def __init__(self, board):
self.board = board
self.twin_board = self.board.twin()
self.data_structure = DataStructure()
self.twin_data_structure = DataStructure()
self.states_explored = -1
current_state = self.board
current_twin_state = self.twin_board
while True:
self.states_explored += 1
# print(current_state.moves_to_reach)
# print(current_state)
if current_state.is_solved():
self.solution = self._form_solution(current_state)
break
elif current_twin_state.is_solved():
self.moves = -1
self.solution = []
break
for neighbor in current_state.neighbors():
if current_state.previous is None or not neighbor.has_same_data(current_state.previous):
self.data_structure.add(neighbor)
for neighbor in current_twin_state.neighbors():
if current_twin_state.previous is None or not neighbor.has_same_data(current_twin_state.previous):
self.twin_data_structure.add(neighbor)
current_state = self.data_structure.get_min()
current_twin_state = self.twin_data_structure.get_min()
def heapsort(arr):
""" Implements heapsort
O(n*log(n))
"""
heap = Heap(arr)
for i in range(heap.size - 1, 0, -1):
heap.heap[0], heap.heap[heap.size - 1] = heap.heap[heap.size -
1], heap.heap[0]
heap.size -= 1
heap.max_heapify(0)
return heap.heap # Ordered array
def heap_sort(num_arr):
"""
Returns num_arr sorted in ascending fashion. The original array is not modified.
Sorting is implemented using heap sort algorithm.
The algorithm has O(n * log(n)) complexity.
How it works: The array is put into max heap. The root of max heap is always the largest number. The sorting is done
by repeated popping of the root.
This implementation does not conserve the order of equal elements ("unstable sort").
"""
hp = Heap(num_arr)
result = []
while not hp.is_empty():
result.insert(0, hp.pop_max())
return result
def test_find_open_with_empty_aunt(self):
node17 = HeapNode(17)
node15 = HeapNode(15)
node11 = HeapNode(11)
node6 = HeapNode(6)
node10 = HeapNode(10)
node17.left = node15
node17.right = node11
node15.left = node6
node15.right = HeapNode(10)
heap = Heap(node17)
self.assertEqual(heap[-1].value, 10)
self.assertEqual(heap.find_open(), (node11, 'left'))
def test_create_many(self):
def is_invariant_node(i, my_heap):
if i < 0 or i >= my_heap.size:
raise IndexError(f"Index i should be between [0 and {my_heap.size})")
if i != 0:
pt = (i - 1) // 2
if my_heap.arr[pt] < my_heap.arr[i]:
return False
lf, rt = 2*i + 1, 2*i + 2
if lf >= my_heap.size:
return True
elif rt == my_heap.size:
if my_heap.arr[lf] > my_heap.arr[i]:
return False
else:
if my_heap.arr[i] < max(my_heap.arr[lf], my_heap.arr[rt]):
return False
return True
def check_heap_inv(my_heap):
is_invariant = True
for i in range(my_heap.size):
is_invariant = is_invariant and is_invariant_node(i, my_heap)
return is_invariant
n_cases = 100
n_nums = 50
for _ in range(n_cases):
num_list = list(np.random.rand(n_nums))
h = Heap(num_list)
self.assertTrue(check_heap_inv(h), "Heap invariant check failed")
def test_find_open_with_single_child_aunt(self):
node17 = HeapNode(17)
node15 = HeapNode(15)
node11 = HeapNode(11)
node6 = HeapNode(6)
node10 = HeapNode(10)
node7 = HeapNode(7)
node17.left = node15
node17.right = node11
node15.left = node6
node15.right = HeapNode(10)
node11.left = node7
heap = Heap(node17)
self.assertEqual(heap[-1].value, 7)
self.assertEqual(heap.find_open(), (node11, 'right'))
def test_create(self):
num_list = [1, 4, 7, 5, -3, 2, 8, 9]
h = Heap(num_list)
result = [9, 5, 8, 4, -3, 2, 7, 1]
self.assertTrue(h.arr == result, f"Heap construction failed {h.arr}")
