Linear Data Structures LIFO Polish notation Context Saving

Linear Data Structures LIFO – Polish notation Context Saving

Arithmetic Expression Infix: 1+2 x 3+1/2 = ? (1+(2 x 3)+1)/2 (1+(2 x 3))+(1/2) ((1+2)x(3+1))/2 == 4=7. 5 6 Postfix (Polish notation): Let A, B, be operands, ♦ an operator. Instead of A♦B, write AB♦

Arithmetic Expression (2) Example: Infix: ((1+2)x(3+1))/2 Infix: (1+(2 x 3))+(1/2) Postfix: ((1+2)x(3+1))2/ (1+2)(3+1)x 2/ (1+2)31+x 2/ 12+31+x 2/ Postfix: (1+(2 x 3))(1/2)+ (1+(2 x 3))12/+ 1(2 x 3)+12/+ 123 x+12/+

Arithmetic Expression (3) Advantage of Polish Notation: No ambiguity! A-B-C =? (A-B)-C A-(B-C) AB-C- ABC--

Arithmetic Expression (4) But how do we read it? Can the Polish people really understand this? 12+31+x 2/

Arithmetic Expression (5) Algorithm for Computing Postfix Arithmetic Expression: Data Structures: A[1. . n] - a legal arithmetic expression in postfix notation. E - a stack of evaluated parts of the expression. Output: Top of stack.

Arithmetic Expression (6) The Algorithm For i=1 to n do If A[i] is not an operator then PUSH(E, A[i]) else POP(E, X) POP(E, Y) PUSH(E, Y A[i] X) (remember: A[i] is operator) end. For POP(E, Solution)

Arithmetic Expression (7) Example: 12+31+x 2/ operator 1 + 2 =3 2 1 3 ((1+2)x(3+1))/2=6

Arithmetic Expression (7) Example: 12+31+x 2/ operator 3 + 1 =4 1 3 4 3 ((1+2)x(3+1))/2=6

Arithmetic Expression (7) Example: 12+31+x 2/ operator 3 x 4 =12 4 2 12 3 ((1+2)x(3+1))/2=6

Arithmetic Expression (7) Example: 12+31+x 2/ ((1+2)x(3+1))/2=6 6 operator 12 / 2 =6 2 12 6

Arithmetic Expression (8) Exercise: Use LIFO to write a simple algorithm that recognizes whether an input array is a legal arithmetic expression in postfix notation.

Context Saving Telephone switches Then… Now: digital. Huge programs, thousands of lines of code. No loops, no functions.

Context Saving (2) Software: Variable I Loops: Subroutines: A CALL B B CALL C C CALL A

Context Saving (3) Software: Recursive Subroutines: A CALL A Example: Sudoku. Context saving: LIFO.