Question

Determine the runtime complexity of the following. Use O() notation, but the function that you place within the parentheses of O() should be the upper bound on the runtime of the algorithm or function. Unless otherwise specified, N is the problem size or the number of elements in the container (even if N does not appear in the code or algorithm you are given), and all other values are constants.

For graphs, use |V| and |E| for the size of the graph/problem. For the code segments, you should assume that all variables and functions exist and are defined appropriately to make the code work properly. And that’s always the case with algorithms.

a) for (i=0; i for (j=0; j matrix[i][j] = 0.0;

b) for (i=N; i>0; i/=3)
cout << i << endl;

c) HALVE-ME(i) {
if (i == 0) return;
HALVE-ME(i/2);
}

Answer 1

7,576 answers

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

1)

Since it has 2 nested loops both over n. So, the big time complexity is O(n^2)

2)

Since at every iteration it is dividing i by 3. So, total iterations will be log3(n). o, it is O(log(n))

3)

Recurrence of it is

T(n)=T(n/2)+1

So, it is also O(log(n))

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