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If the efficiency of the algorithm doIt can be expressed as O(n) = n2 , cal-culate the efficiency of the following program segment:for (i = 1; i <= n;; i++)for (j = 1; j < n, j++)doIt (...)

Question

If the efficiency of the algorithm doIt can be expressed as O(n) = n2 , cal-culate the efficiency of the following program segment:for (i = 1; i <= n;; i++)for (j = 1; j < n, j++)doIt (...)

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Solution

To calculate the efficiency of the given program segment, we need to analyze the nested loops and the function call to "doIt()".

  1. The outer loop runs from i = 1 to i <= n. This loop iterates n times.

  2. Inside the outer loop, there is another nested loop that runs from j = 1 to j < n. This loop also iterates n times.

  3. Within the nested loop, there is a function call to "doIt()". The time complexity of this function is given as O(n) = n^2.

Now, let's calculate the overall efficiency of the program segment:

  • The outer loop runs n times.
  • The nested loop runs n times for each iteration of the outer loop.
  • The function "doIt()" is called n^2 times in total.

Therefore, the overall efficiency of the program segment can be expressed as O(n) = n * n * n^2 = n^4.

So, the efficiency of the given program segment is O(n) = n^4.

This problem has been solved

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