def greedy_make_change(n):
C = Array.indexed(1, 6)
d = Array([1, 2, 5, 10, 20, 50])
for i in rbetween(d.length, 1):
C[i] = math.floor(n / d[i])
n %= d[i]
return C
def get_shortest_bitonic_path_length_bruteforce(points):
n = points.length
min_length = math.inf
for k in between(0, n - 2):
for right_path in itertools.combinations(between(2, n - 1), k):
left_path = [x for x in rbetween(n - 1, 2) if x not in right_path]
path_length = get_path_length(points, [1] + list(right_path) + [n] + left_path + [1])
min_length = min(min_length, path_length)
return min_length
def greedy_activity_selector_(s, f):
n = s.length - 2
A = {'a' + str(n)}
i = n
for m in rbetween(n - 1, 1):
if f[m] <= s[i]:
A.add('a' + str(m))
i = m
return A
def get_assembly_time_based_on_lines(lines, last_line, a, t, e, x, n):
i = last_line
assembly_time = x[i]
for j in rbetween(n, 2):
assembly_time += a[i, j]
if i != lines[i, j]:
i = lines[i, j]
assembly_time += t[i, j - 1]
assembly_time += a[i, 1] + e[i]
return assembly_time
def get_assembly_time_based_on_lines(lines, last_line, a, t, e, x, n):
i = last_line
assembly_time = x[i]
for j in rbetween(n, 2):
assembly_time += a[i, j]
if i != lines[i, j]:
i = lines[i, j]
assembly_time += t[i, j - 1]
assembly_time += a[i, 1] + e[i]
return assembly_time
def get_shortest_bitonic_path_length_bruteforce(points):
n = points.length
min_length = math.inf
for k in between(0, n - 2):
for right_path in itertools.combinations(between(2, n - 1), k):
left_path = [x for x in rbetween(n - 1, 2) if x not in right_path]
path_length = get_path_length(points, [1] + list(right_path) +
[n] + left_path + [1])
min_length = min(min_length, path_length)
return min_length
def josephus(n, m):
T = RedBlackTree(sentinel=OSNode(None))
for j in between(1, n):
x = OSNode(j)
os_insert(T, x)
j = 1
for k in rbetween(n, 1):
j = (j + m - 1) % k + 1
x = os_select(T.root, j)
print(x.key)
os_delete(T, x)
def counting_sort(A, B, k):
C = Array.indexed(0, k)
for i in between(0, k):
C[i] = 0
for j in between(1, A.length):
C[A[j]] = C[A[j]] + 1
for i in between(1, k):
C[i] = C[i] + C[i - 1]
for j in rbetween(A.length, 1):
B[C[A[j]]] = A[j]
C[A[j]] = C[A[j]] - 1
def _sort_by_character(A, p, r, position):
k = ord('z') - ord('a')
C = Array([0] * (k + 1), start=0)
for j in between(p, r):
x = ord(A[j][position - 1]) - ord('a')
C[x] += 1
for i in between(1, k):
C[i] += C[i - 1]
B = Array.indexed(1, r - p + 1)
for j in rbetween(r, p):
x = ord(A[j][position - 1]) - ord('a')
B[C[x]] = A[j]
C[x] -= 1
A.elements[p - 1:r] = B.elements
def josephus_simulate(n, m):
L = List()
singly_linked_list_insert(L, SNode(n))
x = L.head
for i in rbetween(n - 1, 1):
singly_linked_list_insert(L, SNode(i))
x.next = L.head
for i in between(1, n):
for j in between(1, m):
x = x.next
print(x.next.key)
if L.head is x.next:
L.head = x.next.next
x.next = x.next.next
def _sort_by_character(A, p, r, position):
k = ord('z') - ord('a')
C = Array([0] * (k + 1), start=0)
for j in between(p, r):
x = ord(A[j][position - 1]) - ord('a')
C[x] += 1
for i in between(1, k):
C[i] += C[i - 1]
B = Array.indexed(1, r - p + 1)
for j in rbetween(r, p):
x = ord(A[j][position - 1]) - ord('a')
B[C[x]] = A[j]
C[x] -= 1
A.elements[p - 1:r] = B.elements
def fuzzy_partition(A, p, r):
j = random(p, r)
A[r], A[j] = A[j], A[r]
x = A[r].low
i = p - 1
for j in between(p, r - 1):
if A[j].low <= x:
i = i + 1
A[i], A[j] = A[j], A[i]
A[i + 1], A[r] = A[r], A[i + 1]
q = i + 1
for k in rbetween(i, p):
if A[k].high >= x:
q = q - 1
A[q], A[k] = A[k], A[q]
return q, i + 1
def jobs_scheduling(t, p, d):
n = p.length
a = Array(list(between(1, n)))
_sort_jobs_by_deadlines(a, t, p, d)
for i in between(1, n):
d[i] = min(d[i], n ** 2)
P = Array.indexed(0, d[n])
