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def next_point(
point_x: float, point_y: float, incoming_gradient: float
) -> tuple[float, float, float]:
# normal_gradient = gradient of line through which the beam is reflected
# outgoing_gradient = gradient of reflected line
normal_gradient = point_y / 4 / point_x
s2 = 2 * normal_gradient / (1 + normal_gradient * normal_gradient)
c2 = (1 - normal_gradient * normal_gradient) / (
1 + normal_gradient * normal_gradient
)
outgoing_gradient = (s2 - c2 * incoming_gradient) / (c2 + s2 * incoming_gradient)
# to find the next point, solve the simultaeneous equations:
# y^2 + 4x^2 = 100
# y - b = m * (x - a)
# ==> A x^2 + B x + C = 0
quadratic_term = outgoing_gradient**2 + 4
linear_term = 2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
constant_term = (point_y - outgoing_gradient * point_x) ** 2 - 100
x_minus = (
-linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term)
) / (2 * quadratic_term)
x_plus = (
-linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term)
) / (2 * quadratic_term)
# two solutions, one of which is our input point
next_x = x_minus if isclose(x_plus, point_x) else x_plus
next_y = point_y + outgoing_gradient * (next_x - point_x)
return next_x, next_y, outgoing_gradient | project_euler |
def solution(first_x_coord: float = 1.4, first_y_coord: float = -9.6) -> int:
num_reflections: int = 0
point_x: float = first_x_coord
point_y: float = first_y_coord
gradient: float = (10.1 - point_y) / (0.0 - point_x)
while not (-0.01 <= point_x <= 0.01 and point_y > 0):
point_x, point_y, gradient = next_point(point_x, point_y, gradient)
num_reflections += 1
return num_reflections | project_euler |
def _modexpt(base: int, exponent: int, modulo_value: int) -> int:
if exponent == 1:
return base
if exponent % 2 == 0:
x = _modexpt(base, exponent // 2, modulo_value) % modulo_value
return (x * x) % modulo_value
else:
return (base * _modexpt(base, exponent - 1, modulo_value)) % modulo_value | project_euler |
def solution(base: int = 1777, height: int = 1855, digits: int = 8) -> int:
# calculate base↑↑height by right-assiciative repeated modular
# exponentiation
result = base
for _ in range(1, height):
result = _modexpt(base, result, 10**digits)
return result | project_euler |
def solution(limit: int = 1000000) -> int:
limit = limit + 1
frequency = [0] * limit
for first_term in range(1, limit):
for n in range(first_term, limit, first_term):
common_difference = first_term + n / first_term
if common_difference % 4: # d must be divisble by 4
continue
else:
common_difference /= 4
if (
first_term > common_difference
and first_term < 4 * common_difference
): # since x,y,z are positive integers
frequency[n] += 1 # so z>0 and a>d ,also 4d<a
count = sum(1 for x in frequency[1:limit] if x == 10)
return count | project_euler |
def next_term(a_i, k, i, n):
# ds_b - digitsum(b)
ds_b = sum(a_i[j] for j in range(k, len(a_i)))
c = sum(a_i[j] * base[j] for j in range(min(len(a_i), k)))
diff, dn = 0, 0
max_dn = n - i
sub_memo = memo.get(ds_b)
if sub_memo is not None:
jumps = sub_memo.get(c)
if jumps is not None and len(jumps) > 0:
# find and make the largest jump without going over
max_jump = -1
for _k in range(len(jumps) - 1, -1, -1):
if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
max_jump = _k
break
if max_jump >= 0:
diff, dn, _kk = jumps[max_jump]
# since the difference between jumps is cached, add c
new_c = diff + c
for j in range(min(k, len(a_i))):
new_c, a_i[j] = divmod(new_c, 10)
if new_c > 0:
add(a_i, k, new_c)
else:
sub_memo[c] = []
else:
sub_memo = {c: []}
memo[ds_b] = sub_memo
if dn >= max_dn or c + diff >= base[k]:
return diff, dn
if k > ks[0]:
while True:
# keep doing smaller jumps
_diff, terms_jumped = next_term(a_i, k - 1, i + dn, n)
diff += _diff
dn += terms_jumped
if dn >= max_dn or c + diff >= base[k]:
break
else:
