Conditional Properties

if not (el = val), then index of value val in [ node (el, left, right), remain ] with current index idx = index of value val in remain with current index (idx + 1)

if not (el = val), then index of value val in [ node (el, w, p), remain ] with current index idx = index of value val in remain with current index (idx + 1)

if the following are true:

• not (left = val)
• not (right = val)

then find parent index of [ node (el, left, right), remain ] = find parent index of remain

if x = value, then stack [ x, y ] contains value = True

if not (x = value), then stack [ x, y ] contains value = stack y contains value

if entry_key = key, then output of function store_compute where input key is key, value is value, map is [ entry entry_key: entry_value, remaining ], and processed map is kvs = result of dumping kvs to [ entry key: value, remaining ]

if not (entry_key = key), then output of function store_compute where input key is key, value is value, map is [ entry entry_key: entry_value, remaining ], and processed map is kvs = output of function store_compute where input key is key, value is value, map is remaining, and processed map is [ entry entry_key: entry_value, kvs ]

if entry_key = key, then output of function delete_entry where input key is key, map is [ pair (entry_key, value), remaining ], and processed is kvs = result of dumping kvs to remaining

if not (entry_key = key), then output of function delete_entry where input key is key, map is [ pair (entry_key, value), remaining ], and processed is kvs = output of function delete_entry where input key is key, map is remaining, and processed is [ pair (entry_key, value), kvs ]

if (length of stack xs) % 2 = 0, then length of xs is even

if (length of stack xs) % 2 = 1, then length of xs is odd

if i < max_size, then get subtower map[ i, rest ] = get subtower maprest

if not (i < max_size), then get subtower map[ i, rest ] = result

if the following are true:

• not (one = x)
• not (two = x)

then find other one = x

if the following are true:

• the element at index src of stack towers = src_tower
• get subtowersrc_tower = sub_tower
• length of sub_tower is even

then towers of hanoi towers = towers of hanoi top disks towers

if the following are true:

• the element at index src of stack towers = src_tower
• get subtowersrc_tower = sub_tower
• length of sub_tower is odd

then towers of hanoi towers = towers of hanoi top disks towers

if the following are true:

• the element at index src of stack towers = [ 1, rest ]
• the element at index dst of stack towers = dst_tower

then towers of hanoi top towers = move disk towers is even

if the following are true:

• the element at index src of stack towers = [ x, rest ]
• the element at index dst of stack towers = dst_tower
• x > 1

then towers of hanoi top towers = towers of hanoi (move disk towers is even)

if the element at index i of stack tree = node (v, (-1), (-1)), then Height of a tree tree and index i = 1

if the element at index i of stack tree = node (v, left, (-1)), then Height of a tree tree and index i = (Height of a tree tree and index left) + 1

if the element at index i of stack tree = node (v, (-1), right), then Height of a tree tree and index i = (Height of a tree tree and index right) + 1

if the following are true:

• the element at index i of stack tree = node (v, a, b)
• Height of a tree tree and index a > Height of a tree tree and index b

then Height of a tree tree and index i = (Height of a tree tree and index a) + 1

if the following are true:

• the element at index i of stack tree = node (v, a, b)
• Height of a tree tree and index a < Height of a tree tree and index b

then Height of a tree tree and index i = (Height of a tree tree and index b) + 1

if the following are true:

• the element at index i of stack tree = node (v, a, b)
• Height of a tree tree and index a = Height of a tree tree and index b

then Height of a tree tree and index i = (Height of a tree tree and index a) + 1

if the following are true:

• val < a
• the element at index i of stack tree = node (a, left, right)

then output of the bst_insert function where input tree is tree, value is val and index is i = output of the bst_insert function where input tree is tree, value is val and index is left

if the following are true:

• val > a
• the element at index i of stack tree = node (a, left, right)

then output of the bst_insert function where input tree is tree, value is val and index is i = output of the bst_insert function where input tree is tree, value is val and index is right

if the following are true:

