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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
  • a)
    Ω(n2)
  • b)
    Ω(nlog n) and O(n2)
  • c)
    θ(n)
  • d)
    O(n)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let A[1, ..., n] be an array storing a bit (1 or 0) at each location, ...
Please note that inside the else condition, f() is called first, then counter is set to 0. Consider the following cases:
a) All 1s in A[]: Time taken is Θ(n) as only counter++ is executed n times.
b) All 0s in A[]: Time taken is Θ(n) as only f(0) is called n times
c) Half 1s, then half 0s: Time taken is  Θ(n) as only f(n/2) is called once.
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Most Upvoted Answer
Let A[1, ..., n] be an array storing a bit (1 or 0) at each location, ...
Please note that inside the else condition, f() is called first, then counter is set to 0. Consider the following cases:
a) All 1s in A[]: Time taken is Θ(n) as only counter++ is executed n times.
b) All 0s in A[]: Time taken is Θ(n) as only f(0) is called n times
c) Half 1s, then half 0s: Time taken is  Θ(n) as only f(n/2) is called once.
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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)Ω(n2)b)Ω(nlog n) and O(n2)c)θ(n)d)O(n)Correct answer is option 'C'. Can you explain this answer?
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