def test_delete(self):
# 17 7 15 15
# / \ / \ / \ / \
# 15 11 --> 15 11 --> 7 11 --> 10 11
# / \ / / \ / \ / \
# 6 10 7 6 10 6 10 6 7
heap = Heap(max_heap())
heap[2].value = 11
heap.delete_root()
self.assertTrue(test_binary_node(heap.root, 15, 10, 11, None))
self.assertTrue(test_binary_node(heap.root.left, 10, 6, 7, 15))
self.assertTrue(test_binary_node(heap.root.right, 11, None, None, 15))
self.assertTrue(test_binary_node(heap.root.left.left, 6, None, None, 10))
self.assertTrue(test_binary_node(heap.root.left.right, 7, None, None, 10))
# 15 7 11
# / \ / \ / \
# 10 11 --> 10 11 --> 10 7
# / \ / /
# 6 7 6 6
heap.delete_root()
self.assertTrue(test_binary_node(heap.root, 11, 10, 7, None))
self.assertTrue(test_binary_node(heap.root.left, 10, 6, None, 11))
self.assertTrue(test_binary_node(heap.root.right, 7, None, None, 11))
self.assertTrue(test_binary_node(heap.root.left.left, 6, None, None, 10))
# 11 6 10
# / \ / \ / \
# 10 7 --> 10 7 --> 6 7
# /
# 6
heap.delete_root()
self.assertTrue(test_binary_node(heap.root, 10, 6, 7, None))
self.assertTrue(test_binary_node(heap.root.left, 6, None, None, 10))
self.assertTrue(test_binary_node(heap.root.right, 7, None, None, 10))
# 10 7
# / \ --> /
# 6 7 6
heap.delete_root()
self.assertTrue(test_binary_node(heap.root, 7, 6, None, None))
self.assertTrue(test_binary_node(heap.root.left, 6, None, None, 7))
# 7
# / --> 6
# 6
heap.delete_root()
self.assertTrue(test_binary_node(heap.root, 6, None, None, None))
# 6 --> None
heap.delete_root()
self.assertFalse(heap.root)
def test_insertion_with_percolation(self):
# 17
# / \
# 15 10
# / \ /
# 6 10 7
# 6
six = HeapNode(6)
heap = Heap(six)
self.assertTrue(test_binary_node(heap.root, 6, None, None, None))
# 6 10
# / --> /
# 10 6
heap.insert(10)
self.assertTrue(test_binary_node(heap.root, 10, 6, None, None))
self.assertTrue(test_binary_node(heap.root.left, 6, None, None, 10))
# 10 10
# / \ --> / \
# 6 7 6 7
heap.insert(7)
self.assertTrue(test_binary_node(heap.root, 10, 6, 7, None))
self.assertTrue(test_binary_node(heap.root.left, 6, None, None, 10))
self.assertTrue(test_binary_node(heap.root.right, 7, None, None, 10))
# 10 15
# / \ --> / \
# 6 7 10 7
# / /
# 15 6
heap.insert(15)
self.assertTrue(test_binary_node(heap.root, 15, 10, 7, None))
self.assertTrue(test_binary_node(heap.root.left, 10, 6, None, 15))
self.assertTrue(test_binary_node(heap.root.right, 7, None, None, 15))
self.assertTrue(test_binary_node(heap.root.left.left, 6, None, None, 10))
# 15 17
# / \ --> / \
# 10 7 15 7
# / \ / \
# 6 17 6 10
heap.insert(17)
self.assertTrue(test_binary_node(heap.root, 17, 15, 7, None))
self.assertTrue(test_binary_node(heap.root.left, 15, 6, 10, 17))
self.assertTrue(test_binary_node(heap.root.right, 7, None, None, 17))
self.assertTrue(test_binary_node(heap.root.left.left, 6, None, None, 15))
self.assertTrue(test_binary_node(heap.root.left.right, 10, None, None, 15))
# 17 17
# / \ --> / \
# 15 7 15 11
# / \ / / \ /
# 6 10 11 6 10 7
heap.insert(11)
self.assertTrue(test_binary_node(heap.root, 17, 15, 11, None))
self.assertTrue(test_binary_node(heap.root.left, 15, 6, 10, 17))
self.assertTrue(test_binary_node(heap.root.right, 11, 7, None, 17))
self.assertTrue(test_binary_node(heap.root.left.left, 6, None, None, 15))
self.assertTrue(test_binary_node(heap.root.left.right, 10, None, None, 15))
self.assertTrue(test_binary_node(heap.root.right.left, 7, None, None, 11))
def test_bubble(self):
