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 (...)
Solution
To calculate the efficiency of the given program segment, we need to analyze the nested loops and the function call to "doIt()".
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The outer loop runs from i = 1 to i <= n. This loop iterates n times.
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Inside the outer loop, there is another nested loop that runs from j = 1 to j < n. This loop also iterates n times.
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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.
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