def find_shortest_part(matrix):
N = len(matrix)
# info will store the info data structure (dictionary) for each cell
info = [[ { 'path': None, 'd': 10 ** 9 } for x in range(N)] for x in range(N)]
info[0][0]['d'] = matrix[0][0]
info[0][0]['path'] = []
not_visited = []
for y in range(len(matrix)):
for x in range(len(matrix[y])):
not_visited.append( P2D(x, y) )
while True:
rest = sorted(not_visited, key=lambda p: info[p.y][p.x]['d'])
project_euler.report_progress( 1 - len(rest) / N ** 2 )
if len(rest) == 0: break # all is visited
current = rest[0]
neighbors = list(get_neighbors(matrix, current))
for neighbor in neighbors:
dist = info[current.y][current.x]['d'] + matrix[neighbor.y][neighbor.x]
if info[neighbor.y][neighbor.x]['d'] > dist: # found shorter way
info[neighbor.y][neighbor.x]['d'] = dist
info[neighbor.y][neighbor.x]['path'] = list(info[current.y][current.x]['path']) + [ P2D(current.x, current.y) ]
not_visited.remove( current )
min_d = info[-1][-1]['d']
min_path = info[-1][-1]['path'] + [ P2D(N-1, N-1) ]
print ("MIN distance: {0}, PATH: {1}".format(min_d, min_path))
import project_euler
import math
max = 50 * 10 ** 6
primes = project_euler.eratosphen_primes( math.sqrt( max ) )
values = set()
done = 0
for p_sq in primes:
done += 1
project_euler.report_progress( done / len(primes) )
for p_cube in primes:
if p_sq ** 2 + p_cube ** 3 > max: break
for p_dsq in primes:
v = p_sq ** 2 + p_cube ** 3 + p_dsq ** 4
if v < max: values.add( v )
else: break
print( len(values) )
def checkOnRightTriangle(P, Q):
a = P[0] ** 2 + P[1] ** 2
b = Q[0] ** 2 + Q[1] ** 2
c = (P[0] - Q[0]) ** 2 + (P[1] - Q[1]) ** 2
(a, b, c) = sorted([a, b, c])
return c == a + b
n = 50
r = 0
for x1 in range(n + 1):
project_euler.report_progress( x1 / n )
for y1 in range(n + 1):
for x2 in range(n + 1):
for y2 in range(n + 1):
if x1 == 0 and y1 == 0 or x2 == 0 and y2 == 0:
continue
if x1 == x2 and y1 == y2:
continue
if checkOnRightTriangle( (x1, y1), (x2, y2) ):
r += 1
print( r // 2 )