Update treap.py (#1358)

* Update treap.py

check merge()

* Update treap.py

random() is used. its difficult to write doctests
l->left
r->right
key->value
add __repr__ and __str__ in preorder

data_structures/binary_tree/treap.py

@@ -2,129 +2,173 @@ from random import random
 from typing import Tuple
 
 
-class Node:
+class Node(object):
     """
     Treap's node
-    Treap is a binary tree by key and heap by priority
+    Treap is a binary tree by value and heap by priority
     """
-
-    def __init__(self, key: int):
-        self.key = key
+    def __init__(self, value: int = None):
+        self.value = value
         self.prior = random()
-        self.l = None
-        self.r = None
+        self.left = None
+        self.right = None
 
+    def __repr__(self):
+        from pprint import pformat
 
-def split(root: Node, key: int) -> Tuple[Node, Node]:
+        if self.left is None and self.right is None:
+            return "'%s: %.5s'" % (self.value, self.prior)
+        else:
+            return pformat(
+                {
+                    "%s: %.5s"
+                    % (self.value, self.prior): (self.left, self.right)
+                },
+                indent=1,
+            )
+
+    def __str__(self):
+        value = str(self.value) + " "
+        left = str(self.left or "")
+        right = str(self.right or "")
+        return value + left + right
+
+def split(root: Node, value: int) -> Tuple[Node, Node]:
     """
-    We split current tree into 2 trees with key:
+    We split current tree into 2 trees with value:
 
-    Left tree contains all keys less than split key.
-    Right tree contains all keys greater or equal, than split key
+    Left tree contains all values less than split value.
+    Right tree contains all values greater or equal, than split value
     """
     if root is None:  # None tree is split into 2 Nones
         return (None, None)
-    if root.key >= key:
+    elif root.value is None:
+        return (None, None)
+    else:
+        if value < root.value:
             """
             Right tree's root will be current node.
-        Now we split(with the same key) current node's left son
+            Now we split(with the same value) current node's left son
             Left tree: left part of that split
             Right tree's left son: right part of that split
             """
-        l, root.l = split(root.l, key)
-        return (l, root)
+            left, root.left = split(root.left, value)
+            return (left, root)
         else:
             """
             Just symmetric to previous case
             """
-        root.r, r = split(root.r, key)
-        return (root, r)
-
+            root.right, right = split(root.right, value)
+            return (root, right)
 
 def merge(left: Node, right: Node) -> Node:
     """
     We merge 2 trees into one.
-    Note: all left tree's keys must be less than all right tree's
-    """
-    if (not left) or (not right):
-        """
-        If one node is None, return the other
+    Note: all left tree's values must be less than all right tree's
     """
+    if (not left) or (not right):   # If one node is None, return the other
         return left or right
-    if left.key > right.key:
+    elif left.prior < right.prior:
         """
         Left will be root because it has more priority
         Now we need to merge left's right son and right tree
         """
-        left.r = merge(left.r, right)
+        left.right = merge(left.right, right)
         return left
     else:
         """
         Symmetric as well
         """
-        right.l = merge(left, right.l)
+        right.left = merge(left, right.left)
         return right
 
-
-def insert(root: Node, key: int) -> Node:
+def insert(root: Node, value: int) -> Node:
     """
     Insert element
 
-    Split current tree with a key into l, r,
+    Split current tree with a value into left, right,
     Insert new node into the middle
-    Merge l, node, r into root
+    Merge left, node, right into root
     """
-    node = Node(key)
-    l, r = split(root, key)
-    root = merge(l, node)
-    root = merge(root, r)
-    return root
+    node = Node(value)
+    left, right = split(root, value)
+    return merge(merge(left, node), right)
 
-
-def erase(root: Node, key: int) -> Node:
+def erase(root: Node, value: int) -> Node:
     """
     Erase element
 
-    Split all nodes with keys less into l,
-    Split all nodes with keys greater into r.
-    Merge l, r
+    Split all nodes with values less into left,
+    Split all nodes with values greater into right.
+    Merge left, right
     """
-    l, r = split(root, key)
-    _, r = split(r, key + 1)
-    return merge(l, r)
+    left, right = split(root, value-1)
+    _, right = split(right, value)
+    return merge(left, right)
 
-
-def node_print(root: Node):
+def inorder(root: Node):
     """
     Just recursive print of a tree
     """
-    if not root:
+    if not root:    # None
         return
-    node_print(root.l)
-    print(root.key, end=" ")
-    node_print(root.r)
+    else:
+        inorder(root.left)
+        print(root.value, end=" ")
+        inorder(root.right)
 
 
-def interactTreap():
+def interactTreap(root, args):
     """
     Commands:
-    + key to add key into treap
-    - key to erase all nodes with key
+    + value to add value into treap
+    - value to erase all nodes with value
 
-    After each command, program prints treap
+        >>> root = interactTreap(None, "+1")
+        >>> inorder(root)
+        1 
+        >>> root = interactTreap(root, "+3 +5 +17 +19 +2 +16 +4 +0")
+        >>> inorder(root)
+        0 1 2 3 4 5 16 17 19 
+        >>> root = interactTreap(root, "+4 +4 +4")
+        >>> inorder(root)
+        0 1 2 3 4 4 4 4 5 16 17 19 
+        >>> root = interactTreap(root, "-0")
+        >>> inorder(root)
+        1 2 3 4 4 4 4 5 16 17 19 
+        >>> root = interactTreap(root, "-4")
+        >>> inorder(root)
+        1 2 3 5 16 17 19 
+        >>> root = interactTreap(root, "=0")
+        Unknown command
     """
-    root = None
-    while True:
-        cmd = input().split()
-        cmd[1] = int(cmd[1])
-        if cmd[0] == "+":
-            root = insert(root, cmd[1])
-        elif cmd[0] == "-":
-            root = erase(root, cmd[1])
+    for arg in args.split():
+        if arg[0] == "+":
+            root = insert(root, int(arg[1:]))
+
+        elif arg[0] == "-":
+            root = erase(root, int(arg[1:]))
+
         else:
             print("Unknown command")
-        node_print(root)
 
+    return root
+
+def main():
+    """After each command, program prints treap"""
+    root = None
+    print("enter numbers to creat a tree, + value to add value into treap, - value to erase all nodes with value. 'q' to quit. ")
+
+    args = input()
+    while args != 'q':
+        root = interactTreap(root, args)
+        print(root)
+        args = input()
+
+    print("good by!")
+    pass
 
 if __name__ == "__main__":
-    interactTreap()
+    import doctest
+    doctest.testmod()
+    main()