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# GATE CS 2022 : Algorithm -1

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Question 1

The recurrence equation
T (1) = 1
T (n) = 2T (n–1) + n, n 2
evaluates to

Question 2

Match the following:
List - I
(P) Prim’s algorithm for minimum spanning tree
(Q) Floyd-Warshall algorithm for all pairs shortest paths
(R) Mergesort
(S) Hamiltonian circuit
List - II
(i) Backtracking
(ii) Greedy method
(iii) Dynamic programming
(iv) Divide and conquer

Question 3

Match List-I with List-II and select the correct answer using the codes given below the lists: Question 4

Consider an array A in which upto some index I , integers are stored which is sorted  and after that NULL values are stored. Let the size of array be n, then the time taken to find the value of I is :

Question 5

Consider an array with 12 elements as : 9 , 11 , 7 , 8 , 2 , 4 , 20 , 22 , 30 , 6 , 50 , 32 with same order as written. Partition algorithm is applied separately 3 times on the array with 3 different pivots. The first time pivot was 11 , second time was 22 and third time was 32. The number of elements to left of pivot be x, y and z in three cases respectively. Find the value of |x+2y+3z| ____________.

Question 6

In case of quicksort best case, 45 seconds is taken by input size 128 to run. In 4 minutes what size of input can be sorted (In nearest Power of 2)?
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