# ============================================================== # convert numeric infix expression to a # Reverse Polish Expression (RPN) # # Note: TOS is top of stack # ============================================================== start-sub is a '(' character end-sub is a ')' character # -------------------------------------------------------------- function process_sub_end (stack,rpn_tokens): while the stack is not empty: if TOS is start-sub: return True append token to rpn_tokens # ---- did not find start-sub return False # -------------------------------------------------------------- stack = empty stack rpn_tokens = empty list for each token in tokens: # ---- token is a number If the token is a number: append the token to the RPN token list continue # --- token is a start-sub If the token is a start-sub: push the token onto the stack continue # --- token is an end-sub If the token is an end-sub: tf = process_sub_end(stack,rpn_tokens) if tf is False: return syntax error / exit program continue # ---- if the stack is empty if the stack is empty: push the token onto stack continue # ---- if token is a math operator and # ---- the token precedence is greater than TOS if the token is in [**,//,*,/,+,-,%] and the token as a higher precedence than TOS: push the token onto the stack continue # ---- if the token precedence is less than or equal to TOS loop: if the stack is empty: break if the TOS is sub-start or end-sub: break if the token precedence is less that or equal to TOS: pop TOS from the stack append the token to the RPN token list else: break push the token onto the stack continue # ---- move remaining stack tokens to the RPN token list while the stack is not empty: if TOS is sub-start: return False if TOS is sub-start: return False pop the TOS from the stack append the TOS to the end of the RPN token list continue results = pop the TOS from the stack If the stack is not empty there is a syntax error else display the results