# would be too small a jump, just compute sequential terms instead
_diff, terms_jumped = compute(a_i, k, i + dn, n)
diff += _diff
dn += terms_jumped
jumps = sub_memo[c]
# keep jumps sorted by # of terms skipped
j = 0
while j < len(jumps):
if jumps[j][1] > dn:
break
j += 1
# cache the jump for this value digitsum(b) and c
sub_memo[c].insert(j, (diff, dn, k))
return (diff, dn) | project_euler |
def compute(a_i, k, i, n):
if i >= n:
return 0, i
if k > len(a_i):
a_i.extend([0 for _ in range(k - len(a_i))])
# note: a_i -> b * 10^k + c
# ds_b -> digitsum(b)
# ds_c -> digitsum(c)
start_i = i
ds_b, ds_c, diff = 0, 0, 0
for j in range(len(a_i)):
if j >= k:
ds_b += a_i[j]
else:
ds_c += a_i[j]
while i < n:
i += 1
addend = ds_c + ds_b
diff += addend
ds_c = 0
for j in range(k):
s = a_i[j] + addend
addend, a_i[j] = divmod(s, 10)
ds_c += a_i[j]
if addend > 0:
break
if addend > 0:
add(a_i, k, addend)
return diff, i - start_i | project_euler |
def add(digits, k, addend):
for j in range(k, len(digits)):
s = digits[j] + addend
if s >= 10:
quotient, digits[j] = divmod(s, 10)
addend = addend // 10 + quotient
else:
digits[j] = s
addend = addend // 10
if addend == 0:
break
while addend > 0:
addend, digit = divmod(addend, 10)
digits.append(digit) | project_euler |
def solution(n: int = 10**15) -> int:
digits = [1]
i = 1
dn = 0
while True:
diff, terms_jumped = next_term(digits, 20, i + dn, n)
dn += terms_jumped
if dn == n - i:
break
a_n = 0
for j in range(len(digits)):
a_n += digits[j] * 10**j
return a_n | project_euler |
def check(number: int) -> bool:
check_last = [0] * 11
check_front = [0] * 11
# mark last 9 numbers
for _ in range(9):
check_last[int(number % 10)] = 1
number = number // 10
# flag
f = True
# check last 9 numbers for pandigitality
for x in range(9):
if not check_last[x + 1]:
f = False
if not f:
return f
# mark first 9 numbers
number = int(str(number)[:9])
for _ in range(9):
check_front[int(number % 10)] = 1
number = number // 10
# check first 9 numbers for pandigitality
for x in range(9):
if not check_front[x + 1]:
f = False
return f | project_euler |
def check1(number: int) -> bool:
check_last = [0] * 11
# mark last 9 numbers
for _ in range(9):
check_last[int(number % 10)] = 1
number = number // 10
# flag
f = True
# check last 9 numbers for pandigitality
for x in range(9):
if not check_last[x + 1]:
f = False
return f | project_euler |
def solution() -> int:
a = 1
b = 1
c = 2
# temporary Fibonacci numbers
a1 = 1
b1 = 1
c1 = 2
# temporary Fibonacci numbers mod 1e9
# mod m=1e9, done for fast optimisation
tocheck = [0] * 1000000
m = 1000000000
for x in range(1000000):
c1 = (a1 + b1) % m
a1 = b1 % m
b1 = c1 % m
if check1(b1):
tocheck[x + 3] = 1
for x in range(1000000):
c = a + b
a = b
b = c
# perform check only if in tocheck
if tocheck[x + 3] and check(b):
return x + 3 # first 2 already done
return -1 | project_euler |
def vector_product(point1: tuple[int, int], point2: tuple[int, int]) -> int:
return point1[0] * point2[1] - point1[1] * point2[0] | project_euler |
def contains_origin(x1: int, y1: int, x2: int, y2: int, x3: int, y3: int) -> bool:
point_a: tuple[int, int] = (x1, y1)
point_a_to_b: tuple[int, int] = (x2 - x1, y2 - y1)
point_a_to_c: tuple[int, int] = (x3 - x1, y3 - y1)
a: float = -vector_product(point_a, point_a_to_b) / vector_product(
point_a_to_c, point_a_to_b
)
b: float = +vector_product(point_a, point_a_to_c) / vector_product(
point_a_to_c, point_a_to_b
)
return a > 0 and b > 0 and a + b < 1 | project_euler |
def solution(filename: str = "p102_triangles.txt") -> int:
data: str = Path(__file__).parent.joinpath(filename).read_text(encoding="utf-8")
triangles: list[list[int]] = []
for line in data.strip().split("\n"):
triangles.append([int(number) for number in line.split(",")])
ret: int = 0
triangle: list[int]
for triangle in triangles:
ret += contains_origin(*triangle)
return ret | project_euler |
def solution(exponent: int = 30) -> int:
# To find how many total games were lost for a given exponent x,
# we need to find the Fibonacci number F(x+2).
fibonacci_index = exponent + 2
phi = (1 + 5**0.5) / 2
fibonacci = (phi**fibonacci_index - (phi - 1) ** fibonacci_index) / 5**0.5
return int(fibonacci) | project_euler |
def is_prime(number: int) -> bool:
if 1 < number < 4:
# 2 and 3 are primes
return True
elif number < 2 or number % 2 == 0 or number % 3 == 0:
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
return False
# All primes number are in format of 6k +/- 1
for i in range(5, int(math.sqrt(number) + 1), 6):
if number % i == 0 or number % (i + 2) == 0:
return False
return True | project_euler |
def solution(n: int = 7) -> int:
pandigital_str = "".join(str(i) for i in range(1, n + 1))
perm_list = [int("".join(i)) for i in permutations(pandigital_str, n)]
pandigitals = [num for num in perm_list if is_prime(num)]
return max(pandigitals) if pandigitals else 0 | project_euler |
def is_prime(number: int) -> bool:
if 1 < number < 4:
# 2 and 3 are primes
return True
elif number < 2 or number % 2 == 0 or number % 3 == 0:
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
return False
# All primes number are in format of 6k +/- 1
for i in range(5, int(math.sqrt(number) + 1), 6):
if number % i == 0 or number % (i + 2) == 0:
return False
return True | project_euler |
def compute_nums(n: int) -> list[int]:
if not isinstance(n, int):
raise ValueError("n must be an integer")
if n <= 0:
raise ValueError("n must be >= 0")
list_nums = []
for num in range(len(odd_composites)):
i = 0
while 2 * i * i <= odd_composites[num]:
rem = odd_composites[num] - 2 * i * i
if is_prime(rem):
break
i += 1
else:
list_nums.append(odd_composites[num])
if len(list_nums) == n:
return list_nums
return [] | project_euler |
def get_totients(max_one: int) -> list[int]:
totients = [0] * max_one
for i in range(0, max_one):
totients[i] = i
for i in range(2, max_one):
if totients[i] == i:
for j in range(i, max_one, i):
totients[j] -= totients[j] // i
return totients | project_euler |
def has_same_digits(num1: int, num2: int) -> bool:
return sorted(str(num1)) == sorted(str(num2)) | project_euler |
def solution(max_n: int = 10000000) -> int:
min_numerator = 1 # i
min_denominator = 0 # φ(i)
totients = get_totients(max_n + 1)
for i in range(2, max_n + 1):
t = totients[i]
if i * min_denominator < min_numerator * t and has_same_digits(i, t):
min_numerator = i
min_denominator = t
return min_numerator | project_euler |
def solution():
total = 0
for i in range(1, 1001):
total += i**i
return str(total)[-10:] | project_euler |
def partition(number_to_partition: int) -> set[int]:
if number_to_partition < 0:
return set()
elif number_to_partition == 0:
return {1}
ret: set[int] = set()
prime: int
sub: int
for prime in primes:
if prime > number_to_partition:
continue
for sub in partition(number_to_partition - prime):
ret.add(sub * prime)
return ret | project_euler |
def solution(number_unique_partitions: int = 5000) -> int | None:
for number_to_partition in range(1, NUM_PRIMES):
if len(partition(number_to_partition)) > number_unique_partitions:
return number_to_partition
return None | project_euler |
def solution(limit=28123):
sum_divs = [1] * (limit + 1)
for i in range(2, int(limit**0.5) + 1):
sum_divs[i * i] += i
for k in range(i + 1, limit // i + 1):
sum_divs[k * i] += k + i
abundants = set()
res = 0
for n in range(1, limit + 1):
if sum_divs[n] > n:
abundants.add(n)
if not any((n - a in abundants) for a in abundants):
res += n
return res | project_euler |
def solution():
result = list(map("".join, permutations("0123456789")))
return result[999999] | project_euler |
def log_difference(number: int) -> float:
log_number = math.log(2, 10) * number
difference = round((log_number - int(log_number)), 15)
return difference | project_euler |
def solution(number: int = 678910) -> int:
power_iterator = 90
position = 0
lower_limit = math.log(1.23, 10)
upper_limit = math.log(1.24, 10)
previous_power = 0
while position < number:
difference = log_difference(power_iterator)
if difference >= upper_limit:
power_iterator += 93
elif difference < lower_limit:
power_iterator += 196
else:
previous_power = power_iterator
power_iterator += 196
position += 1
return previous_power | project_euler |
def triangle_number_generator():
for n in range(1, 1000000):
yield n * (n + 1) // 2 | project_euler |
def count_divisors(n):
divisors_count = 1
i = 2
while i * i <= n:
multiplicity = 0
while n % i == 0:
n //= i
multiplicity += 1
divisors_count *= multiplicity + 1
i += 1
if n > 1:
divisors_count *= 2
return divisors_count | project_euler |
def solution():
return next(i for i in triangle_number_generator() if count_divisors(i) > 500) | project_euler |
def count_divisors(n):
n_divisors = 1
i = 2
while i * i <= n:
multiplicity = 0
while n % i == 0:
n //= i
multiplicity += 1
n_divisors *= multiplicity + 1
i += 1
if n > 1:
n_divisors *= 2
return n_divisors | project_euler |
def solution():
t_num = 1
i = 1
while True:
i += 1
t_num += i
if count_divisors(t_num) > 500:
break
return t_num | project_euler |
def solution(n: int = 20) -> int:
n = 2 * n # middle entry of odd rows starting at row 3 is the solution for n = 1,
