Introduction to the Design and Analysis of
Algorithms
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Introduction to the Design and Analysis of
Algorithms
Note: Present Algorithms in Pseudocode Give an algorithm...
Design and analysis of algorithms Type in answer Problem 5. Given a sorted array of distinct...
Design and analysis of algorithms
Type in answer
Problem 5. Given a sorted array of distinct integers A[1- -n], you want to find out whether there is an index I for which Ai-i. Give a divide-and-conquer algorithm that runs in time O(log n)
Problem 3: (5 2 points) Design an algorithm that takes an array of positive integers A...
Problem 3: (5 2 points) Design an algorithm that takes an array of positive integers A of length n and a positive integer T as an input and finds the largest N < T such that N can be written as a sum of some elements of A and returns such a representation of N. The complexity of the algorithms has to be O(nT). For example, for A 3,7, 10 and T 19, the output is 17 7+10, because we...
12. 10 points) Use pseudocode to write out algorithms for the following problems. (a) Assume n is any integer with...
12. 10 points) Use pseudocode to write out algorithms for the following problems. (a) Assume n is any integer with n 2 7. Write out an algorithm SumofCertainIntenger in pseudocode that uses n as input variable. Use a "for" loop to compute the sum (Gk +4) (b) Assume m is any integer with m 2 5. Write out an algorithm ProductOfCertainInte- gers in pseudocode that uses m as input variable. Use a "while" loop to compute the product IT (é+4)....
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) Design a greedy algorithm that solves the problem; describe your algorithm with clear pseudocode; and...
1) Design a greedy algorithm that solves the problem; describe your algorithm with clear pseudocode; and prove the time efficiency class of your algorithm: If x, y are two adjacent elements in a sequence, with x before y, we say that the pair x, y is in order when x <= y and the pair is out of order when x > y. For example, in the string “BEGGAR” the pair G, A are out of order, but all the...
1. Design an algorithm to find all the non-common elements in two sorted lists of numbers....
1. Design an algorithm to find all the non-common elements in two sorted lists of numbers. What is the maximum number of comparisons your algorithm makes if the lengths of the two given lists are m and n, ?respectively 2. Estimate how many times faster it will be to find ged(98765, 56789) by Euclid's algorithm compared with the algorithm based on checking consecutive integers from min{m, n} down to gcd(m, n). 3. For each of the following functions, indicate how...
DESCRIPTION Implement a program in C++ that generates a specified number of random integers, records them...
DESCRIPTION Implement a program in C++ that generates a specified number of random integers, records them in three arrays, then sorts the arrays with Insertion Sort, Merge Sort, and Quick Sort, respectively. Augment the three sorting algorithms with counters and report the number of characteristic operations each performs in sorting the (same) random values. INPUT The program reads from the terminal the number of random integers to generate, a seed value for the pseudo-random number generator, and a character that...
8. [10 points) Consider the following algorithm procedure Algorithm(: integer, n: positive integer; 81,...a s integers with vhilei<r print (l, r, mı, arn, 》 if z > am then 1:= m + 1 if za...
8. [10 points) Consider the following algorithm procedure Algorithm(: integer, n: positive integer; 81,...a s integers with vhilei<r print (l, r, mı, arn, 》 if z > am then 1:= m + 1 if za then anstwer-1 return answer 18 and the (a) Assume that this algorithm receives as input the numbersz-32 and corresponding sequence of integers 2 | 3 1 1 4151617| 8| 9 | 10 İ 11 İ 12 | 13 | 14|15 | 16 | 17 |...
a. Use pseudocode to specify a brute-force algorithm that takes as input a list of n...
a. Use pseudocode to specify a brute-force algorithm that takes as input a list of n positive integers and determines whether there are two distinct elements of the list that have as their sum a third element of the list. That is, whether there exists i, j.k such that iヂj, i关k,j关k and ai + aj = ak. The algorithm should loop through all triples of elements of the list checking whether the sum of the first two is the third...
1. Please write a Divide-and-Conquer Java algorithm solving the following problem: Given an "almost sorted" array...
1. Please write a Divide-and-Conquer Java algorithm solving the following problem: Given an "almost sorted" array of distinct integers, and an integer x, return the index of x in the array. If the element x is not present in the array, return -1. "Almost sorted" means the following. Assume you had a sorted array A[0…N], and then split it into two pieces A[0…M] and A[M+1…N], and move the second piece upfront to get the following: A[M+1]…A[N]A[0]…A[M]. Thus, the "almost sorted"...
Design and analysis of algorithms
Type in answer
Problem 5. Given a sorted array of distinct integers A[1- -n], you want to find out whether there is an index I for which Ai-i. Give a divide-and-conquer algorithm that runs in time O(log n)
Problem 3: (5 2 points) Design an algorithm that takes an array of positive integers A of length n and a positive integer T as an input and finds the largest N < T such that N can be written as a sum of some elements of A and returns such a representation of N. The complexity of the algorithms has to be O(nT). For example, for A 3,7, 10 and T 19, the output is 17 7+10, because we...
12. 10 points) Use pseudocode to write out algorithms for the following problems. (a) Assume n is any integer with n 2 7. Write out an algorithm SumofCertainIntenger in pseudocode that uses n as input variable. Use a "for" loop to compute the sum (Gk +4) (b) Assume m is any integer with m 2 5. Write out an algorithm ProductOfCertainInte- gers in pseudocode that uses m as input variable. Use a "while" loop to compute the product IT (é+4)....
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. Design an algorithm to find all the non-common elements in two sorted lists of numbers. What is the maximum number of comparisons your algorithm makes if the lengths of the two given lists are m and n, ?respectively 2. Estimate how many times faster it will be to find ged(98765, 56789) by Euclid's algorithm compared with the algorithm based on checking consecutive integers from min{m, n} down to gcd(m, n). 3. For each of the following functions, indicate how...
8. [10 points) Consider the following algorithm procedure Algorithm(: integer, n: positive integer; 81,...a s integers with vhilei<r print (l, r, mı, arn, 》 if z > am then 1:= m + 1 if za then anstwer-1 return answer 18 and the (a) Assume that this algorithm receives as input the numbersz-32 and corresponding sequence of integers 2 | 3 1 1 4151617| 8| 9 | 10 İ 11 İ 12 | 13 | 14|15 | 16 | 17 |...
a. Use pseudocode to specify a brute-force algorithm that takes as input a list of n positive integers and determines whether there are two distinct elements of the list that have as their sum a third element of the list. That is, whether there exists i, j.k such that iヂj, i关k,j关k and ai + aj = ak. The algorithm should loop through all triples of elements of the list checking whether the sum of the first two is the third...
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