Suppose one has matrix

The problem is to find number e if two pairs of numbers (a,b,c,d) is given (using only simple arithmetic operations (+, -, /, *)(brackets are allowed)).

For two given matrices

,

Find e using only simple arithmetic operations (+, -, /, *) (brackets are allowed).

e = 106 (one can run MathPuzzle.sql to check this cd - ab).

1. Generate all possible combination of 4 letters expressions (using reverse polish notation).
2. Replace 4 letters with given numbers.
3. Use Dijkstra's Two-Stack Algorithm to calculate the final value.
4. Find solution to the problem by SQL query.

1. Stack.typ is ordinary stack structure implimented in PL/SQL.
2. MathPuzzle.pck this file contains declaration and body which allow to solve current problem

• function is_operand(x varchar2) return boolean
  Function returns True if current element of the string is operand
• function get_infix_from_postfix(string_ varchar2) return varchar2
  Function return infix notation from postfix
  723*- --> 7 - 2*3.
• function can_add_operator(string_ varchar2) return boolean
  The function returns True if we can add operator to current expression:
  we scan the list and add +1 to counter when we meet a letter
  and we add -1 when we meet an operator (it reduces
  last two letters into 1 (say ab+ <--> a + b)
• function concat (ilist1 as_array, ilist2 as_array) return as_array
  Function returns two concatinated collections
• function possible_elements(items as_array, string_ varchar2) return as_array
  The function returns a list, that contains operators and
  letters, one of which we can add to the current expression.
• procedure rec(exp varchar2)
  Main procedure that generates all possible 4 letters expressions and writes them into table.
• function calculator (in_string varchar2 default '(1+((2+3)(45)))') return number
  Function returns evaluation of expression using Dijkstra's Two-Stack Algorithm
• function substitute_letter_to_numbers(in_str varchar2, a number, b number,c number, d number) return varchar2
  Function returns numerical expression
  (((b+a)*c)+d) --> (((1+2)*3)+4) if a=1, b=2, c=3, d=4

3. MathPuzzle.sql is the example of usage

1. Run Stack.typ
2. Run MathPuzzle.pck
3. Run "begin MathPuzzle.rec(''); end;" to fill main table
4. One can run queries agains filled table rpn_combinations