(5/5)

# How many time Tukey\'s approach is faster than regular Quick Sort.

INSTRUCTIONS TO CANDIDATES

Tukey's ninther

Tukey proposed an idea (see quick sort lecture slides) to find a better median in random arrays so that quick sort uses less comparisons. It gets approximate median of 9 items from the data array to find a pivot item. This assignment to test if a quick sort initiated with "Tukey's ninther's " is faster than regular quick sort algorithm. You need to compare these two approaches in the sorting of 256K 4-char strings, randomly created between aaaa - ZZZZ. Random strings has only a-z, A-Z letters.

Repeat the comparison 100 times and report

- Average running time in millisecond of Tukey's approach and regular Quick Sort.

- How many time Tukey's approach is faster than regular Quick Sort.

- What is t-value? Assuming run times are normally distributed with same variance, use t-test to compare their normal distributions. Please see https:/ en.wikipedia.org/wiki/Student%27s_t- test#Independent_two-sample_t-test

Your program should report above metrics as output, similar to

Tukey QS Ave: 125 ms, Reg. QS: 129 ms Tukey QS was faster in 51% of 100 runs. T-value for two distributions is 2.26.

Hint: Do not forget to randomize the data; and make sure that both algorithms sorts same data for comparison.

You can see how Tukey's ninther is used in a java implementation here.

Do not include unnecessary headers and functions. Code syntax will be graded.

(5/5)

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