Homework Answers
A min-heap is a binary tree such that - the data contained in each node is less than (or equal to) the data in that node’s children. - the binary tree is complete A max-heap is a binary tree such that - the data contained in each node is greater than (or equal to) the data in that node’s children. - the binary tree is complete
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Assuming that finding the minimum value in an array of length n takes Ohm(n) time, prove...
Write a function named stats, that takes an array and the number of elements in the...
Write a function named stats, that takes an array and the number of elements in the array as arguments. It must compute and print the minimum value in the array, maximum value in the array and the average value of all the values inside the array. Your function MUST be named stats Your function has two parameters in the following order: an array of type double The number of elements in the array, type int Your function should NOT return...
Assume L is an array, length(L) returns the number of records in the array, and qsort(L,i,j)...
Assume L is an array, length(L) returns the number of records in the array, and qsort(L,i,j) sorts the records of L from i toj (leaving the records sorted in L) using the Quicksort algorithm. What is the average-case complexity for the following code fragment? for (i = @; i<length(L); i++) asort(1, 0, 1); Consider the time for each pass of the for loop, and sum them all together. Prove the upper and lower bound, then argue for an average case....
vas Х Assume Lis an array, length(L) returns the number of records in the array, and...
vas Х Assume Lis an array, length(L) returns the number of records in the array, and qsort(L. 1.j) sorts the records of Lfrom itoj (leaving the records sorted in L) using the Quicksort algorithm. What is the average-case complexity for the following code fragment? for (i = 0; i<length(); i++) asort(1, 0, 1); Consider the time for each pass of the for loop, and sum them all together. Prove the upper and lower bound, then argue for an average case....
C++ Question 14 10 Assume Lis an array, length(L) returns the number of records in the...
C++
Question 14 10 Assume Lis an array, length(L) returns the number of records in the array, and qsort(L, 1. j) sorts the records of L from i toj (leaving the records sorted in L) using the Quicksort algorithm. What is the average-case complexity for the following code fragment? for (i = 0; i<length(); i++) asort(L, 0, 1); Consider the time for each pass of the for loop, and sum them all together. Prove the upper and lower bound, then...
Define a function called get_n_largest(numbers, n) which takes a list of integers and a value n...
Define a function called get_n_largest(numbers, n) which takes a
list of integers and a value n as parameters and returns a
NEW list which contains the n
largest values in the parameter list. The values in the
returned list should be in increasing order. The
returned list must always be of length n. If the number of values
in the original list is less than n, the value
None should be repeated at the end of the returned list to...
(5 marks; questions to Reza) In Lecture 5, Travis said you can prove QuickSort takes N(n...
(5 marks; questions to Reza) In Lecture 5, Travis said you can prove QuickSort takes N(n log n) time in the best case the same way he proved any comparison-based sorting algorithm takes (n log n) time in the worst case. Give that proof. Notice it doesn't follow directly: e.g., Insertion Sort takes O(n) time in the best case. You can assume QuickSort divides each array into elements less than or equal to the pivot (including the pivot itself) and...
Assume L is an array, length(L) returns the number of records in the array, and qsort(L, i, j) sorts the records of L from i to j (leaving the records sorted in L) using the Quicksort algorithm. What is the averagecase time complexity for each of the foll
Assume L is an array, length (L) returns the number of records in the array, and qsort \((L, \quad i, j)\) sorts the records of \(L\) from \(i\) to \(j\) (leaving the records sorted in L) using the Quicksort algorithm. What is the average-case complexity for the following code fragment?$$ \begin{array}{c} \text { for }(\mathrm{i}=0 ; \text { i<length }(\mathrm{L}) ; \mathrm{i}++) \\ \text { qsort }(\mathrm{L}, 0, \mathrm{i}) ; \end{array} $$You should provide a formula for computing the total...
An m×n array A of real numbers is a Monge array if for all i,j,k, and l such that 1≤i<k≤m and ...
