_probabilities[arg_max][state]
* emission_probabilities[state][observation]
)
pointers[(state, observation)] = arg_max
# The final observation
final_observation = observations_space[len(observations_space) - 1]
# argmax for given final observation
arg_max = ""
max_probability = -1
for k_state in states_space:
probability = probabilities[(k_state, final_observation)]
if probability > max_probability:
max_probability = probability
arg_max = k_state
last_state = arg_max
# Process pointers backwards
previous = last_state
result = []
for o in range(len(observations_space) - 1, -1, -1):
result.append(previous)
previous = pointers[previous, observations_space[o]]
result.reverse()
return result | dynamic_programming |
def _validation(
observations_space: Any,
states_space: Any,
initial_probabilities: Any,
transition_probabilities: Any,
emission_probabilities: Any,
) -> None:
_validate_not_empty(
observations_space,
states_space,
initial_probabilities,
transition_probabilities,
emission_probabilities,
)
_validate_lists(observations_space, states_space)
_validate_dicts(
initial_probabilities, transition_probabilities, emission_probabilities
) | dynamic_programming |
def _validate_not_empty(
observations_space: Any,
states_space: Any,
initial_probabilities: Any,
transition_probabilities: Any,
emission_probabilities: Any,
) -> None:
if not all(
[
observations_space,
states_space,
initial_probabilities,
transition_probabilities,
emission_probabilities,
]
):
raise ValueError("There's an empty parameter") | dynamic_programming |
def _validate_lists(observations_space: Any, states_space: Any) -> None:
_validate_list(observations_space, "observations_space")
_validate_list(states_space, "states_space") | dynamic_programming |
def _validate_list(_object: Any, var_name: str) -> None:
if not isinstance(_object, list):
raise ValueError(f"{var_name} must be a list")
else:
for x in _object:
if not isinstance(x, str):
raise ValueError(f"{var_name} must be a list of strings") | dynamic_programming |
def _validate_dicts(
initial_probabilities: Any,
transition_probabilities: Any,
emission_probabilities: Any,
) -> None:
_validate_dict(initial_probabilities, "initial_probabilities", float)
_validate_nested_dict(transition_probabilities, "transition_probabilities")
_validate_nested_dict(emission_probabilities, "emission_probabilities") | dynamic_programming |
def _validate_nested_dict(_object: Any, var_name: str) -> None:
_validate_dict(_object, var_name, dict)
for x in _object.values():
_validate_dict(x, var_name, float, True) | dynamic_programming |
def _validate_dict(
_object: Any, var_name: str, value_type: type, nested: bool = False
) -> None:
if not isinstance(_object, dict):
raise ValueError(f"{var_name} must be a dict")
if not all(isinstance(x, str) for x in _object):
raise ValueError(f"{var_name} all keys must be strings")
if not all(isinstance(x, value_type) for x in _object.values()):
nested_text = "nested dictionary " if nested else ""
raise ValueError(
f"{var_name} {nested_text}all values must be {value_type.__name__}"
) | dynamic_programming |
def __init__(self) -> None:
self.sequence = [0, 1] | dynamic_programming |
def get(self, index: int) -> list:
if (difference := index - (len(self.sequence) - 2)) >= 1:
for _ in range(difference):
self.sequence.append(self.sequence[-1] + self.sequence[-2])
return self.sequence[:index] | dynamic_programming |
def main():
print(
"Fibonacci Series Using Dynamic Programming\n",
"Enter the index of the Fibonacci number you want to calculate ",
"in the prompt below. (To exit enter exit or Ctrl-C)\n",
sep="",
)
fibonacci = Fibonacci()
while True:
prompt: str = input(">> ")
if prompt in {"exit", "quit"}:
break
try:
index: int = int(prompt)
except ValueError:
print("Enter a number or 'exit'")
continue
print(fibonacci.get(index)) | dynamic_programming |
def maximum_non_adjacent_sum(nums: list[int]) -> int:
if not nums:
return 0
max_including = nums[0]
max_excluding = 0
for num in nums[1:]:
max_including, max_excluding = (
max_excluding + num,
max(max_including, max_excluding),
)
return max(max_excluding, max_including) | dynamic_programming |
def __init__(
self,
sample: list[list[float]],
target: list[int],
learning_rate: float = 0.01,
epoch_number: int = 1000,
bias: float = -1,
) -> None:
self.sample = sample
if len(self.sample) == 0:
raise ValueError("Sample data can not be empty")
self.target = target
if len(self.target) == 0:
raise ValueError("Target data can not be empty")
if len(self.sample) != len(self.target):
raise ValueError("Sample data and Target data do not have matching lengths")
self.learning_rate = learning_rate
self.epoch_number = epoch_number
self.bias = bias
self.number_sample = len(sample)
self.col_sample = len(sample[0]) # number of columns in dataset
self.weight: list = [] | neural_network |
def training(self) -> None:
for sample in self.sample:
sample.insert(0, self.bias)
for _ in range(self.col_sample):
self.weight.append(random.random())
self.weight.insert(0, self.bias)
epoch_count = 0
while True:
has_misclassified = False
for i in range(self.number_sample):
u = 0
for j in range(self.col_sample + 1):
u = u + self.weight[j] * self.sample[i][j]
y = self.sign(u)
if y != self.target[i]:
for j in range(self.col_sample + 1):
self.weight[j] = (
self.weight[j]
+ self.learning_rate
* (self.target[i] - y)
* self.sample[i][j]
)
has_misclassified = True
# print('Epoch: \n',epoch_count)
epoch_count = epoch_count + 1
# if you want control the epoch or just by error
if not has_misclassified:
print(("\nEpoch:\n", epoch_count))
print("------------------------\n")
# if epoch_count > self.epoch_number or not error:
break | neural_network |
def sort(self, sample: list[float]) -> None:
if len(self.sample) == 0:
raise ValueError("Sample data can not be empty")
sample.insert(0, self.bias)
u = 0
for i in range(self.col_sample + 1):
u = u + self.weight[i] * sample[i]
y = self.sign(u)
if y == -1:
print(("Sample: ", sample))
print("classification: P1")
else:
print(("Sample: ", sample))
print("classification: P2") | neural_network |
def sign(self, u: float) -> int:
return 1 if u >= 0 else -1 | neural_network |
def sigmoid(x):
return 1 / (1 + np.exp(-1 * x)) | neural_network |
def __init__(
self, units, activation=None, learning_rate=None, is_input_layer=False
):
self.units = units
self.weight = None
self.bias = None
self.activation = activation
if learning_rate is None:
learning_rate = 0.3
self.learn_rate = learning_rate
self.is_input_layer = is_input_layer | neural_network |
def initializer(self, back_units):
self.weight = np.asmatrix(np.random.normal(0, 0.5, (self.units, back_units)))
self.bias = np.asmatrix(np.random.normal(0, 0.5, self.units)).T
if self.activation is None:
self.activation = sigmoid | neural_network |
def cal_gradient(self):
# activation function may be sigmoid or linear
if self.activation == sigmoid:
gradient_mat = np.dot(self.output, (1 - self.output).T)
gradient_activation = np.diag(np.diag(gradient_mat))
else:
gradient_activation = 1
return gradient_activation | neural_network |
def forward_propagation(self, xdata):
self.xdata = xdata
if self.is_input_layer:
# input layer
self.wx_plus_b = xdata
self.output = xdata
return xdata
else:
self.wx_plus_b = np.dot(self.weight, self.xdata) - self.bias
self.output = self.activation(self.wx_plus_b)
return self.output | neural_network |