# 17 17 100
# / \ / \ / \
# 15 10 --> 15 100 --> 15 17
# / \ / \ / \ / \ / \ / \
# 6 10 7 100 6 10 7 10 6 10 7 10
heap = Heap(max_heap())
parent = heap.root.right
last = HeapNode(100)
parent.right = last
last.parent = parent
heap.bubble(last)
self.assertTrue(test_binary_node(heap.root, 100, 15, 17, None))
self.assertTrue(test_binary_node(heap.root.right, 17, 7, 10, 100))
self.assertTrue(test_binary_node(heap.root.right.left, 7, None, None, 17))
self.assertTrue(test_binary_node(heap.root.right.right, 10, None, None, 17))
# 100 100 100
# / \ / \ / \
# 15 17 --> 15 17 --> 99 17
# / \ / \ / \ / \ / \ / \
# 6 10 7 10 99 10 7 10 15 10 7 10
# / / /
# 99 6 6
parent = heap.root.left.left
last = HeapNode(99)
last.parent = parent
parent.left = last
heap.bubble(last)
self.assertTrue(test_binary_node(heap.root, 100, 99, 17, None))
self.assertTrue(test_binary_node(heap.root.left, 99, 15, 10, 100))
self.assertTrue(test_binary_node(heap.root.left.left, 15, 6, None, 99))
self.assertTrue(test_binary_node(heap.root.left.right, 10, None, None, 99))
self.assertTrue(test_binary_node(heap.root.left.left.left, 6, None, None, 15))
# 100 100 100
# / \ / \ / \
# 99 17 --> 99 17 --> 100 17
# / \ / \ / \ / \ / \ / \
# 15 10 7 10 15 100 7 10 15 99 7 10
# / \ / / \ / / \ /
# 6 12 100 6 12 10 6 12 10
fifteen = heap.root.left.left
twelve = HeapNode(12)
twelve.parent = fifteen
fifteen.right = twelve
ten = heap.root.left.right
last = HeapNode(100)
ten.left = last
last.parent = ten
heap.bubble(last)
self.assertTrue(test_binary_node(heap.root, 100, 100, 17, None))
self.assertTrue(test_binary_node(heap.root.left, 100, 15, 99, 100))
self.assertTrue(test_binary_node(heap.root.left.left, 15, 6, 12, 100))
self.assertTrue(test_binary_node(heap.root.left.right, 99, 10, None, 100))
def test_insert(self):
node17 = HeapNode(17)
heap = Heap(node17)
heap.insert(15)
self.assertTrue(test_binary_node(heap.root, 17, 15, None, None))
self.assertTrue(test_binary_node(heap.root.left, 15, None, None, 17))
heap.insert(10)
self.assertTrue(test_binary_node(heap.root, 17, 15, 10, None))
self.assertTrue(test_binary_node(heap.root.left, 15, None, None, 17))
self.assertTrue(test_binary_node(heap.root.right, 10, None, None, 17))
heap.insert(6)
self.assertTrue(test_binary_node(heap.root, 17, 15, 10, None))
self.assertTrue(test_binary_node(heap.root.left, 15, 6, None, 17))
self.assertTrue(test_binary_node(heap.root.right, 10, None, None, 17))
self.assertTrue(test_binary_node(heap.root.left.left, 6, None, None, 15))
heap.insert(10)
self.assertTrue(test_binary_node(heap.root, 17, 15, 10, None))
self.assertTrue(test_binary_node(heap.root.left, 15, 6, 10, 17))
self.assertTrue(test_binary_node(heap.root.right, 10, None, None, 17))
self.assertTrue(test_binary_node(heap.root.left.left, 6, None, None, 15))
self.assertTrue(test_binary_node(heap.root.left.right, 10, None, None, 15))
heap.insert(7)
self.assertTrue(test_binary_node(heap.root, 17, 15, 10, None))
self.assertTrue(test_binary_node(heap.root.left, 15, 6, 10, 17))
self.assertTrue(test_binary_node(heap.root.right, 10, 7, None, 17))
self.assertTrue(test_binary_node(heap.root.left.left, 6, None, None, 15))
self.assertTrue(test_binary_node(heap.root.left.right, 10, None, None, 15))
self.assertTrue(test_binary_node(heap.root.right.left, 7, None, None, 10))
def test_heap_iteration(self):
heap = Heap(max_heap())
self.assertEqual([int(str(n)) for n in heap.breadth()], [17, 15, 10, 6, 10, 7])
self.assertEqual([int(str(n)) for n in heap], [17, 15, 10, 6, 10, 7])
self.assertEqual(heap.flatten(), [17, 15, 10, 6, 10, 7])