Given that the efficiency of an algorithm is 5n2 , if a step in this algorithmtakes 1 nanosecond (10–9 seconds), how long does it take the algorithm toprocess an input of size 1000?
Question
Given that the efficiency of an algorithm is 5n2 , if a step in this algorithmtakes 1 nanosecond (10–9 seconds), how long does it take the algorithm toprocess an input of size 1000?
Solution
To determine how long it takes for the algorithm to process an input of size 1000, we need to calculate the time complexity of the algorithm.
The given efficiency of the algorithm is 5n^2, where n represents the input size. In this case, n = 1000.
Substituting the value of n into the efficiency equation, we get:
Efficiency = 5 * (1000)^2 = 5 * 1000000 = 5000000
Since each step in the algorithm takes 1 nanosecond (10^-9 seconds), we can calculate the total time taken by multiplying the efficiency by the time per step:
Total time = Efficiency * Time per step = 5000000 * 10^-9 = 5 seconds
Therefore, it takes the algorithm 5 seconds to process an input of size 1000.
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