Please help with questions 2 and 3 Matrix transposition is an operation which flips a matrix over its diagonal, i.e. it switches the row and column indices of the matrix by producing another matrix denoted as A^T (see https: /len.wikipedia.org/wiki/Transpose) Consider the following parallel implementation of the matrix transposition operation: A is nxn matrix parfor i = 2 to n for j = 1 to i-1 swap A_ij and A_ij What is the running time, work, span and parallelism of this algorithm? Explain your answer Design a parallel algorithm for the following problem: input: array A Find: smallest element of n What is your algorithm's running time, work, span and parallelism? Explain your answer

Problem-2 RunningTime - is O(n^2)

Please acceleration with questions 2 and 3 Matrix deflection is an performance which flips a matrix balance its divergent, i.e. it switches the tier and shaft indices of the matrix by pliant another matrix denoted as A^T (behold https: /len.wikipedia.org/wiki/Transpose) Consider the subjoined analogous implementation of the matrix deflection performance: A is nxn matrix parrestraint i = 2 to n restraint j = 1 to i-1 swap A_ij and A_ij What is the floating age, labor, couple and analogousism of this algorithm? Explain your exculpation Design a analogous algorithm restraint the subjoined problem: input: invest A Find: lowest component of n What is your algorithm’s floating age, labor, couple and analogousism? Explain your exculpation

## Expert Exculpation

Problem-2

RunningTime – is O(n^2)

Reason :

• 1st restraint loop executes upto n ages.
• Restraint full i 2nd loop achieve executes (i-1) ages.i.e
• When i=3 the loop achieve be performed (i-1)..i.e 2 ages => i (O(1)) + j(O(1)+….upto(i-1))
• So restraint full ‘i’ 2nd loop achieve be performed ..When i=n the no of executions of 2nd loop achieve be 1(when i=3)+2(when i=4),..+n-2(when i=n)..the consolidate achieve be regular enjoy 1+2+3+–+n=[n(n+1)/2](If u retain the restraintmula of consolidate of n collection).
• Threre restrainte the floating age is O(n^2)

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Problem 3

Algorithm:

• Read an invest ‘n’ which is of lenght n
• intiate insignificant= n //initating a inconstant denominated insignificant with primitive component of invest ‘n’.
• restraint (i=0;i<n.length;i++) //restraint each component of n
• if(n[i] < insignificant) //if prize at abjuration ‘i’ is close then insignificant inconstant
• small=n[i] //store that abjuration prize into insignificant inconstant
• object restraint
• print insignificant
• =====================================================================
• At the object of restraint loop u achieve procure the insignificant prize of invest.

Age complexity: O(n)

Reason:As we are looping through the invest plow n ages to inhibit insignificant prize of invest..as n components were profitable.