Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 2, Problem 4P
(a)
Program Plan Intro
To list the five inversions of the array
(b)
Program Plan Intro
To find the most inversions from the set
(c)
Program Plan Intro
To find the relation between the running time of the insertion sort and the number of inversions in the input array.
(d)
Program Plan Intro
To describe an
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VelTech Codeathon Jan Finals
Test will be
Lowest Common Multiple (LCM)
You are given an array of positive integers, arr, of size array length. You are asked to build set S which
consists of the LCM of every pair of adjacent elements in arr. Your task is to find the largest element in set S
For example, for the array (1, 2, 3, 4), set S = { Icm(1,2), Icrm(2,3), Icrm(3,4) } = (2, 6, 12). The largest element is
Fill you
12
Notes
The array contains only positive integers.
Adjacent elements may NOT be circular, ie. they may not wrap around the end of the array
Definition of LCM
A multiple of a number, num, is a number that can be divided by num. For example, the multiples of 5 are 5, 10,
15, 20, 25, and so on, The lowest common multiple (LCM) of two numbers, a and b, is the smallest positive
number that is a multiple of both a and b
Example 1
Input
4
1324
Output
9.
Explanation
set S= (lcm(1, 3), Icm(3, 2), Icm(2, 4) ) = (3, 6, 4)
Largest element 6
Example 2
Pro
Input
7329 12
Output
36…
Number of times you need to assign a value (let say -1) to all elements of a 4-demnsional array A[k, l, m, n] (to initialize it) can be expressed mathematically as product of sets cardinalities
Write a pseudo-code that does this assignment.
Write pseudo code for bubble sort and dry run that pseudo code for an array with elements.
14, 33, 27, 35, 10
Chapter 2 Solutions
Introduction to Algorithms
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- Q: Consider an array consisting of the following sequence: 1, 4, 9, 16, 25, 49, …, n [10] Suppose a number in the sequence is missing. Write the mathematical process to find the missing number, i.e. some equation. What is the time complexity of finding the missing number in the sequence?arrow_forwardQ: Consider an array consisting of the following sequence: 1, 4, 9, 16, 25, 49, …, n Suppose a number in the sequence is missing. (a). Write the mathematical process to find the missing number, i.e. some equation. (b). What is the time complexity of finding the missing number in the sequence?arrow_forwardConsider the array A with elements:[0,5,3,10]What is the value of *(A + 3)arrow_forward
- Q3/ (a) Lets C is a 3x3 matrix, find out TWO ONLY of the following: 1. Sum of the first column. 2 The results of multiply C matrix by 3. 3. The determinate of C matrix. (b) Write a Cprogram to enter different four-integer numbers into One -Dimensional Array, print its elements, and find sum of the results.arrow_forwardUse one-dimensional arrays to solve the following problem. Read in two sets of numbers, each having 10 numbers. After reading all values, display all the unique elements in the collection of both sets of numbers. Use the smallest possible array to solve this problem.arrow_forwardFind peak element in the array in C language. Peak Element is the element of the array which is GREATER THAN EQUAL TO its neighbours, that is, for an element at i th index, the neighbour elements at index i-1 & i+1 must be greater than equal to element at Ith position.arrow_forward
- Answer in java script Create a function that returns true if the first array can be nested inside the second. arr1 can be nested inside arr2 if: 1. arr1's min is greater than arr2 's min. 2. arr1's max is less than arr2 's max. Examples canNest([1, 2, 3, 4], [0, 6]) true canNest ([3, 1], [4, 0]) → true canNest ([9, 9, 8], [8, 9]) → false canNest([1, 2, 3, 4], [2, 3]) - falsearrow_forwardQ3: Write a program for reading one dimensional array X(I), then arange its element ascending (4eha) then print matrix after change.arrow_forward1r. ""Implementation of the Misra-Gries algorithm.Given a list of items and a value k, it returns the every item in the listthat appears at least n/k times, where n is the length of the array By default, k is set to 2, solving the majority problem. For the majority problem, this algorithm only guarantees that if there isan element that appears more than n/2 times, it will be outputed. If thereis no such element, any arbitrary element is returned by the algorithm.Therefore, we need to iterate through again at the end. But since we have filtredout the suspects, the memory complexity is significantly lower thanit would be to create counter for every element in the list. For example:Input misras_gries([1,4,4,4,5,4,4])Output {'4':5}Input misras_gries([0,0,0,1,1,1,1])Output {'1':4}Input misras_gries([0,0,0,0,1,1,1,2,2],3)Output {'0':4,'1':3}Input misras_gries([0,0,0,1,1,1]Output None""".arrow_forward
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