Expression tree is a binary tree in which each internal node corresponds to operator and each leaf node corresponds to operand so for example expression tree for 3 + ((5+9)*2) would be:
Inorder traversal of expression tree produces infix version of given postfix expression (same with preorder traversal it gives prefix expression)
Evaluating the expression represented by expression tree:
Let t be the expression tree
If t is not null then
If t.value is operand then
A = solve(t.left)
B = solve(t.right)
// calculate applies operator 't.value'
// on A and B, and returns value
Return calculate(A, B, t.value)
Construction of Expression Tree:
Now For constructing expression tree we use a stack. We loop through input expression and do following for every character.
1) If character is operand push that into stack
2) If character is operator pop two values from stack make them its child and push current node again.
At the end only element of stack will be root of expression tree.