# 2, 3,...
k = n // 2
return int(factorial(n) / (factorial(k) * factorial(n - k))) | project_euler |
def is_prime(number: int) -> bool:
if 1 < number < 4:
# 2 and 3 are primes
return True
elif number < 2 or number % 2 == 0 or number % 3 == 0:
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
return False
# All primes number are in format of 6k +/- 1
for i in range(5, int(math.sqrt(number) + 1), 6):
if number % i == 0 or number % (i + 2) == 0:
return False
return True | project_euler |
def search(target: int, prime_list: list) -> bool:
left, right = 0, len(prime_list) - 1
while left <= right:
middle = (left + right) // 2
if prime_list[middle] == target:
return True
elif prime_list[middle] < target:
left = middle + 1
else:
right = middle - 1
return False | project_euler |
def solution():
prime_list = [n for n in range(1001, 10000, 2) if is_prime(n)]
candidates = []
for number in prime_list:
tmp_numbers = []
for prime_member in permutations(list(str(number))):
prime = int("".join(prime_member))
if prime % 2 == 0:
continue
if search(prime, prime_list):
tmp_numbers.append(prime)
tmp_numbers.sort()
if len(tmp_numbers) >= 3:
candidates.append(tmp_numbers)
passed = []
for candidate in candidates:
length = len(candidate)
found = False
for i in range(length):
for j in range(i + 1, length):
for k in range(j + 1, length):
if (
abs(candidate[i] - candidate[j])
== abs(candidate[j] - candidate[k])
and len({candidate[i], candidate[j], candidate[k]}) == 3
):
passed.append(
sorted([candidate[i], candidate[j], candidate[k]])
)
found = True
if found:
break
if found:
break
if found:
break
answer = set()
for seq in passed:
answer.add("".join([str(i) for i in seq]))
return max(int(x) for x in answer) | project_euler |
def solution(m: int = 100) -> int:
memo = [[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:
memo[n][k] += memo[n - k - 1][k]
return memo[m][m - 1] - 1 | project_euler |
def solution(filename: str = "input.txt") -> int:
with open(os.path.join(os.path.dirname(__file__), filename)) as input_file:
matrix = [
[int(element) for element in line.split(",")]
for line in input_file.readlines()
]
rows = len(matrix)
cols = len(matrix[0])
minimal_path_sums = [[-1 for _ in range(cols)] for _ in range(rows)]
for i in range(rows):
minimal_path_sums[i][0] = matrix[i][0]
for j in range(1, cols):
for i in range(rows):
minimal_path_sums[i][j] = minimal_path_sums[i][j - 1] + matrix[i][j]
for i in range(1, rows):
minimal_path_sums[i][j] = min(
minimal_path_sums[i][j], minimal_path_sums[i - 1][j] + matrix[i][j]
)
for i in range(rows - 2, -1, -1):
minimal_path_sums[i][j] = min(
minimal_path_sums[i][j], minimal_path_sums[i + 1][j] + matrix[i][j]
)
return min(minimal_path_sums_row[-1] for minimal_path_sums_row in minimal_path_sums) | project_euler |
def solution(target: int = 2000000) -> int:
triangle_numbers: list[int] = [0]
idx: int
for idx in range(1, ceil(sqrt(target * 2) * 1.1)):
triangle_numbers.append(triangle_numbers[-1] + idx)
# we want this to be as close as possible to target
best_product: int = 0
# the area corresponding to the grid that gives the product closest to target
area: int = 0
# an estimate of b, using the quadratic formula
b_estimate: float
# the largest integer less than b_estimate
b_floor: int
# the largest integer less than b_estimate
b_ceil: int
# the triangle number corresponding to b_floor
triangle_b_first_guess: int
# the triangle number corresponding to b_ceil
triangle_b_second_guess: int
for idx_a, triangle_a in enumerate(triangle_numbers[1:], 1):
b_estimate = (-1 + sqrt(1 + 8 * target / triangle_a)) / 2
b_floor = floor(b_estimate)
b_ceil = ceil(b_estimate)
triangle_b_first_guess = triangle_numbers[b_floor]
triangle_b_second_guess = triangle_numbers[b_ceil]
if abs(target - triangle_b_first_guess * triangle_a) < abs(
target - best_product
):
best_product = triangle_b_first_guess * triangle_a
area = idx_a * b_floor
if abs(target - triangle_b_second_guess * triangle_a) < abs(
target - best_product
):
best_product = triangle_b_second_guess * triangle_a
area = idx_a * b_ceil
return area | project_euler |
def solution(numerator: int = 3, denominator: int = 7, limit: int = 1000000) -> int:
max_numerator = 0
max_denominator = 1
for current_denominator in range(1, limit + 1):
current_numerator = current_denominator * numerator // denominator
if current_denominator % denominator == 0:
current_numerator -= 1
