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Right option is (a) true

The best EXPLANATION: If the first element of an array is 0 then it is not POSSIBLE to reach the END. HOWEVER, if 0 is present at other POSITIONS then we may/may not be able to reach the end.

The CORRECT answer is (d) 4

The best I can explain: There are 4 possible ways in which we can REACH the END of the array. The possible paths are – 1->3->5->8->9, 1->3->5->9, 1->3->8->9, 1->3->9.

Right answer is (B) false

Easy EXPLANATION - It is possible to find the minimum number of steps to REACH the end of an ARRAY in O(N) time complexity. So it is the fastest possible method of finding the minimum number of steps to reach the end of an array.

Correct answer is (d) not possible to reach the END

Best explanation: Each element of the ARRAY represents the maximum NUMBER of steps that can be taken forward from that element. So we cannot move any further after reaching the second element HENCE it is impossible to reach the end of the array.

Right ANSWER is (d) not possible to reach the end

Easy explanation - Each ELEMENT of the array REPRESENTS the maximum number of STEPS that can be taken forward from that element. So as the first element here is 0 so we cannot MOVE any further from the first element. Thus, it is not possible to reach the end of the array.

Right answer is (d) ALGORITHM

Explanation: The predefined function for reversing an array is reverse() in C++ which comes under the library called an algorithm. It requires 2 ARGUMENTS the first being the POINTER to the STARTING INDEX of the array and the second being the pointer to the last index of the array.

Right answer is (a) REVERSE()

EASY EXPLANATION - The predefined function for REVERSING an array is reverse() in javascript. It does not requires any argument.

Right option is (a) reverse()

For EXPLANATION: The PREDEFINED FUNCTION for reversing an array is reverse() in C++. It is defined under the library ALGORITHM and requires 2 arguments.

The correct choice is (B) false

Explanation: Array ROTATION and array REVERSAL are different operations and thus they GIVE different outputs when applied to the same array.

The correct choice is (a) (n-1) / 2

The BEST I can explain: The number of swaps REQUIRED for an odd element and an even element ARRAY is different because in an odd element array the position of the middle element does not need to be changed. So the number of swaps will be (n-1) / 2.

The correct answer is (d) 2,4,5,3

Easy explanation - The resulting ARRAY UPON REVERSING after reversal is ARR[]={2,4,5,3}. We can implement an algorithm for this PURPOSE in various possible ways.

The correct choice is (a) True

The best explanation: Time complexity of JUGGLING algorithm is O(n) which LIKE that of reversal algorithm. They ALSO have the same SPACE complexity.

The CORRECT answer is (b) O(n)

Easy explanation - TIME complexity of JUGGLING ALGORITHM is O(n). Its auxiliary space complexity is O(1).

Right ANSWER is (a) rotate elements one by one

To explain: The MAXIMUM time complexity is REQUIRED by the algorithm that rotates elements one by one. It REQUIRES O(n*d) time.

The CORRECT ANSWER is (d) algorithm

Easy explanation - The predefined function for rotating an array is rotate() in C++ which comes under the LIBRARY called algorithm. It requires 3 ARGUMENTS the first being the pointer to the starting index of the array and the last being the pointer to the last index of the array. The MIDDLE argument is the pointer to the element that becomes the first element in the rotated array.

The correct OPTION is (c) 3

To explain: The predefined function for ROTATING an array is rotate() in C++ which comes under the LIBRARY called an algorithm. It requires 3 ARGUMENTS.

Right option is (a) ROTATE()

To EXPLAIN: The predefined function for rotating an array is rotate() in C++. It is defined under the LIBRARY ALGORITHM and requires 3 arguments.

The CORRECT answer is (a) true

The best I can explain: The auxiliary space requirement of the mentioned algorithm is O(1). So it QUALIFIES to be an in PLACE algorithm.

Correct OPTION is (b) 3, 4, 5, 1, 2

To explain: When the given ARRAY is ROTATED by 2 then the resulting array will be

Rotation 1: {2,3,4,5,1}

Rotation 2: {3,4,5,1,2}.

THUS, the final array is {3,4,5,1,2}.

Right ANSWER is (a) O(n)

Best EXPLANATION: The SPACE complexity required by the code will be O(n). It is the same as the space complexity of the code of standard MERGE sort.

Right choice is (a) true

The EXPLANATION is: The TIME complexity of the CODE that determines the number of inversions in an array using self balancing BST is O(n log n) which is lesser than the time complexity taken by the code that USES loops.

Right answer is (d) O(n log n)

Easiest EXPLANATION - When a self BALANCING BST LIKE an AVL tree is USED to calculate the number of inversions in an array then the time complexity is O(n log n) as AVL insert takes O(log n) time.

Right ANSWER is (d) O(n log n)

Explanation: The CODE of MERGE sort is slightly modified in order to calculate the number of inversions in an array. So the TIME complexity of merge sort remains unaffected and hence the time complexity is O(n log n).

The CORRECT choice is (a) true

The best explanation: The time complexity of the CODE that determines the number of inversions in an array using merge SORT is O(n LOG n) which is LESSER than the time complexity taken by the code that uses loops.

