def calk_wil_tree_for_one_level(prev_list_at_level, display_option):
list_at_level= copy.deepcopy(prev_list_at_level)
# print list_at_level
list_len = len(list_at_level)
# print 'list_len = ', list_len
to_be_inserted_list = []
for i in range(list_len):
l_child = [0, 0]
l_child[0] = list_at_level[i][0]
l_child[1] = list_at_level[i][0] + list_at_level[i][1]
to_be_inserted_list.append(l_child)
r_child = [0, 0]
r_child[0] = list_at_level[i][0] + list_at_level[i][1]
r_child[1] = list_at_level[i][1]
to_be_inserted_list.append(r_child)
# print to_be_inserted_list
# print list_at_level
if(display_option):
print_fare_fraction_list(to_be_inserted_list)
print " "
return to_be_inserted_list
def fare_plus_fare(n):
fare_list = get_fare_list(n)
print "================================="
print_fare_fraction_list(fare_list)
fare_list_len = len(fare_list)
fare_plus_fare_list = []
for i in range(fare_list_len):
for j in range(fare_list_len):
a1 = fare_list[i][0]
b1 = fare_list[i][1]
a2 = fare_list[j][0]
b2 = fare_list[j][1]
c, d = add_two_fract(a1, b1, a2, b2)
tmp = [c, d]
fare_plus_fare_list.append(tmp)
fare_plus_fare_list_len = len(fare_plus_fare_list)
print "\n=== =============================================="
print_fare_fraction_list(fare_plus_fare_list)
print "\n=== fare_list_len = %d, fare_plus_fare_list_len = %d,"%(fare_list_len, fare_plus_fare_list_len)
return fare_plus_fare_list
def ster_broc_tree(prev_list_at_level, display_option):
list_at_level= copy.deepcopy(prev_list_at_level)
# print list_at_level
list_len = len(list_at_level)
to_be_inserted_list = []
for i in range(list_len - 1):
tmp = [0, 0]
tmp[0] = list_at_level[i][0] + list_at_level[i + 1][0]
tmp[1] = list_at_level[i][1] + list_at_level[i + 1][1]
to_be_inserted_list.append(tmp)
# print to_be_inserted_list
# interleave to_be_inserted_list with list_at_level
# Note, to_be_insert_list is one item less than list_at_level.
# And they are both sorted.
# Since both are lists which can have many items, it is important
# to have an effective way to interleave those two data.
# For example, if we just use normal list insert function.
# It can be very slow.
# Method_1:, we use extended slice syntax in Python.
# start_1 = time.time()
new_list = list_at_level + to_be_inserted_list
new_list[::2] = list_at_level
new_list[1::2] = to_be_inserted_list
# end_1 = time.time()
# print "method_1: ", (end_1 - start_1)
'''
# Method_2:
start_2 = time.time()
new_list_2 = [val for pair in zip(list_at_level , list_at_level ) for val in pair]
end_2 = time.time()
print "method_2: ", (end_2 - start_2)
# Method_3:
start_3 = time.time()
for i in range(len(to_be_inserted_list)):
tmp = to_be_inserted_list[i]
list_at_level.insert(2*i + 1, tmp)
end_3 = time.time()
print "method_3: ", (end_3 - start_3)
'''
# print list_at_level
half_len = len(new_list)/2 + 1
if(display_option):
print_fare_fraction_list(new_list[:half_len ])
print " "
return new_list, to_be_inserted_list
def fare_plus_fare_sorted_by_deno(fare_plus_fare_list):
fare_plus_fare_2d_arr = np.asarray(fare_plus_fare_list)
print fare_plus_fare_2d_arr
print "!!!!!!!!!!!!! The following sorting function is WRONG !!!!!!!!!!!!!!!!!!1"
print "\n===================== sorted = axis = 0========================="
fare_plus_fare_sorted_by_denom_2d_arr = np.sort(fare_plus_fare_2d_arr, axis=0)
print fare_plus_fare_sorted_by_denom_2d_arr
