Algorithm Problem - Counting Number of Inversions
We are given a sequence ofndistinct numbers a1,...,an. We define an inversion to be a pair i<j such that ai>aj. Give an O(nlogn) algorithm to count the number of inversions. (Hint: assume that your algorithmreturns a sorted array of input sequences, as well as the number of inversions. Divide the input sequencesinto two halves, then count inversions and sort each half by doing recursive calls, and find a way to mergethese two sorted halves and to count the number of inversion between them.)
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ALGORITHM PROBLEM: A) Significant Inversions: We are given a sequence of n arbitrary but distinct real...
ALGORITHM PROBLEM: A) Significant Inversions: We are given a sequence of n arbitrary but distinct real numbers <a1 , a2 ,..., an>. We define a significant inversion to be a pair i < j such that ai > 2 aj . Design and analyze an O(n log n) time algorithm to count the number of significant inversions in the given sequence. [Hint: Use divide-&-conquer. Do the “combine” step carefully] B) The Maximum-Sum Monotone Sub-Array Problem: Input: An array A[1..n] of...
ALgorithm problem
Recall the problem of ¯nding the number of inversions. As in the text, we are given asequence of numbers a1; : : : ; an, which we assume are all distinct, and we de¯ne an inversionto be a pair i < j such that ai > aj .We motivated the problem of counting inversions as a good measure of how di®erent twoorderings are. However, one might feel that this measure is two sensitive. Let's call a pair asigni¯cant inversion if...
2. Using Python, implement the Divide-and-Conquer algorithm to count the number of inversions between two arrays....
2. Using Python, implement the Divide-and-Conquer algorithm to count the number of inversions between two arrays. The algorithm is based on Mergesort and counts the inversions while merging the sorted lists.
the question from the course COMP 4040 that Analysis of Algorithms if you want to answer it by code please use C or C++...
the question from the course COMP 4040 that Analysis of
Algorithms
if you want to answer it by code please use C or C++
5. Algorithm Design (20 points) Input: array A contains n distinct numbers from 1 to n, in arbitrary order. Output: number of inversions (defined as the number of pair(i, j) of array indices with i < j and A[i] > Aj]) (a) (5 points) What array with elements from the set {1, 2, ..., n) has...
1. Which is the best sorting algorithm for larger arrays if all the items can not...
1. Which is the best sorting algorithm for larger arrays if all the items can not fit in main memory? selection sort insertion sort quicksort Merge sort 2. Which sorting algorithm sorts items without comparing them? quick sort radix sort merge sort Insertion sort 3 What is the average running time for quicksort? O(n2) O(logn) O(nlogn) O(n) O(n2logn) 4. Examine the steps of the following algorithm and write the name of the algorithm described in the blank provided: Recursively divide...
I am working on the divide/conquer algorithm. I am having a trouble with a print for...
I am working on the divide/conquer algorithm. I am having a trouble with a print for output from reading the file. Here is my work. When you see I put the comment with TODO. that one I am struck with readfile. I wonder if you'd able to help me to fix the readfile to find a single number. Here is the input3.txt (1 12 13 24 35 46 57 58 69). after that, the output should be 0. int mergeInversion(int...
c++ code Lab Exercises This assignment consists of two exercises. Exercise 1- Count Inversions Exercise Objectives...
c++
code
Lab Exercises This assignment consists of two exercises. Exercise 1- Count Inversions Exercise Objectives Define and call functions ✓ Using Array Using nested loop ✓ Using input/output statement Problem Description Inside "Lab2" folder, create a project named "Lab2Ex1". Use this project to write and run a C++ program that produces: Define a constant value called A_SIZE with value of 10. ► Declare an integer 10 array of size A_SIZE called Arr. Define a function called Read that accept...
Please solve using Java and comment your code for clarity. Sample 3. Input: 4 1 231...
Please solve using Java and comment your code for clarity.
Sample 3. Input: 4 1 231 Output: 0 This sequence also does not have a majority element (note that the element 1 appears twice and hence is not a majority element). Problem Introduction Majority rule is a decision rule that selects the alternative which has a majority, that is, more than half the votes. Given a sequence of elements (1.02....,On, you would like to check whether it contains an element...
4 Problem 4 -Extra Credit Given an array A, we say that elements A and Al...
4 Problem 4 -Extra Credit Given an array A, we say that elements A and Al are swapped if J >「 but Alj]< A[i]. For example, if A - [8,5,9,7], then there are a total of3 swapped pairs, namely 8 and 5; 8 and 7; and 9 and 7 Describe a recursive algorithm that given an array A, determines the number of swapped pairs in the array in O(n log(n)) time. To analyze the algorithm, you must state the recurrence...
(a) Prove the following loop invariant by induction on the number of loop iterations: Loop Invariant:...
(a) Prove the following loop invariant by induction on the
number of loop iterations: Loop Invariant: After the kth iteration
of the for loop, total = a1 + a2 + · · · + ak and L contains
all elements from a1 , a2 , . . . ,
ak that are greater than the sum of all previous terms of the
sequence.
(b) Use the loop invariant to prove that the algorithm is
correct, i.e., that it returns a...
the question from the course COMP 4040 that Analysis of
Algorithms
if you want to answer it by code please use C or C++
5. Algorithm Design (20 points) Input: array A contains n distinct numbers from 1 to n, in arbitrary order. Output: number of inversions (defined as the number of pair(i, j) of array indices with i < j and A[i] > Aj]) (a) (5 points) What array with elements from the set {1, 2, ..., n) has...
c++
code
Lab Exercises This assignment consists of two exercises. Exercise 1- Count Inversions Exercise Objectives Define and call functions ✓ Using Array Using nested loop ✓ Using input/output statement Problem Description Inside "Lab2" folder, create a project named "Lab2Ex1". Use this project to write and run a C++ program that produces: Define a constant value called A_SIZE with value of 10. ► Declare an integer 10 array of size A_SIZE called Arr. Define a function called Read that accept...
Please solve using Java and comment your code for clarity.
Sample 3. Input: 4 1 231 Output: 0 This sequence also does not have a majority element (note that the element 1 appears twice and hence is not a majority element). Problem Introduction Majority rule is a decision rule that selects the alternative which has a majority, that is, more than half the votes. Given a sequence of elements (1.02....,On, you would like to check whether it contains an element...
4 Problem 4 -Extra Credit Given an array A, we say that elements A and Al are swapped if J >「 but Alj]< A[i]. For example, if A - [8,5,9,7], then there are a total of3 swapped pairs, namely 8 and 5; 8 and 7; and 9 and 7 Describe a recursive algorithm that given an array A, determines the number of swapped pairs in the array in O(n log(n)) time. To analyze the algorithm, you must state the recurrence...
(a) Prove the following loop invariant by induction on the
number of loop iterations: Loop Invariant: After the kth iteration
of the for loop, total = a1 + a2 + · · · + ak and L contains
all elements from a1 , a2 , . . . ,
ak that are greater than the sum of all previous terms of the
sequence.
(b) Use the loop invariant to prove that the algorithm is
correct, i.e., that it returns a...
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