An m×n
array A
of real numbers is a Monge array if for all i,j,k,
and l
such that 1≤i<k≤m
and 1≤j<l≤n
, we have
>A[i,j]+a[k,l]≤A[i,l]+A[k,j]>
In other words, whenever we pick two rows and two columns of a
Monge array and consider the four elements at the intersections of
the rows and columns, the sum of the upper-left and lower-right
elements is less than or equal to the sum of the lower-left and
upper-right elements. For example, the following...
6. Consider the following basic problem. You're given an array A consisting of n integers A[1],...
6. Consider the following basic problem. You're given an array A consisting of n integers A[1], A[2], , Aln]. You'd like to output a two-dimensional n-by-n array B in which B[i, j] (for i <j) contains the sum of array entries Ali] through Aj]-that is, the sum A[i] Ai 1]+ .. +Alj]. (The value of array entry B[i. Λ is left unspecified whenever i >j, so it doesn't matter what is output for these values.) Here's a simple algorithm to...
Please answer by mathematical language: An array of n elements is almost sorted if and only...
Please answer by mathematical language: An array of n elements is almost sorted if and only if every element is at most k spots away from its actual location. Assuming that you can only perform pairwise comparisons, formally prove that any algorithm which can sort almost sorted arrays must have running time Ω(n log k), You may assume that n is a multiple of k.
Assume L is an array, length(L) returns the number of records in the array, and qsort(L,i,j) sorts the records of L from i toj (leaving the records sorted in L) using the Quicksort algorithm. What is the average-case complexity for the following code fragment? for (i = @; i<length(L); i++) asort(1, 0, 1); Consider the time for each pass of the for loop, and sum them all together. Prove the upper and lower bound, then argue for an average case....
vas Х Assume Lis an array, length(L) returns the number of records in the array, and qsort(L. 1.j) sorts the records of Lfrom itoj (leaving the records sorted in L) using the Quicksort algorithm. What is the average-case complexity for the following code fragment? for (i = 0; i<length(); i++) asort(1, 0, 1); Consider the time for each pass of the for loop, and sum them all together. Prove the upper and lower bound, then argue for an average case....
C++
Question 14 10 Assume Lis an array, length(L) returns the number of records in the array, and qsort(L, 1. j) sorts the records of L from i toj (leaving the records sorted in L) using the Quicksort algorithm. What is the average-case complexity for the following code fragment? for (i = 0; i<length(); i++) asort(L, 0, 1); Consider the time for each pass of the for loop, and sum them all together. Prove the upper and lower bound, then...
Define a function called get_n_largest(numbers, n) which takes a
list of integers and a value n as parameters and returns a
NEW list which contains the n
largest values in the parameter list. The values in the
returned list should be in increasing order. The
returned list must always be of length n. If the number of values
in the original list is less than n, the value
None should be repeated at the end of the returned list to...
(5 marks; questions to Reza) In Lecture 5, Travis said you can prove QuickSort takes N(n log n) time in the best case the same way he proved any comparison-based sorting algorithm takes (n log n) time in the worst case. Give that proof. Notice it doesn't follow directly: e.g., Insertion Sort takes O(n) time in the best case. You can assume QuickSort divides each array into elements less than or equal to the pivot (including the pivot itself) and...
An m×n
array A
of real numbers is a Monge array if for all i,j,k,
and l
such that 1≤i<k≤m
and 1≤j<l≤n
, we have
>A[i,j]+a[k,l]≤A[i,l]+A[k,j]>
In other words, whenever we pick two rows and two columns of a
Monge array and consider the four elements at the intersections of
the rows and columns, the sum of the upper-left and lower-right
elements is less than or equal to the sum of the lower-left and
upper-right elements. For example, the following...
6. Consider the following basic problem. You're given an array A consisting of n integers A[1], A[2], , Aln]. You'd like to output a two-dimensional n-by-n array B in which B[i, j] (for i <j) contains the sum of array entries Ali] through Aj]-that is, the sum A[i] Ai 1]+ .. +Alj]. (The value of array entry B[i. Λ is left unspecified whenever i >j, so it doesn't matter what is output for these values.) Here's a simple algorithm to...
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