Implement a program in c that read in a postfix expression (only with integers as operands and basic mathematics operators: +, -, * and /) and construct an expression tree for this expression. Also implement the three traversal methods: pre-order traversal, in-order traversal and post-order traversal. Apply these three traversal methods to this expression tree and print out the prefix, infix and postfix expression correspondingly. You need also implement a binary tree node class.