# ISRO | ISRO CS 2018 | Question 24

An array A consists of n integers in locations A[0], A[1] ….A[n-1]. It is required to shift the elements of the array cyclically to the left by k places, where 1 <= k <= (n-1). An incomplete algorithm for doing this in linear time, without using another array is given below. Complete the algorithm by filling in the blanks. Assume alt the variables are suitably declared.

## C++

 `min = n; i = 0;` `while` `(___________) {   ` `     ``temp = A[i]; j = i;` `     ``while` `(________) {` `     ``A[j] = ________    ` `     ``j= (j + k) mod n ;` `     ``If ( j< min ) then` `         ``min = j;` `}` `A[(n + i â€” k) mod n] = _________` `i = __________`

(A)

i > min; j!= (n+i)mod n; A[j + k]; temp; i + 1 ;

(B)

i < min; j!= (n+i)mod n; A[j + k]; temp; i + 1;

(C)

i > min; j!= (n+i+k)mod n; A[(j + k)]; temp; i + 1;

(D)

i < min; j!= (n+i-k)mod n; A[(j + k)mod n]; temp; i + 1;

Explanation:

In the five blanks given in the question, the last two blanks must be temp and i+1 because all the given options for the fourth and fifth blanks have temp and i+1. Now, for the first blank, it must be imin then the control goes out of the while loop in the initial case when i=0 and min=n So, the first blank is i < min which implies either option (B) or option (D) is correct. Assume option (B) is correct then in the bracket of while we have j!=(n+i)modn That means whenever j becomes equal to (n+i)modn then control goes out of the while loop. Now (n+i)modn=i and j is always equal to i because in line 3 of the code we are assigning the value of i to j. So, if option (B) is true control never enters the second while loop but it has to enter the second while loop to shift the nos. K places left. Hence, option (D) is correct.

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