print_fare_fraction_list(fare_plus_fare_sorted_by_denom_2d_arr)
print "\n===================== sorted = axis = 1========================="
fare_plus_fare_sorted_by_denom_2d_arr = np.sort(fare_plus_fare_2d_arr, axis=1)
print fare_plus_fare_sorted_by_denom_2d_arr
print_fare_fraction_list(fare_plus_fare_sorted_by_denom_2d_arr)
return fare_plus_fare_sorted_by_denom_2d_arr
def extract_diagonal_from_calk_wil_tree(tree_as_breadth_1st_trav_list_upto_level, diagonal, display_option = True):
list_for_diagonal = []
# print "================= extract_diagonal_from_calk_wil_tree ======================="
# print_fare_fraction_list(tree_as_breadth_1st_trav_list_upto_level)
n = get_num_of_complete_level_for_a_list(tree_as_breadth_1st_trav_list_upto_level)
for level in range(1, n + 1):
num_of_items_at_level, start_pos_of_level = num_of_item_at_level(level)
if(num_of_items_at_level >= diagonal):
position_for_diagnoal = start_pos_of_level + diagonal - 1
list_for_diagonal.append(tree_as_breadth_1st_trav_list_upto_level[position_for_diagnoal - 1])
# print "start_pos_of_level + diagonal - 1 ", start_pos_of_level + diagonal - 1
if(display_option):
print_fare_fraction_list(list_for_diagonal)
return list_for_diagonal
def detect_gbc_pair_in_fare_sequence(n, fare_fraction_list, smallest_largest_pair_only):
# print "detect_gbc_pair_in_fare_sequence n %d"%(n)
list_len = len(fare_fraction_list)
gbc_result_list = []
gbc_result_str_list = []
gbc_a1_n_list=[]
b_1_max = 0 # largest denominator in the sequence if go though entire fare_fraction_list
try:
for i in range(list_len):
b_1 = fare_fraction_list[i][1]
if(b_1 > b_1_max):
b_1_max = b_1
if(b_1 == n):
a_1 = fare_fraction_list[i][0]
gbc_a1_n_list.append([a_1, b_1])
if a_1 in prime_list:
for j in range(i + 1, list_len):
b_2 = fare_fraction_list[j][1]
if(b_2 == n):
a_2 = fare_fraction_list[j][0]
if a_2 in prime_list:
# print "n_3 ", n, 'a1/b1 = %d/%d'%(a_1, b_1), 'a2/b2 = %d/%d'%(a_2, b_2),
if((a_2 + a_1) == n):
i_plus_j = i + j
j_minus_i = j - i
list_len_minus_j = list_len - j
result_str = "list_len = %5d, i + j = %5d, i = %5d, j = %5d, j_minus_i = %5d, list_len_minus_j = %5d, %d/%d , %d/%d, %5.2f %5.2f %5.2f "%(list_len, i_plus_j, i, j, j_minus_i, list_len_minus_j, a_1, b_1, a_2, b_2, float(i)/a_1, float(j)/a_2, float(list_len)/n)
print result_str
gbc_conf =[i, j, a_1, b_1, a_2, b_2]
gbc_result_list.append(gbc_conf)
gbc_result_str_list.append(result_str)
# if only check smallest_largest_pair
if(smallest_largest_pair_only):
# use exception to break from inner loop
raise Exception("catch this")
except:
pass
tmpstr = "n =%3d, denominator_max =%6d, "%(n, b_1_max)
# sys.stdout.write(tmpstr)
on_screen = False
out_str = print_fare_fraction_list(gbc_a1_n_list,on_screen )
# sys.stdout.write("\n")
return_str = tmpstr + out_str
gbc_conf_len = len(gbc_result_list)
tmp_i = 0
tmp_j = 0
tmp_a_1 = 0
tmp_b_1 = 0
tmp_a_2 = 0
tmp_b_2 = 0
# print "gbc_conf_len: ", gbc_conf_len
for i in range(gbc_conf_len):
tmp_i += gbc_result_list[i][0]
tmp_j += gbc_result_list[i][1]
tmp_a_1 += gbc_result_list[i][2]
tmp_b_1 += gbc_result_list[i][3]
tmp_a_2 += gbc_result_list[i][4]
tmp_b_2 += gbc_result_list[i][5]
# print "tmp i %4d, j %4d, a_1 %4d, b_1 %4d, a_2 %4d, b_2 %4d"%(tmp_i, tmp_j, tmp_a_1, tmp_b_1, tmp_a_2, tmp_b_2)
# only show the lst
#if(gbc_conf_len >= 1):
# print gbc_result_str_list[gbc_conf_len - 1]
return return_str