Let A[1, n] be an array storing a bit (1 or 0) at each location, and f(m) is a function whose time complexity is (m). Consider the following program fragment written in a C like language:counter = 0;for (i=1; i=n; i++){ if a[i] == 1) counter++;else {f (counter);counter = 0;}}The complexity of this program fragment isa)b)c)d)Correct answer is option 'C'. Can you explain this answer? - EduRev Computer Science Engineering (CSE) Question

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Let A[1, …n] be an array storing a bit (1 or 0) at each location, and f(m) is a function whose time complexity is θ(m). Consider the following program fragment written in a C like language:

counter = 0;

for (i=1; i<=n; i++)

{ if a[i] == 1) counter++;

else {f (counter);

counter = 0;}

}

The complexity of this program fragment is

Correct answer is option 'C'. Can you explain this answer?

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Let A[1, …n] be an array storing a bit (1 or 0) at each location...

The key part in the code is "counter = 0" in the else part as we can see below.

Lets take the best case. This happens when

for all i,and then the loop executes with time complexity θ(1) for each iteration and hence overall time complexity of θ(n) and we can say time complexity of the code fragment is Ω(n) and hence options a and b are false.

Now, consider the worst case. This happens when a[i] = 0 or when else part is executed. Here, the time complexity of each iteration will be θ(Counter) and after each else, counter is reset to 0. Let k iterations go to the else part during the worst case. Then the worst case time complexity will be

where X_i is the value of the counter when,

is called. But due to Counter =0after each call to f(), we have,

Since the time complexity is

we can say it is θ(n) Option (C). (Option D is false because the small o
needs the growth rate to be STRICTLY lower and not equal to or lower as the case for big 0)

IF Counter = 0was not there in else part, then time complexity would be

as in worst case we can have equal number of 0's and 1's in array a giving time complexity

would give

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Let A[1, …n] be an array storing a bit (1 or 0) at each location, and f(m) is a function whose time complexity is θ(m). Consider the following program fragment written in a C like language:counter = 0;for (i=1; i<=n; i++){ if a[i] == 1) counter++;else {f (counter);counter = 0;}}The complexity of this program fragment isa)b)c)d)Correct answer is option 'C'. Can you explain this answer?

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