if current_numerator * max_denominator > current_denominator * max_numerator:
max_numerator = current_numerator
max_denominator = current_denominator
return max_numerator | project_euler |
def solution(number: int = 1000000) -> int:
partitions = [1]
for i in itertools.count(len(partitions)):
item = 0
for j in itertools.count(1):
sign = -1 if j % 2 == 0 else +1
index = (j * j * 3 - j) // 2
if index > i:
break
item += partitions[i - index] * sign
item %= number
index += j
if index > i:
break
item += partitions[i - index] * sign
item %= number
if item == 0:
return i
partitions.append(item)
return 0 | project_euler |
def unique_prime_factors(n: int) -> set:
i = 2
factors = set()
while i * i <= n:
if n % i:
i += 1
else:
n //= i
factors.add(i)
if n > 1:
factors.add(n)
return factors | project_euler |
def upf_len(num: int) -> int:
return len(unique_prime_factors(num)) | project_euler |
def equality(iterable: list) -> bool:
return len(set(iterable)) in (0, 1) | project_euler |
def run(n: int) -> list:
# Incrementor variable for our group list comprehension.
# This serves as the first number in each list of values
# to test.
base = 2
while True:
# Increment each value of a generated range
group = [base + i for i in range(n)]
# Run elements through out unique_prime_factors function
# Append our target number to the end.
checker = [upf_len(x) for x in group]
checker.append(n)
# If all numbers in the list are equal, return the group variable.
if equality(checker):
return group
# Increment our base variable by 1
base += 1 | project_euler |
def solution(n: int = 4) -> int:
results = run(n)
return results[0] if len(results) else None | project_euler |
def solution():
constant = []
i = 1
while len(constant) < 1e6:
constant.append(str(i))
i += 1
constant = "".join(constant)
return (
int(constant[0])
* int(constant[9])
* int(constant[99])
* int(constant[999])
* int(constant[9999])
* int(constant[99999])
* int(constant[999999])
) | project_euler |
def solution(n: int = 1000000) -> int:
largest_number = 1
pre_counter = 1
counters = {1: 1}
for input1 in range(2, n):
counter = 0
number = input1
while True:
if number in counters:
counter += counters[number]
break
if number % 2 == 0:
number //= 2
counter += 1
else:
number = (3 * number) + 1
counter += 1
if input1 not in counters:
counters[input1] = counter
if counter > pre_counter:
largest_number = input1
pre_counter = counter
return largest_number | project_euler |
def solution():
file_path = os.path.join(os.path.dirname(__file__), "num.txt")
with open(file_path) as file_hand:
return str(sum(int(line) for line in file_hand))[:10] | project_euler |
def solution(n: int = 1000) -> int:
f1, f2 = 1, 1
index = 2
while True:
i = 0
f = f1 + f2
f1, f2 = f2, f
index += 1
for _ in str(f):
i += 1
if i == n:
break
return index | project_euler |
def fibonacci_generator() -> Generator[int, None, None]:
a, b = 0, 1
while True:
a, b = b, a + b
yield b | project_euler |
def solution(n: int = 1000) -> int:
answer = 1
gen = fibonacci_generator()
while len(str(next(gen))) < n:
answer += 1
return answer + 1 | project_euler |
def fibonacci(n: int) -> int:
if n == 1 or not isinstance(n, int):
return 0
elif n == 2:
return 1
else:
sequence = [0, 1]
for i in range(2, n + 1):
sequence.append(sequence[i - 1] + sequence[i - 2])
return sequence[n] | project_euler |
def fibonacci_digits_index(n: int) -> int:
digits = 0
index = 2
while digits < n:
index += 1
digits = len(str(fibonacci(index)))
return index | project_euler |
def solution(n: int = 1000) -> int:
return fibonacci_digits_index(n) | project_euler |
def solution():
total_sum = 0
temp_sum = 0
with open(os.path.dirname(__file__) + "/p022_names.txt") as file:
name = str(file.readlines()[0])
name = name.replace('"', "").split(",")
name.sort()
for i in range(len(name)):
for j in name[i]:
temp_sum += ord(j) - ord("A") + 1
total_sum += (i + 1) * temp_sum
temp_sum = 0
return total_sum | project_euler |
def solution():
with open(os.path.dirname(__file__) + "/p022_names.txt") as file:
names = str(file.readlines()[0])
names = names.replace('"', "").split(",")
names.sort()
name_score = 0
total_score = 0
for i, name in enumerate(names):
for letter in name:
name_score += ord(letter) - 64
total_score += (i + 1) * name_score
name_score = 0
return total_score | project_euler |
def next_number(number: int) -> int:
sum_of_digits_squared = 0
while number:
