GATE CS 1997

Shared Data
mutex:semaphore = 1:/* initialized to 1*/
process[3]:semaphore = 0; /*all initialized to 0 */
R_requested [3]:boolean = false; /*all initialized to false */
busy: boolean = false; /*initialized to false */

Code for processes
begin process
my-priority:integer;
my-priority:=____; /*in the range 1...3*/
repeat
    request_R(my-priority);
    P (proceed [my-priority]);
    {use shared resource R}
    release_R (my-priority);
forever
end process;

Procedures
procedure request_R(priority);
P(mutex);
if busy = true then
    R_requested [priority]:=true;
else
 begin
    V(proceed [priority]);
    busy:=true;
 end
V(mutex);

A priority queue Q is used to implement a stack S that stores characters. PUSH(C) is implemented as INSERT(Q, C, K) where K is an appropriate integer key chosen by the implementation. POP is implemented as DELETEMIN(Q). For a sequence of operations, the keys chosen are in

[5-Marks question] Consider a graph whose vertices are points in the plane with integer co-ordinates (x,y) such that 1≤x≤n and 1≤y≤n, where n≥2 is an integer. Two vertices (x1,y1) and (x2,y2) are adjacent iff ∣ x1−x2 ∣ ≤ 1 and ∣ y1–y2 ∣ ≤1. The weight of an edge {(x1,y1),(x2,y2)} is √_{(x1–x2)²+(y1–y2)²}  a.  What is the weight of a minimum weight-spanning tree in this graph? Write only the answer without any explanations. b.  What is the weight of a maximum weight-spanning tree in this graph? Write only the answer without any explanations.

(A) All pairs shortest path          (1) Greedy
(B) Quick Sort                       (2) Depth-First search
(C) Minimum weight spanning tree     (3) Dynamic Programming
(D) Connected Components             (4) Divide and and Conquer

Codes:
     A    B    C    D 
a    2    4    1    3
b    3    4    1    2
c    3    4    2    1
d    4    1    2    3

An array A contains n≥1 positive integers in the locations A[1], A[2],... A[n]. The following program fragment prints the length of a shortest sequence of consecutive elements of A, A[i], A[i+1],...A[j] such that the sum of their values is ≥M, a given positive number. It prints ‘n+1’ if no such sequence exists. Complete the program by filling in the boxes. In each case use the simplest possible expression. Write only the line number and the contents of the box.

type list = record
next:↑ list; val: integer   end

program what:
    var z: integer
    procedure recur(x):
    begin if x <= 40 then
        begin x:x+z
            recur(x);
            z:=x+10
        end
    end(*recur*)
begin(*what*)
    z=10;
    recur(z);
    writeln(z)
end