r3 - type Int_Array is array (Integer range...

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Recitation R3 Response to 'Muddiest Part of the Recitation Cards' (10 respondents) 1) When do we need all the log identities in finding Big-O ? You don’t need all of the log identities at all times. You have to pick and choose the required identity in order to solve/ simplify the recurrence equation. For example, when you have to find the base case, you use n = 2 k , then you can represent k as log 2 n 2) In algorithm classes, do they prove similar forms to the master method for different recurrence equations? Is that the non-simplified master-method ? What we looked at in class is the solution to recurrence equations of the form: T(n) = aT(n/b) + cn k The form that you will see in algorithm classes, treats the second term in the right hand side to be generic i.e. T(n) = aT(n/b) + f(n) In this case, the master theorem appears as shown below: 3) Why cannot I from example 2 be expressed in terms of N ? Example 2, uses the following code snippet
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Unformatted text preview: type Int_Array is array (Integer range <>) of Integer; procedure Measure (A : Int_Array ) is Sum : Integer := 0; begin for I in A'range loop for J in 1 . . I loop - only change to Ex 1 Sum := Sum + A(J); end loop ; end loop ; end Measure; The I value in the outer loop changes in every iteration with a maximum value of n. It cannot be expressed as a simple function in n. 4) Still muddy about coming up with T(n) equations from recurrence problems. Specifically unclear on how to solve for O(n) w/o Master method . When you are not using the master method, use iteration (Lecture 13 last semester) to solve the recurrence equation. If the T(n) is a homogeneous function in n (all the terms are functions of n), then find the most significant term to determine the Big-O. See examples in both the Recitation 3 and Lecture 9 slides. 6) No mud, cool stuff, good lecture (6 students)...
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r3 - type Int_Array is array (Integer range...

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