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Natasha_Volkova [10]
3 years ago
12

) Suppose algorithm A takes 10 seconds to handle a data set of 1000 records. Suppose the algorithm A is of complexity O(n2). Ans

wer the following: (i) Approximately how long will it take to handle a data set of 1500 records? Why? (ii) How long will it take to handle a data set of 5000 records? Can you come up with a reason why this will not be entirely accurate but will just be an approximation?
Computers and Technology
1 answer:
Mice21 [21]3 years ago
8 0

Answer:

i) The time taken for 1500 records = 15 seconds.

ii) The time taken for 1500 records = 50 seconds.

Explanation:

A is an O(n) algorithm.

An algorithm with O(n) efficiency is described as a linearly increasing algorithm, this mean that the rate at which the input increases is linear to the time needed to compute that algorithm with n inputs.

From the question, it is given that for 1000 records, the time required is: 10 seconds.

Algorithm time taken is O(n)

Hence,

1) For 1,500 records

=> 10/1000 = x/1500

=> 10x1500/1000 = x

x = 15 seconds

Thus, the time taken for 1500 records = 15 seconds.

2) For 5,000 records

=> 10/1000 = x/5000

=> 10x5000/1000 = x

x = 50 seconds

Thus, the time taken for 1500 records = 50 seconds.

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Answer:

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Explanation:

1) To answer that, you should have to know The Rouché-Capelli Theorem. This theorem establishes a connection between how a linear system behaves and the ranks of its coefficient matrix (A) and its counterpart the augmented matrix.

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rank(A)

Then the system is consistent and has a unique solution.

<em>E.g.</em>

\left\{\begin{matrix}x-3y-2z=6 \\ 2x-4y-3z=8 \\ -3x+6y+8z=-5  \end{matrix}\right.

2) Writing it as Linear system

A=\begin{pmatrix}1 & -3 &-2 \\  2& -4 &-3 \\ -3 &6  &8 \end{pmatrix} B=\begin{pmatrix}6\\ 8\\ 5\end{pmatrix}

rank(A) =\left(\begin{matrix}7 & 0 & 0 \\0 & 7 & 0 \\0 & 0 & 7\end{matrix}\right)=3

3) The Rank (A) is 3 found through Gauss elimination

(A|B)=\begin{pmatrix}1 & -3 &-2  &6 \\  2& -4 &-3  &8 \\  -3&6  &8  &-5 \end{pmatrix}

rank(A|B)=\left(\begin{matrix}1 & -3 & -2 \\0 & 2 & 1 \\0 & 0 & \frac{7}{2}\end{matrix}\right)=3

4) The rank of (A|B) is also equal to 3, found through Gauss elimination:

So this linear system is consistent and has a unique solution.

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