question C.... explain please and write it in a paragraph format if possible. Ou
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question C.... explain please and write it in a paragraph format if possible.
Outlook Print MAT 2540 - Writing Assignment 1 For each of the items below, write a paragraph addressing each question. (a) Suppose that you step into an elevator at City Tech. There are 7 people in the elevator (including you) and 3 different buttons have been pushed. What is the largest number of people that you can guarantee will exit the elevator at one of the 3 floors selected? Explain. (b) Explain why 1 +2+3+ (n-1)+n O(n). (c) Describe an algorithm, and write the pseudocode, that computes the Lucas numbers. (See problem 11 in section 8.2). pe here to search DOLLExplanation / Answer
Answers of the questions (3 Parts):
(a)
In the elevator there are 7 people (including me). Since 3 buttons are pressed so on each of these floors one or more person will get down. Taking the minumum of 2 floors as one, it is aparent that 2 person will get down on these two floors.
Therfore reamining will be 5 which will get on the third. This means a maximum of 5 people will get down on any floor in this condition.
Assumption: if the button is pressed means at least one will get down. This is not done by misatke.
(b)
The series is
1+2+3+…………….. +(n-1)+n
By Gauss method this is equal to n(n+1)/2
Converting this into Big O notation O((n^2+n)/2) which will give you O(n^2) time compelxity for doing this calculation.
Normally this is implemneted using for loop as
For (i=0;i<n;i++){
For (j=i+1;j<N;j++
Statement;
}
}
which will be excuted in O(n^2) complexity.
(c)
Edward lucas who gave the Fibonacci series has also provided another series called lucas numbers. This is like this
2 1 3 4 7 11 18. . . . . . . . .
The Fibonacci series is 0 1 1 2 3 5 8 13 . . . . . .
From the analysis of these two series it is apaent that Lucas numbers are just like Fibonacci series except that starting numbers in Lucas numbers are 2 and 1.
Repsenting Lucas numner n
L(n)=(L(n-1)+L(n-2) with initial L1=2 an L2=1
Pseudo Code:
START
Read No of Lucas Number (n)
Iniatialize L1=2
L2=1
Write L1 and L2
Repeat n-2 times ( from 3 to n){
L(n)=L(n-2)+L(n-1)
Write L(n)
}
STOP.
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