Let A be an array of non-decreasing N integers. Write an algorithm that returns the number...

Let A be an array of non-decreasing N integers. Write an algorithm that returns the number of pairs of integers in A that are equal. Analyze your algorithm thoroughly. Your analysis should include a thorough examination of both the best and the worst-case scenarios. This includes a description of what the best and worst cases would look like. You should include both space and time in your analysis, but keep in mind that space refers to “extra space,” meaning in addition to the space already used for the input.

Hint: You can assume there is a (1) function called nChoose2(int n) that calculates the value of C(n, 2).

Expert Solution

Solution:

The array is given to us in sorted order and the order is increasing order, which means the smallest to the largest the elements in the array are sorted.

Algorithm:

Begin
set count to 0, //count= 0
for every element in the array
for j=0 to array[i]<=array[i]
compare it to its right-hand side of elements until our element is smaller than the element present in the right-hand side, //if(array[i]==array[j])
if two elements are found equal
count++
end for
end for
Display count //This is the number of pairs of integers that are equal
End

Analysis:

So the array is already sorted, now there is a for loop in the code which is running n number of times to traverse the complete array considering there is n number of elements in the array. Now another loop is ran through in the algorithm which is running until a greater number is spotted in the array. This loop will be running twice or thrice each time because then the condition will terminate, this will make the overall complexity of the algorithm as cn, where c is some positive constant.

The time complexity will be T(n)= O(n).

Space complexity is O(1), since no extra space is taken.

Hit the thumbs up if you liked the answer. :)

venereology answered 1 year ago

Let iqsort(A, 1, n) be an algorithm that sorts an array A with n integers. It...

Let iqsort(A, 1, n) be an algorithm that sorts an array A with n integers. It works as follows: iqsort(A, p, q){ if p ≥ q, return; r=partition(A, p, q); //run quick sort on the low part quicksort(A, p, r − 1); //run insert sort on the high part insertsort(A, r + 1, q); } Compute the best-case, worst-case, and average-case complexities of iqsort.

One dimensional dynamic array Write a function that returns the number of integers in an input...

One dimensional dynamic array Write a function that returns the number of integers in an input file stream with the following interface: int findNumber(ifstream &x); Then, use this number to dynamically allocate an integer array. Write another function that reads each number in an input file stream and assign the value to the corresponding array element with the following interface: void assignNumber(ifstream &x, int y[ ]); In your main( ), first open “in.dat” as an input file. Next, apply findNumber(...

please write in c++ Algorithm Design problem: Counting inversions: given an array of n integers, find...

please write in c++ Algorithm Design problem: Counting inversions: given an array of n integers, find out the total number of inversions in the given sequence. For example, for the sequence of 2, 4, 1, 3, 5, there are three inversions (2,1), (4,1), and (4,3). Give a brute-force algorithm with running time of O(n^2). Using the technique of divide-and-conquer, design an algorithm with running time of O(nlog n).

1. Given an array of integers a dimension n. If the array contains the same number...

1. Given an array of integers a dimension n. If the array contains the same number of even and odd elements get (a1 + an) (a2 + an-1) ... 2. Given an array of integers dimension n. All array elements with even numbers preceding the first element to the maximum, multiplied by the maximum. 3. Given an array of dimension n. Insert after each zero element of the element in the middle (or the amount of secondary elements for even...

Let A[1..n] be an array of distinct positive integers, and let t be a positive integer....

Let A[1..n] be an array of distinct positive integers, and let t be a positive integer. (a) Assuming that A is sorted, show that in O(n) time it can be decided if A contains two distinct elements x and y such that x + y = t. (b) Use part (a) to show that the following problem, re- ferred to as the 3-Sum problem, can be solved in O(n2) time: 3-Sum Given an array A[1..n] of distinct positive integers, and...

write code to count the number of odd integers in an array of 100 random integers...

write code to count the number of odd integers in an array of 100 random integers in the range [0,99].

The following algorithm returns true if the n items in an array are all distinct, i.e.,...

The following algorithm returns true if the n items in an array are all distinct, i.e., if no two items are equal to each other, otherwise it returns false. 1 ALGORITHM UniqueElements(A[1..n]) 2 // Determine whether all the elements in an array are distinct 3 // Input: Array A[1..n] 4 // Output: “true” if all elements of A are distinct, “false” otherwise 5 for i ← 1 to n – 1 do 6 for j ← i + 1 to...

write a method that returns the index of the second smallest element in an array of integers. If the number of such elements is greater than 1.

write a method that returns the index of the second smallest element in an array of integers. If the number of such elements is greater than 1. return the second smallest index. Use the following header:public static int index of seconds sma11eststenent tint array

Let A be an integer array of length n. Design a divide and conquer algorithm (description...

Let A be an integer array of length n. Design a divide and conquer algorithm (description and pseudo code) to find the index of an element of the minimum value in the array. If there are several such elements, your algorithm must return the index of the rightmost element. For instance, if A = {0,2,4,5,2,0,3,10}, then the algorithm should return 5, which is the index of the second 0.

Python: Write a function that receives a one dimensional array of integers and returns a Python...

Python: Write a function that receives a one dimensional array of integers and returns a Python tuple with two values - minimum and maximum values in the input array. You may assume that the input array will contain only integers and will have at least one element. You do not need to check for those conditions. Restrictions: No built-in Python data structures are allowed (lists, dictionaries etc). OK to use a Python tuple to store and return the result. Below...

Question