# Increased Speed Slightly by checking every 5 digits together.
sum_of_digits_squared += DIGITS_SQUARED[number % 100000]
number //= 100000
return sum_of_digits_squared | project_euler |
def chain(number: int) -> bool:
if CHAINS[number - 1] is not None:
return CHAINS[number - 1] # type: ignore
number_chain = chain(next_number(number))
CHAINS[number - 1] = number_chain
while number < 10000000:
CHAINS[number - 1] = number_chain
number *= 10
return number_chain | project_euler |
def solution(number: int = 10000000) -> int:
for i in range(1, number):
if CHAINS[i] is None:
chain(i + 1)
return CHAINS[:number].count(False) | project_euler |
def try_key(ciphertext: list[int], key: tuple[int, ...]) -> str | None:
decoded: str = ""
keychar: int
cipherchar: int
decodedchar: int
for keychar, cipherchar in zip(cycle(key), ciphertext):
decodedchar = cipherchar ^ keychar
if decodedchar not in VALID_INTS:
return None
decoded += chr(decodedchar)
return decoded | project_euler |
def filter_valid_chars(ciphertext: list[int]) -> list[str]:
possibles: list[str] = []
for key in product(LOWERCASE_INTS, repeat=3):
encoded = try_key(ciphertext, key)
if encoded is not None:
possibles.append(encoded)
return possibles | project_euler |
def filter_common_word(possibles: list[str], common_word: str) -> list[str]:
return [possible for possible in possibles if common_word in possible.lower()] | project_euler |
def solution(filename: str = "p059_cipher.txt") -> int:
ciphertext: list[int]
possibles: list[str]
common_word: str
decoded_text: str
data: str = Path(__file__).parent.joinpath(filename).read_text(encoding="utf-8")
ciphertext = [int(number) for number in data.strip().split(",")]
possibles = filter_valid_chars(ciphertext)
for common_word in COMMON_WORDS:
possibles = filter_common_word(possibles, common_word)
if len(possibles) == 1:
break
decoded_text = possibles[0]
return sum(ord(char) for char in decoded_text) | project_euler |
def solution(n: int = 1000) -> int:
prev_numerator, prev_denominator = 1, 1
result = []
for i in range(1, n + 1):
numerator = prev_numerator + 2 * prev_denominator
denominator = prev_numerator + prev_denominator
if len(str(numerator)) > len(str(denominator)):
result.append(i)
prev_numerator = numerator
prev_denominator = denominator
return len(result) | project_euler |
def solution(gon_side: int = 5) -> int:
if gon_side < 3 or gon_side > 5:
raise ValueError("gon_side must be in the range [3, 5]")
# Since it's 16, we know 10 is on the outer ring
# Put the big numbers at the end so that they are never the first number
small_numbers = list(range(gon_side + 1, 0, -1))
big_numbers = list(range(gon_side + 2, gon_side * 2 + 1))
for perm in permutations(small_numbers + big_numbers):
numbers = generate_gon_ring(gon_side, list(perm))
if is_magic_gon(numbers):
return int("".join(str(n) for n in numbers))
raise ValueError(f"Magic {gon_side}-gon ring is impossible") | project_euler |
def generate_gon_ring(gon_side: int, perm: list[int]) -> list[int]:
result = [0] * (gon_side * 3)
result[0:3] = perm[0:3]
perm.append(perm[1])
magic_number = 1 if gon_side < 5 else 2
for i in range(1, len(perm) // 3 + magic_number):
result[3 * i] = perm[2 * i + 1]
result[3 * i + 1] = result[3 * i - 1]
result[3 * i + 2] = perm[2 * i + 2]
return result | project_euler |
def is_magic_gon(numbers: list[int]) -> bool:
if len(numbers) % 3 != 0:
raise ValueError("a gon ring should have a length that is a multiple of 3")
if min(numbers[::3]) != numbers[0]:
return False
total = sum(numbers[:3])
return all(sum(numbers[i : i + 3]) == total for i in range(3, len(numbers), 3)) | project_euler |
def prime_sieve(limit: int) -> list[int]:
is_prime = [True] * limit
is_prime[0] = False
is_prime[1] = False
is_prime[2] = True
for i in range(3, int(limit**0.5 + 1), 2):
index = i * 2
while index < limit:
is_prime[index] = False
index = index + i
primes = [2]
for i in range(3, limit, 2):
if is_prime[i]:
primes.append(i)
return primes | project_euler |
def solution(ceiling: int = 1_000_000) -> int:
primes = prime_sieve(ceiling)
length = 0
largest = 0
for i in range(len(primes)):
for j in range(i + length, len(primes)):
sol = sum(primes[i:j])
if sol >= ceiling:
break
if sol in primes:
length = j - i
largest = sol
return largest | project_euler |
def solution(n: int = 998001) -> int:
answer = 0
for i in range(999, 99, -1): # 3 digit numbers range from 999 down to 100
for j in range(999, 99, -1):
product_string = str(i * j)
if product_string == product_string[::-1] and i * j < n:
answer = max(answer, i * j)
return answer | project_euler |
def solution(n: int = 998001) -> int:
# fetches the next number
for number in range(n - 1, 9999, -1):
str_number = str(number)
