# Solution to https://projecteuler.net/problem=67
import utilities
triangle = []
def main():
triangle = utilities.read_to_2d_list("euler-067-data.txt")
for i in range(1, len(triangle)):
for j in range(len(triangle[i])):
max_val = 0
if j != 0:
max_val = triangle[i - 1][j - 1]
if j != len(triangle[i]) - 1 and triangle[i - 1][j] > max_val:
max_val = triangle[i - 1][j]
triangle[i][j] += max_val
return max(triangle[len(triangle) - 1])
if __name__ == "__main__":
utilities.print_runtime(main)
while groups[m] != val:
next_m = groups[m]
groups[m] = val
m = next_m
return val
def main():
group_counts = [1] * MAX
groups = {i: i for i in range(MAX)}
call_index = 1
call_count = 0
while group_counts[find_call_group(groups, PM_NUMBER)] < MAX // 100 * 99:
lagged_fibonacci(2)
caller = lagged_fib_cache[call_index] % MAX
called = lagged_fib_cache[call_index + 1] % MAX
call_index += 2
if caller != called:
call_count += 1
caller_group = find_call_group(groups, caller)
called_group = find_call_group(groups, called)
if caller_group != called_group:
group_counts[caller_group] += group_counts[called_group]
group_counts[called_group] = 0
groups[called_group] = caller_group
return call_count
if __name__ == "__main__":
utils.print_runtime(main)
