def _min_heap_insert(A, z):
A.heap_size = A.heap_size + 1
i = A.heap_size
A[i] = z
while i > 1 and A[parent(i)].f > A[i].f:
A[i], A[parent(i)] = A[parent(i)], A[i]
i = parent(i)
def _min_heap_insert(A, z):
A.heap_size = A.heap_size + 1
i = A.heap_size
A[i] = z
while i > 1 and A[parent(i)].f > A[i].f:
A[i], A[parent(i)] = A[parent(i)], A[i]
i = parent(i)
def _heap_decrease_pair_key(A, i, pair):
if pair[0].key > A[i][0].key:
raise RuntimeError('new key is larger than current key')
A[i] = pair
while i > 1 and A[parent(i)][0].key > A[i][0].key:
A[i], A[parent(i)] = A[parent(i)], A[i]
i = parent(i)
def _heap_increase_element_key(A, i, x):
if x.key < A[i].key:
raise RuntimeError('new key is smaller than current key')
A[i] = x
while i > 1 and A[parent(i)].key < A[i].key:
A[i], A[parent(i)] = A[parent(i)], A[i]
i = parent(i)
def heap_decrease_key(A, i, key):
if key > A[i]:
raise RuntimeError('new key is larger than current key')
A[i] = key
while i > 1 and A[parent(i)] > A[i]:
A[i], A[parent(i)] = A[parent(i)], A[i]
i = parent(i)
def heap_increase_key(A, i, key):
if key < A[i]:
raise RuntimeError('new key is smaller than current key')
A[i] = key
while i > 1 and A[parent(i)] < A[i]:
A[i], A[parent(i)] = A[parent(i)], A[i]
i = parent(i)
def max_heap_delete(A, i):
A[i], A[A.heap_size] = A[A.heap_size], A[i]
A.heap_size = A.heap_size - 1
max_heapify(A, i)
while i > 1 and A[parent(i)] < A[i]:
A[i], A[parent(i)] = A[parent(i)], A[i]
i = parent(i)
return A[A.heap_size + 1]