Microprocessor and Assembly Language Lecture-15-Recursion Muhammad Hafeez Department of Computer Science GC University Lahore

Today’s Agenda Recursion Theory in Assembly Implementation in 8086 Environment

Recursion A process is recursive if its defined in terms of itself Main Characteristics of a recursive process The Main Problem is break down to simpler problem, each of these simpler problem are solved exactly the way, main problem is solved There must be an escape case One sub problem is solved, proceed to next step of solving main problem

Example: Factorial Non-recursive way Factorial (N) = N x (N-1) x (N-2)x…x3x2x1 Recursive Way: Factorial (N) = N x Factorial (N-1)

Algorithm for Factorial: PROCEDURE FACTORIAL (INPUT:N, OUTPUT: RESULT) IF N =1 THEN RESULT=1 ELSE CALL FACTORIAL(INPUT:N-1, OUTPUT:RESULT) RESULT = N X RESULT END_IF RETURN

Algorithm for Find Max in An Array: If N = 1 then largest entry is A[1], else largest entry is either A[N] or largest of A[1] …A [N-1] PROCEDURE FIND_MAX(INPUT:N, OUPUT:MAX) IF N = 1 THEN MAX = A[1] ELSE CALL FIND_MAX(N-1,MAX) IF A[N] > MAX THEN MAX = A[N] MAX = MAX END_IF RETURN

Revision-Passing Parameters to Procedure on the Stack Write a procedure that adds two words and return the result in AX Pass words to procedure using Stack

The Activation Record Each new call to a recursive procedure require the parameters and local variables to be reinitialized for that particular call When the call is completed the procedure resumes the previous call, on the point it left off. Hence, the procedure needs to ‘remember’ the point, the parameters and local values of the previous call, this is called ‘the activation record’

Example: Activation Record First Call Activation Record 2nd Call

Example: Activation Record First Call Suppose, 3rd call is the escape case, result of this call is computed and stored in a register or memory location to be available to 2nd call and so on..

Implementation of Factorial using Recursion: MODEL SMALL .STACK 100H .CODE MAIN PROC MOV AX,3 ;N = 3 PUSH AX ;N on stack CALL FACTORIAL ;AX has 3 factorial MOV AH,4CH INT 21H ;dos return MAIN ENDP

Implementation of Factorial using Recursion: FACTORIAL PROC NEAR ; computes N factorial ; input: stack on entry - ret. addr.(top), N ; output: AX PUSH BP ;save BP MOV BP,SP ;BP pts to stacktop ;if CMP WORD PTR[BP+4],1 ;N = 1? JG END_IF ;no , N>1 ;then MOV AX,1 ;result = 1 JMP RETURN ;to to return END_IF: MOV CX,[BP+4] ;get N DEC CX ;N-1 PUSH CX ;save on stack CALL FACTORIAL ;recursive call MUL WORD PTR[BP+4] ;RESULT = N*RESULT RETURN: POP BP ;restore BP RET 2 ;return and discard N FACTORIAL ENDP END MAIN