Correct choice is (d) arr[i] > arr[J] and i < j

The explanation is: For two elements to form an inversion the necessary condition is arr[i] > arr[j] and i < j. The NUMBER of inversions in an ARRAY indicate how CLOSE or far the array is from being completely sorted.

The correct option is (a) 0

For EXPLANATION: When an ARRAY is sorted then there cannot be any inversion in the array. As the NECESSARY condition for an inversion is arr[i]>arr[j] and i

Correct choice is (b) measure of how CLOSE or far the array is from being SORTED

For EXPLANATION: The number of inversions in an array INDICATES how close or far the array is from being completely sorted. The array is sorted if the number of inversions are 0.

The correct CHOICE is (b) False

Easiest explanation - Sparse Matrix is a matrix with most of the ELEMENTS as ZERO elements while DENSE Matrix is a matrix with most of the elements as Non-Zero element.

The correct choice is (d) Heap

Easy explanation - Heap is not used to represent SPARSE Matrix while in Dictionary, rows and column numbers are used as Keys and values as Matrix entries, Linked List is used with each node of Four fields (Row, Column, Value, NEXT Node) (2D array is used to represent the Sparse Matrix with THREE fields (Row, Column, Value).

Correct answer is (a) Total NUMBER of Zero elements > (m*N)/2

For explanation: For MATRIX to be SPARSE Matrix, it should contain Zero elements more than the non-zero elements. Total elements of the given matrix is m*n. So if Total number of Zero elements > (m*n)/2, then the matrix is called Sparse Matrix.

The correct choice is (a) True

To EXPLAIN: In ADDITION, the matrix is traversed linearly, hence it has the time COMPLEXITY of O(n) where n is the NUMBER of non-zero elements in the largest matrix amongst two.

Correct answer is (a) HARRY Markowitz

Best EXPLANATION: Harry Markowitz coined the term SPARSE Matrix. James Sylvester coined the term Matrix. Chris Messina coined the term Hashtag and Arthur CAYLEY DEVELOPED the algebraic aspects of a matrix.

Correct choice is (a) Sparsity = 1 – DENSITY

The best explanation: Sparsity of a matrix is EQUAL to 1 minus Density of the matrix. The Sparsity of matrix is defined as the TOTAL NUMBER of Zero VALUED elements divided total number of elements.

Right choice is (c) SPARSE Matrix

To EXPLAIN: Sparse Matrix is a matrix in which most of the elements are ZERO. Identity Matrix is a matrix in which all principle DIAGONAL elements are 1 and REST of the elements are Zero. Unit Matrix is also called Identity Matrix. Zero Matrix is a matrix in which all the elements are Zero.

Right option is (b) INVERSE of A

Explanation: Any square matrix when MULTIPLIED with its inverse GIVES the identity matrix. Note that non square matrices are not INVERTIBLE.

Right option is (d) Graph Plotting

To explain: Adjacency and Incidence MATRICES are used to STORE VERTICES and EDGES of a graph. It is an advantage to plot graphs easily using matrices. But Time complexity of a matrix is O(n^2) and sometimes the internal organization BECOMES tedious. They are all disadvantages of matrices.

The correct ANSWER is (d) Sorting numbers

Best explanation: Numbers uses ARRAYS(1-D) for sorting not matrices(2-D arrays). Solving linear equations is a separate field in Mathematics involving matrices, IMAGE processing stores the PIXELS in the form of matrices, and the graphs are represented with the help of matrices to indicate the nodes and EDGES.

Right option is (d) O(mlogn)

EXPLANATION: Suffix arrays are used to FIND the occurrences of a pattern in a STRING. Pattern of length m will require m characters to compare, so USING suffix array we can find occurrences of a pattern in the string of length n in O(mlogn) time.

Correct option is (c) SUFFIX ARRAY

Explanation: Suffix tree can be CREATED using an LCP array and a suffix array. If we are GIVEN a string of length (n + 1) and its suffix array and LCP array, we can construct the suffix tree in linear time i.e in O(n) time.

The correct CHOICE is (d) 5 0 6 10 2 3 8 4 9 1 7

To EXPLAIN: Correct choice is : 5 0 6 10 2 3 8 4 9 1 7.

Because the suffix array formed will be: 5 eering 0 engineering 6 ering 10 G 2 gineering 3 ineering 8 ing 4 neering 9 ng 1 ngineering 7 ring.

Correct choice is (c) O(n^2logn)

Easy explanation - On average COMPARISON BASED sorting algorithms require O(NLOGN) comparisons. But comparing a suffix TAKES O(n). So, overall TIME to construct the suffix array will be O(nlogn) * O(n) = O(n^2logn).

Right CHOICE is (b) Fasle

Explanation: Suffix ARRAYS are more space efficient than the suffix trees as they just store the original STRING and an array of INTEGER. But working with suffix tree is FASTER than that of the suffix array.

Right answer is (c) depth-first

Best explanation: A suffix tree is a trie, which CONTAINS all the suffixes of the GIVEN STRING as their keys and POSITIONS in the string as their values. So, we can construct a suffix array by performing the depth-first traversal of a suffix tree.