# checks whether 'str_number' is a palindrome.
if str_number == str_number[::-1]:
divisor = 999
# if 'number' is a product of two 3-digit numbers
# then number is the answer otherwise fetch next number.
while divisor != 99:
if (number % divisor == 0) and (len(str(number // divisor)) == 3.0):
return number
divisor -= 1
raise ValueError("That number is larger than our acceptable range.") | project_euler |
def solution(n: int = 600851475143) -> int:
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater than or equal to one.")
i = 2
ans = 0
if n == 2:
return 2
while n > 2:
while n % i != 0:
i += 1
ans = i
while n % i == 0:
n = n // i
i += 1
return int(ans) | project_euler |
def solution(n: int = 600851475143) -> int:
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater than or equal to one.")
prime = 1
i = 2
while i * i <= n:
while n % i == 0:
prime = i
n //= i
i += 1
if n > 1:
prime = n
return int(prime) | project_euler |
def is_prime(number: int) -> bool:
if 1 < number < 4:
# 2 and 3 are primes
return True
elif number < 2 or number % 2 == 0 or number % 3 == 0:
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
return False
# All primes number are in format of 6k +/- 1
for i in range(5, int(math.sqrt(number) + 1), 6):
if number % i == 0 or number % (i + 2) == 0:
return False
return True | project_euler |
def solution(n: int = 600851475143) -> int:
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater than or equal to one.")
max_number = 0
if is_prime(n):
return n
while n % 2 == 0:
n //= 2
if is_prime(n):
return n
for i in range(3, int(math.sqrt(n)) + 1, 2):
if n % i == 0:
if is_prime(n // i):
max_number = n // i
break
elif is_prime(i):
max_number = i
return max_number | project_euler |
def solution(num_picks: int = 20) -> str:
total = math.comb(NUM_BALLS, num_picks)
missing_colour = math.comb(NUM_BALLS - BALLS_PER_COLOUR, num_picks)
result = NUM_COLOURS * (1 - missing_colour / total)
return f"{result:.9f}" | project_euler |
def is_prime(n: int) -> bool:
return seive[n] | project_euler |
def contains_an_even_digit(n: int) -> bool:
return any(digit in "02468" for digit in str(n)) | project_euler |
def find_circular_primes(limit: int = 1000000) -> list[int]:
result = [2] # result already includes the number 2.