• val < a
• the element at index i of stack tree = node (a, (-1), right)

then output of the bst_insert function where input tree is tree, value is val and index is i = result of storing (node (a, (length of stack tree), right)) at index i of stack (result of appending (node (val, (-1), (-1))) to tree)

if the following are true:

• val > a
• the element at index i of stack tree = node (a, left, (-1))

then output of the bst_insert function where input tree is tree, value is val and index is i = result of storing (node (a, left, (length of stack tree))) at index i of stack (result of appending (node (val, (-1), (-1))) to tree)

if the following are true:

• not (left = index)
• not (right = index)

then find referece to node index in tree [ node (x, left, right), rest ] = find referece to node index in tree rest

if find referece to node i in tree tree = False, then find root index in tree = i

if the following are true:

• find root index in tree = ri
• the element at index ri of stack tree = node (root_val, left, right)
• the element at index left of stack tree = node (l_val, l_left, l_right)
• new_val < root_val
• new_val < l_val

then result of inserting new_val to tree tree = result of rotating (output of the bst_insert function where input tree is tree, value is new_val and index is ri) clockwise

if the following are true:

• find root index in tree = ri
• the element at index ri of stack tree = node (root_val, left, right)
• the element at index left of stack tree = node (l_val, l_left, l_right)
• new_val < root_val
• new_val > l_val

then result of inserting new_val to tree tree = result of rotating (result of rotating (output of the bst_insert function where input tree is tree, value is new_val and index is ri) twice) clockwise

if the following are true:

• find root index in tree = ri
• the element at index ri of stack tree = node (root_val, left, right)
• the element at index left of stack tree = node (l_val, l_left, l_right)

then result of rotating tree clockwise = result of storing (node (l_val, l_left, ri)) at index left of stack (result of storing (node (root_val, l_right, right)) at index ri of stack tree)

if the following are true:

• find root index in tree = ri
• the element at index ri of stack tree = node (root_val, left, right)
• the element at index left of stack tree = node (l_val, l_left, g)
• the element at index g of stack tree = node (g_val, g_left, g_right)

then result of rotating tree twice = result of storing (node (root_val, g, right)) at index ri of stack (result of storing (node (g_val, left, g_right)) at index g of stack (result of storing (node (l_val, l_left, g_left)) at index left of stack tree))

if the element at index i of stack tree = node (value, left, right), then find nearest largertree = find nearest largertree

if the following are true:

• val < a
• the element at index i of stack tree = node (a, (-1), right)

then find nearest largertree = i

if the following are true:

• val < a
• the element at index i of stack tree = node (a, left, right)

then find nearest largertree = find nearest largertree

if the following are true:

• val > a
• the element at index i of stack tree = node (a, left, right)

then find nearest largertree = find nearest largertree

if the following are true:

• val = a
• the element at index i of stack tree = node (a, left, right)

then find nearest largertree = find nearest largertree

if the following are true:

• index of value value in tree = i
• the element at index i of stack tree = node (value, (-1), (-1))
• find parent index of tree = p
• the element at index p of stack tree = node (pval, pleft, i)

then pop value from tree tree = result of storing (node (pval, pleft, (-1))) at index p of stack tree

if the following are true:

• index of value value in tree = i
• the element at index i of stack tree = node (value, left, (-1))
• the element at index left of stack tree = node (lvalue, lleft, lright)
• find parent index of tree = p
• the element at index p of stack tree = node (pval, pleft, i)

then pop value from tree tree = result of storing (node (value, (-1), (-1))) at index i of stack (result of storing (node (pval, pleft, left)) at index p of stack tree)

if the following are true:

