Question: https://codility.com/demo/take-sample-test/cartesian_sequence

Question Name: upsilon2012 or CartesianSequence

A straightforward solution would be construct the Cartesian tree, compute its height, and return the height plus one. But any left sub-tree would never be accessed or changed after its construction. And so is their height information. In other words, the height information only needs possible update, when the nodes are on the path from the last node to the root. To improve the performance, we could compute the height while constructing the tree.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 | class Cartesian_Tree(): ''' The class to construct the Cartesian Tree ''' class node(object): # __slots__ keyword is used to improve the performance __slots__ = ('key', 'value', 'right', 'left', 'parent', 'height') def __init__(self, key, value): self.key = key # Node's key self.value = value # Node's value self.right = None # Right Child self.left = None # Left Child self.parent = None # Parent Node self.height = 0 # The height of current sub-tree return def __init__(self, content): # Construction method: # http://en.wikipedia.org/wiki/Cartesian_tree#Efficient_construction self.nodes=[self.node(i, content[i]) for i in xrange(len(content))] self.root = self.nodes[0] for index in xrange(1, len(content)): prior = self.nodes[index-1] current = self.nodes[index] while prior.value <= current.value: # Finding a node with value greater than current node # Update the height information of nodes on the finding path # These nodes will NEVER be accessed again! # AND their height information is final. if prior.left != None: prior.height = max(prior.left.height+1, prior.height) if prior.right != None: prior.height = max(prior.right.height+1, prior.height) if prior.parent == None: # Cannot find the node with greater value # Current node will be the new root node current.left = prior current.height = prior.height + 1 prior.parent = current self.root = current break prior = prior.parent else: # Find the node, to say x, with greater value # x.right will be current node's left son # And current node will be the x's new right son current.left = prior.right current.parent = prior if current.left != None: current.left.parent = current current.height = current.left.height + 1 prior.right = current # Some nodes, on the path from last processed node to root, # might have out-of-date height information. Update them. prior = self.nodes[-1] while prior.parent != None: if prior.parent.height <= prior.height: prior.parent.height = prior.height + 1 prior = prior.parent return def get_height(self): return self.root.height heigth = property(get_height) def solution(A): tree = Cartesian_Tree(A) return tree.heigth+1 |