for num in range(3, limit + 1, 2):
if is_prime(num) and not contains_an_even_digit(num):
str_num = str(num)
list_nums = [int(str_num[j:] + str_num[:j]) for j in range(len(str_num))]
if all(is_prime(i) for i in list_nums):
result.append(num)
return result | project_euler |
def solution() -> int:
return len(find_circular_primes()) | project_euler |
def check_partition_perfect(positive_integer: int) -> bool:
exponent = math.log2(math.sqrt(4 * positive_integer + 1) / 2 + 1 / 2)
return exponent == int(exponent) | project_euler |
def solution(max_proportion: float = 1 / 12345) -> int:
total_partitions = 0
perfect_partitions = 0
integer = 3
while True:
partition_candidate = (integer**2 - 1) / 4
# if candidate is an integer, then there is a partition for k
if partition_candidate == int(partition_candidate):
partition_candidate = int(partition_candidate)
total_partitions += 1
if check_partition_perfect(partition_candidate):
perfect_partitions += 1
if perfect_partitions > 0:
if perfect_partitions / total_partitions < max_proportion:
return int(partition_candidate)
integer += 1 | project_euler |
def is_combination_valid(combination):
return (
int("".join(combination[0:2])) * int("".join(combination[2:5]))
== int("".join(combination[5:9]))
) or (
int("".join(combination[0])) * int("".join(combination[1:5]))
== int("".join(combination[5:9]))
) | project_euler |
def solution():
return sum(
{
int("".join(pandigital[5:9]))
for pandigital in itertools.permutations("123456789")
if is_combination_valid(pandigital)
}
) | project_euler |
def prime_sieve(n: int) -> list[int]:
is_prime = [True] * n
is_prime[0] = False
is_prime[1] = False
is_prime[2] = True
for i in range(3, int(n**0.5 + 1), 2):
index = i * 2
while index < n:
is_prime[index] = False
index = index + i
primes = [2]
for i in range(3, n, 2):
if is_prime[i]:
primes.append(i)
return primes | project_euler |
def digit_replacements(number: int) -> list[list[int]]:
number_str = str(number)
replacements = []
digits = ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"]
for duplicate in Counter(number_str) - Counter(set(number_str)):
family = [int(number_str.replace(duplicate, digit)) for digit in digits]
replacements.append(family)
return replacements | project_euler |
def solution(family_length: int = 8) -> int:
numbers_checked = set()
# Filter primes with less than 3 replaceable digits
primes = {
x for x in set(prime_sieve(1_000_000)) if len(str(x)) - len(set(str(x))) >= 3
}
for prime in primes:
if prime in numbers_checked:
continue
replacements = digit_replacements(prime)
for family in replacements:
numbers_checked.update(family)
primes_in_family = primes.intersection(family)
if len(primes_in_family) != family_length:
continue
return min(primes_in_family)
return -1 | project_euler |
def solution(a: int = 100, b: int = 100) -> int:
# RETURN the MAXIMUM from the list of SUMs of the list of INT converted from STR of
# BASE raised to the POWER
return max(
sum(int(x) for x in str(base**power))
for base in range(a)
for power in range(b)
) | project_euler |
def solution(n: int = 10**6) -> int:
if n <= 0:
raise ValueError("Please enter an integer greater than 0")
phi = list(range(n + 1))
for number in range(2, n + 1):
if phi[number] == number:
phi[number] -= 1
for multiple in range(number * 2, n + 1, number):
phi[multiple] = (phi[multiple] // number) * (number - 1)
answer = 1
for number in range(1, n + 1):
if (answer / phi[answer]) < (number / phi[number]):
answer = number
return answer | project_euler |
def solution() -> int:
script_dir = os.path.dirname(os.path.realpath(__file__))
triangle_path = os.path.join(script_dir, "triangle.txt")
with open(triangle_path) as in_file:
triangle = [[int(i) for i in line.split()] for line in in_file]
while len(triangle) != 1:
last_row = triangle.pop()
curr_row = triangle[-1]
for j in range(len(last_row) - 1):
curr_row[j] += max(last_row[j], last_row[j + 1])
return triangle[0][0] | project_euler |
def solution():
script_dir = os.path.dirname(os.path.realpath(__file__))
triangle = os.path.join(script_dir, "triangle.txt")
with open(triangle) as f:
triangle = f.readlines()
a = []
for line in triangle:
numbers_from_line = []
for number in line.strip().split(" "):
numbers_from_line.append(int(number))
a.append(numbers_from_line)
for i in range(1, len(a)):
for j in range(len(a[i])):
number1 = a[i - 1][j] if j != len(a[i - 1]) else 0
number2 = a[i - 1][j - 1] if j > 0 else 0
a[i][j] += max(number1, number2)
return max(a[-1]) | project_euler |
def is_prime(number: int) -> bool:
if 1 < number < 4:
# 2 and 3 are primes
return True
elif number < 2 or number % 2 == 0 or number % 3 == 0:
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
return False
# All primes number are in format of 6k +/- 1
for i in range(5, int(math.sqrt(number) + 1), 6):
if number % i == 0 or number % (i + 2) == 0:
return False
return True | project_euler |
def solution(ratio: float = 0.1) -> int:
j = 3
primes = 3
while primes / (2 * j - 1) >= ratio:
for i in range(j * j + j + 1, (j + 2) * (j + 2), j + 1):
primes += is_prime(i)
j += 2
return j | project_euler |
def is_digit_cancelling(num: int, den: int) -> bool:
return (
num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
) | project_euler |
def fraction_list(digit_len: int) -> list[str]:
solutions = []
den = 11
last_digit = int("1" + "0" * digit_len)
for num in range(den, last_digit):
while den <= 99:
if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
if is_digit_cancelling(num, den):
solutions.append(f"{num}/{den}")
den += 1
num += 1
den = 10
return solutions | project_euler |
def solution(n: int = 2) -> int:
result = 1.0
for fraction in fraction_list(n):
frac = Fraction(fraction)
result *= frac.denominator / frac.numerator
return int(result) | project_euler |