• index of value value in tree = i
• the element at index i of stack tree = node (value, (-1), right)
• the element at index right of stack tree = node (rvalue, rleft, rright)
• find parent index of tree = p
• the element at index p of stack tree = node (pval, i, pright)

then pop value from tree tree = result of storing (node (value, (-1), (-1))) at index i of stack (result of storing (node (pval, right, pright)) at index p of stack tree)

if the following are true:

• index of value value in tree = i
• find nearest largertree = n
• the element at index n of stack tree = node (larger, nleft, nright)
• the element at index i of stack tree = node (value, left, right)

then pop value from tree tree = result of storing (node (larger, left, right)) at index i of stack (pop larger from tree tree)

if the following are true:

• find root index in tree = ri
• the element at index ri of stack tree = node (rvalue, left, right)
• Height of a tree tree and index left = Height of a tree tree and index right

then result of balancing the tree tree = tree

if the following are true:

• find root index in tree = ri
• the element at index ri of stack tree = node (rvalue, left, right)
• Height of a tree tree and index left > (Height of a tree tree and index right) + 1
• the element at index left of stack tree = node (lvalue, lleft, lright)
• Height of a tree tree and index lleft > Height of a tree tree and index lright

then result of balancing the tree tree = result of rotating tree clockwise

if the following are true:

• find root index in tree = ri
• the element at index ri of stack tree = node (rvalue, left, right)
• Height of a tree tree and index left > (Height of a tree tree and index right) + 1
• the element at index left of stack tree = node (lvalue, lleft, lright)
• Height of a tree tree and index lleft < Height of a tree tree and index lright

then result of balancing the tree tree = result of rotating (result of rotating tree twice) clockwise

if a < b, then output of the merge_stacks function where input stacks are [ a, a_rest ] and [ b, b_rest ], and merged stack is result = output of the merge_stacks function where input stacks are a_rest and [ b, b_rest ], and merged stack is [ a, result ]

if a > b, then output of the merge_stacks function where input stacks are [ a, a_rest ] and [ b, b_rest ], and merged stack is result = output of the merge_stacks function where input stacks are [ a, a_rest ] and b_rest, and merged stack is [ b, result ]

if c > 0, then output of the halve stack function where input stack is [ a, a_rest ], other stack is other, and count is c = output of the halve stack function where input stack is a_rest, other stack is [ a, other ], and count is (c - 1)

if result of halving the stack stack = [ first_half, [ second_half, [ ] ] ], then result of merge sorting stack = result of merging stacks (result of merge sorting first_half) and (result of merge sorting second_half)

if elem = value, then tree [ node (elem, cs), rest ] contains value = True

if not (elem = value), then tree [ node (elem, cs), rest ] contains value = tree rest contains value

if elem = value, then tree [ node (elem, d, p), rest ] contains value = True

if not (elem = value), then tree [ node (elem, d, p), rest ] contains value = tree rest contains value

if tree tree contains value = False, then output of the not_in_tree function where the input tree is tree, the values are [ value, rest ], and the new values are result = output of the not_in_tree function where the input tree is tree, the values are rest, and the new values are [ value, result ]

if tree tree contains value = True, then output of the not_in_tree function where the input tree is tree, the values are [ value, rest ], and the new values are result = output of the not_in_tree function where the input tree is tree, the values are rest, and the new values are result

if the following are true:

• ((length of stack tree) - 1) - index = back_i
• the element at index back_i of stack tree = node (value, cs)

then children of the node at backwards index index of tree tree in graph graph = output of the find_neighbors function where the input graph is graph, node is value, and children are [ ]

if the following are true:

• not (left = value)
• not (right = value)

then output of the find_neighbors function where the input graph is [ pair (left, right), rest ], node is value, and children are result = output of the find_neighbors function where the input graph is rest, node is value, and children are result

if left = value, then output of the find_neighbors function where the input graph is [ pair (left, right), rest ], node is value, and children are result = output of the find_neighbors function where the input graph is rest, node is value, and children are [ right, result ]

if right = value, then output of the find_neighbors function where the input graph is [ pair (left, right), rest ], node is value, and children are result = output of the find_neighbors function where the input graph is rest, node is value, and children are [ left, result ]

if the following are true:

• ((length of stack tree) - 1) - index = back_i
• the element at index back_i of stack tree = node (value, cs)
• elements of numbers that are not in tree tree = new_elements
• result of storing (node (value, new_elements)) at index back_i of stack tree = updated

then result of adding numbers to tree tree as children of the node at backwards index index = result of pushing values new_elements to tree updated

if the following are true:

• children of the node at backwards index i of tree tree in graph graph = children
• result of adding children to tree tree as children of the node at backwards index i = new_tree

then output of the spanning_tree function where the input graph is graph, backwards index is i, and the spanning tree is tree = output of the spanning_tree function where the input graph is graph, backwards index is (i + 1), and the spanning tree is new_tree

if i = (length of stack tree) - 1, then output of the spanning_tree function where the input graph is graph, backwards index is i, and the spanning tree is tree = tree

if the following are true:

• ((length of stack tree) - 1) - index = back_i
• the element at index back_i of stack tree = node (value, distance, previous)

then children of the node at backwards index index of tree tree in graph graph = output of the find_neighbors function where the input graph is graph, node is value, and children are [ ]

if the following are true:

• not (left = value)
• not (right = value)

then output of the find_neighbors function where the input graph is [ edge (left, right, weight), rest ], node is value, and children are result = output of the find_neighbors function where the input graph is rest, node is value, and children are result

if left = value, then output of the find_neighbors function where the input graph is [ edge (left, right, weight), rest ], node is value, and children are result = output of the find_neighbors function where the input graph is rest, node is value, and children are [ pair (right, weight), result ]

if right = value, then output of the find_neighbors function where the input graph is [ edge (left, right, weight), rest ], node is value, and children are result = output of the find_neighbors function where the input graph is rest, node is value, and children are [ pair (left, weight), result ]

if tree tree contains value = False, then output of the separate_nodes function where the input tree is tree, the nodes are [ pair (value, weight), rest ], the existing group is exist, and the new group is new = output of the separate_nodes function where the input tree is tree, the nodes are rest, the existing group is exist, and the new group is [ pair (value, weight), new ]

if index of value value in tree = index, then output of the separate_nodes function where the input tree is tree, the nodes are [ pair (value, weight), rest ], the existing group is exist, and the new group is new = output of the separate_nodes function where the input tree is tree, the nodes are rest, the existing group is [ pair (index, weight), exist ], and the new group is new

if the following are true:

• the element at index child_i of stack tree = node (child_value, child_d, child_prev)
• distance + weight < child_d
• result of storing (node (child_value, (distance + weight), index)) at index child_i of stack tree = updated

then result of updating nodes [ pair (child_i, weight), rest ] in tree tree with parent index index and parent distance distance = result of updating nodes rest in tree updated with parent index index and parent distance distance

if the following are true:

• the element at index child_i of stack tree = node (child_value, child_d, child_prev)
• distance + weight > child_d

then result of updating nodes [ pair (child_i, weight), rest ] in tree tree with parent index index and parent distance distance = result of updating nodes rest in tree tree with parent index index and parent distance distance

if the following are true:

• ((length of stack tree) - 1) - index = back_i
• the element at index back_i of stack tree = node (value, distance, previous)
• result of splitting pairs into nodes that exist in the tree tree and new nodes = pair (exists, new)
• result of updating nodes exists in tree tree with parent index index and parent distance distance = updated

then result of adding or updating children pairs of the node at backwards index index in tree tree = result of pushing nodes new into tree updated where parent is index and parent distance is distance

if the following are true:

• children of the node at backwards index i of tree tree in graph graph = children
• result of adding or updating children children of the node at backwards index i in tree tree = new_tree

then output of the shortest_path function where the input graph is graph, backwards index is i, and tree is tree = output of the shortest_path function where the input graph is graph, backwards index is (i + 1), and tree is new_tree

if i = length of stack tree, then output of the shortest_path function where the input graph is graph, backwards index is i, and tree is tree = tree

if the following are true:

• children of the node top in graph graph = children
• elements of children that are not in tree tree = new_elements
• nodes with values new_elements and parent top = final_elems
• result of dumping final_elems to rest = new_stack

then output of the build_dft_tree function where input graph is graph, tree is tree, and neighbor stack is [ node (top, parent), rest ] = output of the build_dft_tree function where input graph is graph, tree is [ node (top, parent), tree ], and neighbor stack is new_stack

if val < a, then tree (node (a, left, right)) contains val = tree left contains val

if val > a, then tree (node (a, left, right)) contains val = tree right contains val

if val = a, then tree (node (a, left, right)) contains val = True

if val < a, then output of the bst_insert function where the input tree is (node (a, left, right)), value is val, visited is visited, and moves are moves = output of the bst_insert function where the input tree is left, value is val, visited is [ node (a, None, right), visited ], and moves are [ "L", moves ]

if val > a, then output of the bst_insert function where the input tree is (node (a, left, right)), value is val, visited is visited, and moves are moves = output of the bst_insert function where the input tree is right, value is val, visited is [ node (a, left, None), visited ], and moves are [ "R", moves ]

if val < a, then output of the bst_insert function where the input tree is (node (a, None, None)), value is val, visited is visited, and moves are moves = result of building the BST from nodes [ node (a, (node (val, None, None)), None), visited ] and moves moves

if val > a, then output of the bst_insert function where the input tree is (node (a, None, None)), value is val, visited is visited, and moves are moves = result of building the BST from nodes [ node (a, None, (node (val, None, None))), visited ] and moves moves

if height of tree left > height of tree right, then height of tree (node (v, left, right)) = (height of tree left) + 1

if height of tree left < height of tree right, then height of tree (node (v, left, right)) = (height of tree right) + 1

if height of tree left = height of tree right, then height of tree (node (v, left, right)) = (height of tree left) + 1

if the following are true:

• height of tree (node (lv, ll, lr)) > (height of tree right) + 1
• height of tree ll > height of tree lr

then result of balancing the tree (node (v, (node (lv, ll, lr)), right)) = result of rotating (node (v, (node (lv, ll, lr)), right)) clockwise

if the following are true:

• height of tree (node (lv, ll, lr)) > (height of tree right) + 1
• height of tree ll < height of tree lr

then result of balancing the tree (node (v, (node (lv, ll, lr)), right)) = result of rotating (node (v, (node (lv, ll, lr)), right)) twice

if val < a, then output of the bst_delete function where input tree is (node (a, left, right)), value is val, visited is visited, and moves are moves = output of the bst_delete function where input tree is left, value is val, visited is [ node (a, None, right), visited ], and moves are [ "L", moves ]

if val > a, then output of the bst_delete function where input tree is (node (a, left, right)), value is val, visited is visited, and moves are moves = output of the bst_delete function where input tree is right, value is val, visited is [ node (a, left, None), visited ], and moves are [ "R", moves ]

if val = b, then output of the bst_delete function where input tree is (node (a, (node (b, None, (node (c, cl, cr)))), right)), value is val, visited is visited, and moves are moves = result of building the BST from nodes [ node (a, (node (c, cl, cr)), right), visited ] and moves moves

if the following are true:

• val = a
• tree = node (a, (node (l, ll, lr)), (node (r, rl, rr)))
• smallest value in (node (r, rl, rr)) = near

then output of the bst_delete function where input tree is tree, value is val, visited is visited, and moves are moves = result of building the BST from nodes [ result of updating the root of (result of removing near from tree tree) with near, visited ] and moves moves

if x^p = z, then log_xz = p

if log_xz = p, then x^p = z