s = Array([Array.indexed(0, d[n]) for _ in between(1, n)])
for j in between(0, d[n]):
P[j] = 0
for i in between(1, n):
for j in between(0, d[n]):
s[i, j] = 0
for i in between(1, n):
for j in rbetween(d[n], t[i]):
if P[min(j, d[i]) - t[i]] + p[i] > P[j]:
P[j] = P[min(j, d[i]) - t[i]] + p[i]
s[i, j] = 1
return P, s, a
def jobs_scheduling(t, p, d):
n = p.length
a = Array(list(between(1, n)))
_sort_jobs_by_deadlines(a, t, p, d)
for i in between(1, n):
d[i] = min(d[i], n**2)
P = Array.indexed(0, d[n])
s = Array([Array.indexed(0, d[n]) for _ in between(1, n)])
for j in between(0, d[n]):
P[j] = 0
for i in between(1, n):
for j in between(0, d[n]):
s[i, j] = 0
for i in between(1, n):
for j in rbetween(d[n], t[i]):
if P[min(j, d[i]) - t[i]] + p[i] > P[j]:
P[j] = P[min(j, d[i]) - t[i]] + p[i]
s[i, j] = 1
return P, s, a
def test_print_stations(self):
n = random.randint(1, 10)
l = Array([Array.indexed(1, n), Array.indexed(1, n)])
l[1, 1], l[2, 1] = 0, 0
for i in between(2, n):
l[1, i], l[2, i] = random.choice([(1, 1), (1, 2), (2, 2)])
l_star = random.randint(1, 2)
captured_output = io.StringIO()
with redirect_stdout(captured_output):
print_stations(l, l_star, n)
actual_output = captured_output.getvalue().splitlines()
expected_output = []
i = l_star
expected_output.append('line ' + str(i) + ', station ' + str(n))
for j in rbetween(n, 2):
i = l[i, j]
expected_output.append('line ' + str(i) + ', station ' + str(j - 1))
assert_that(actual_output, is_(equal_to(expected_output)))
def test_print_stations_(self):
n = random.randint(1, 10)
l = Array([Array.indexed(1, n), Array.indexed(1, n)])
l[1, 1], l[2, 1] = 0, 0
for i in between(2, n):
l[1, i], l[2, i] = random.choice([(1, 1), (1, 2), (2, 2)])
l_star = random.randint(1, 2)
captured_output = io.StringIO()
with redirect_stdout(captured_output):
print_stations_(l, l_star, n)
actual_output = captured_output.getvalue().splitlines()
expected_output = []
i = l_star
expected_output.append('line ' + str(i) + ', station ' + str(n))
for j in rbetween(n, 2):
i = l[i, j]
expected_output.append('line ' + str(i) + ', station ' + str(j - 1))
expected_output.reverse()
assert_that(actual_output, is_(equal_to(expected_output)))
def activity_scheduler(s, f):
n = s.length
A = Array.indexed(1, n)
F = Array(list(rbetween(n, 1)))
F.top = n
B = RedBlackTree()
# events contains triples (a, b, c) where a = 0 if the event is finish of an activity and 1 if it is start,
# b as the activity number, and c as the start time or the finish time
events = [(0, i + 1, finish_time) for i, finish_time in enumerate(f)] + \
[(1, i + 1, start_time) for i, start_time in enumerate(s)]
events.sort(key=lambda e: (e[2], e[0]))
for e in events:
if e[0] == 1:
hall_number = pop(F)
A[e[1]] = hall_number
rb_insert(B, Node(e[1], data=hall_number), sentinel=B.nil)
else:
hall = rb_search(B.root, e[1], sentinel=B.nil)
push(F, hall.data)
rb_delete(B, hall, sentinel=B.nil)
return A
def heapsort(A):
build_max_heap(A)
for i in rbetween(A.length, 2):
A[1], A[i] = A[i], A[1]
A.heap_size = A.heap_size - 1
max_heapify(A, 1)
def bubble_sort(A):
for i in between(1, A.length):
for j in rbetween(A.length, i + 1):
if A[j] < A[j - 1]:
A[j], A[j - 1] = A[j - 1], A[j]
def _build_min_heap(A):
A.heap_size = A.length
for i in rbetween(math.floor(A.length / 2), 1):
_min_heapify(A, i)
def direct_address_maximum(T):
m = T.length
for i in rbetween(m - 1, 0):
if T[i] is not None:
return T[i]
return None
def _build_min_heap(A):
A.heap_size = A.length
for i in rbetween(math.floor(A.length / 2), 1):
_min_heapify(A, i)
def print_stations(l, l_star, n):
i = l_star
print('line ' + str(i) + ', station ' + str(n))
for j in rbetween(n, 2):
i = l[i, j]
print('line ' + str(i) + ', station ' + str(j - 1))
