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Program to build and evaluate an expression tree using Python
Suppose, we are given the post order traversal of an expression tree. We have to build an expression tree from the given post-order traversal, and then evaluate the expression. We return the root of the expression tree and the evaluated value of the tree.
So, if the input is like
then the output will be -7.
The postfix order given as input of the tree is ['1', '2', '+', '3', '4', '+', '*']. The expression if evaluated, becomes (1 – 2) * (3 + 4); which equals -7.
To solve this, we will follow these steps −
LEFT = 0 RIGHT = 1
Define a function evaluate() . This will take root
if value of root is a numeric value, then
return integer representation of value of root
left_val := evaluate(left of root)
right_val := evaluate(right of root)
if value of root = '+', then
return left_val + right_val
otherwise when value of root = '-', then
return left_val - right_val
otherwise when value of root = '*', then
return left_val * right_val
otherwise when value of root = '/', then
return floor value of (left_val / right_val)
Define a function buildTree() . This will take postfix
root := null
stack := a new list
while postfix is not empty, do
curr := delete last element from postfix
curr_node := a new node containing the value curr
if root is empty, then
root := curr_node
if stack is not empty, then
parent := delete last element from stack
side := parent
if side is same as LEFT, then
left of parent := curr_node
otherwise,
right of parent := curr_node
if curr is not a numerical value, then
insert tuple (curr_node, LEFT) at the end of stack
insert tuple(curr_node, RIGHT) at the end of stack
return root
Let us see the following implementation to get better understanding −
Example
LEFT = 0 RIGHT = 1 class Node(): def __init__(root, val, left = None, right = None): root.val = val root.left = left root.right = right def evaluate(root): if(root.val.isnumeric()): return int(root.val) left_val = evaluate(root.left) right_val = evaluate(root.right) return ( ( root.val == '+' and left_val + right_val ) or ( root.val == '-' and left_val - right_val ) or ( root.val == '*' and left_val * right_val ) or ( root.val == '/' and left_val // right_val ) ) def buildTree(postfix): root = None stack = [] while(postfix): curr = postfix.pop() curr_node = Node(curr) if(not root): root = curr_node if(stack): parent, side = stack.pop() if(side == LEFT): parent.left = curr_node else: parent.right = curr_node if(not curr.isnumeric()): stack.append((curr_node, LEFT)) stack.append((curr_node, RIGHT)) return root root = buildTree(['1', '2', '+', '3', '4', '+', '*']) print(evaluate(root))
Input
['1', '2', '+', '3', '4', '+', '*']
Output
-7
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