WBJECA 2025 — Computer PYQ

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Question

WBJECA 2025 — Computer PYQ

WBJECA | Computer | 2025

A machine needs a minimum of 100 seconds to sort 1000 names by quick sort. The minimum time needed to sort 100 names will be approximately

Choose the correct answer:

Explanation

The average-case time complexity of the Quick Sort algorithm is $O (n lo g n)$ . To find the approximate time for a different number of elements, we can use the ratio of the complexities.

Let $T_{1}$ be the time for $n_{1}$ elements and $T_{2}$ be the time for $n_{2}$ elements. The relationship is proportional to $n lo g n$ :

$\frac{T _{1}}{T _{2}} \approx \frac{n _{1} lo g n _{1}}{n _{2} lo g n _{2}}$

Given data:

$n_{1} = 1000$ , $T_{1} = 100$ seconds
$n_{2} = 100$

Calculation:

Substituting the values into the equation:

$\frac{100}{T _{2}} \approx \frac{1000 lo g _{10} 1000}{100 lo g _{10} 100}$

$\frac{100}{T _{2}} \approx \frac{1000 \times 3}{100 \times 2}$

$\frac{100}{T _{2}} \approx \frac{3000}{200} = 15$

$T_{2} \approx \frac{100}{15} \approx 6.66 seconds$

Rounding to the nearest provided option, we get approximately 6.7 seconds.

Correct Option: (A) 6.7 seconds