Let f(n) be the number of comparisons required to sort a list of n numbers in no

Question

Let f(n) be the number of comparisons required to sort a list of n numbers in nondecreasing order. a) obtain a recursive relation expressing f(n) in terms of f(n-1) with appropriate initial condition.
b) obtain a recursive relation that expresses f(n) in terms of f(n/2) with appropriate initial condition.
c) solve these two recurrence relations and compare the efficency of the two algorithms involved. Let f(n) be the number of comparisons required to sort a list of n numbers in nondecreasing order. a) obtain a recursive relation expressing f(n) in terms of f(n-1) with appropriate initial condition.
b) obtain a recursive relation that expresses f(n) in terms of f(n/2) with appropriate initial condition.
c) solve these two recurrence relations and compare the efficency of the two algorithms involved. a) obtain a recursive relation expressing f(n) in terms of f(n-1) with appropriate initial condition.
b) obtain a recursive relation that expresses f(n) in terms of f(n/2) with appropriate initial condition.
c) solve these two recurrence relations and compare the efficency of the two algorithms involved.

Explanation / Answer

Ans-

o perform an elementary column operation on A, an r x c matrix, take the following steps.

Let's work through an elementary column operation to illustrate the process. For example, suppose we want to interchange the first and second columns of A, a 3 x 2 matrix. To create the elementary column operator E, we interchange the first and second columns of the identity matrix I2.

Then, to interchange the first and second columns of A, we postmultiply A by E, as shown below.

Note that the process for performing an elementary column operation on an r x c matrix is very similar to the process for performing an elementary row operation. The main differences are:

Test Your Understanding

1 0 0 1        0 1 1 0 I2 E

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