def back_propagation(self, gradient):
gradient_activation = self.cal_gradient() # i * i 维
gradient = np.asmatrix(np.dot(gradient.T, gradient_activation))
self._gradient_weight = np.asmatrix(self.xdata)
self._gradient_bias = -1
self._gradient_x = self.weight
self.gradient_weight = np.dot(gradient.T, self._gradient_weight.T)
self.gradient_bias = gradient * self._gradient_bias
self.gradient = np.dot(gradient, self._gradient_x).T
# upgrade: the Negative gradient direction
self.weight = self.weight - self.learn_rate * self.gradient_weight
self.bias = self.bias - self.learn_rate * self.gradient_bias.T
# updates the weights and bias according to learning rate (0.3 if undefined)
return self.gradient | neural_network |
def __init__(self):
self.layers = []
self.train_mse = []
self.fig_loss = plt.figure()
self.ax_loss = self.fig_loss.add_subplot(1, 1, 1) | neural_network |
def add_layer(self, layer):
self.layers.append(layer) | neural_network |
def build(self):
for i, layer in enumerate(self.layers[:]):
if i < 1:
layer.is_input_layer = True
else:
layer.initializer(self.layers[i - 1].units) | neural_network |
def summary(self):
for i, layer in enumerate(self.layers[:]):
print(f"------- layer {i} -------")
print("weight.shape ", np.shape(layer.weight))
print("bias.shape ", np.shape(layer.bias)) | neural_network |
def train(self, xdata, ydata, train_round, accuracy):
self.train_round = train_round
self.accuracy = accuracy
self.ax_loss.hlines(self.accuracy, 0, self.train_round * 1.1)
x_shape = np.shape(xdata)
for _ in range(train_round):
all_loss = 0
for row in range(x_shape[0]):
_xdata = np.asmatrix(xdata[row, :]).T
_ydata = np.asmatrix(ydata[row, :]).T
# forward propagation
for layer in self.layers:
_xdata = layer.forward_propagation(_xdata)
loss, gradient = self.cal_loss(_ydata, _xdata)
all_loss = all_loss + loss
# back propagation: the input_layer does not upgrade
for layer in self.layers[:0:-1]:
gradient = layer.back_propagation(gradient)
mse = all_loss / x_shape[0]
self.train_mse.append(mse)
self.plot_loss()
if mse < self.accuracy:
print("----达到精度----")
return mse
return None | neural_network |
def cal_loss(self, ydata, ydata_):
self.loss = np.sum(np.power((ydata - ydata_), 2))
self.loss_gradient = 2 * (ydata_ - ydata)
# vector (shape is the same as _ydata.shape)
return self.loss, self.loss_gradient | neural_network |
def plot_loss(self):
if self.ax_loss.lines:
self.ax_loss.lines.remove(self.ax_loss.lines[0])
self.ax_loss.plot(self.train_mse, "r-")
plt.ion()
plt.xlabel("step")
plt.ylabel("loss")
plt.show()
plt.pause(0.1) | neural_network |
def example():
x = np.random.randn(10, 10)
y = np.asarray(
[
[0.8, 0.4],
[0.4, 0.3],
[0.34, 0.45],
[0.67, 0.32],
[0.88, 0.67],
[0.78, 0.77],
[0.55, 0.66],
[0.55, 0.43],
[0.54, 0.1],
[0.1, 0.5],
]
)
model = BPNN()
for i in (10, 20, 30, 2):
model.add_layer(DenseLayer(i))
model.build()
model.summary()
model.train(xdata=x, ydata=y, train_round=100, accuracy=0.01) | neural_network |
def __init__(
self, conv1_get, size_p1, bp_num1, bp_num2, bp_num3, rate_w=0.2, rate_t=0.2
):
self.num_bp1 = bp_num1
self.num_bp2 = bp_num2
self.num_bp3 = bp_num3
self.conv1 = conv1_get[:2]
self.step_conv1 = conv1_get[2]
self.size_pooling1 = size_p1
self.rate_weight = rate_w
self.rate_thre = rate_t
self.w_conv1 = [
np.mat(-1 * np.random.rand(self.conv1[0], self.conv1[0]) + 0.5)
for i in range(self.conv1[1])
]
self.wkj = np.mat(-1 * np.random.rand(self.num_bp3, self.num_bp2) + 0.5)
self.vji = np.mat(-1 * np.random.rand(self.num_bp2, self.num_bp1) + 0.5)
self.thre_conv1 = -2 * np.random.rand(self.conv1[1]) + 1
self.thre_bp2 = -2 * np.random.rand(self.num_bp2) + 1
self.thre_bp3 = -2 * np.random.rand(self.num_bp3) + 1 | neural_network |