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Question3 10 pts Let A [L.n] be a max-heap with n > 1 and consider the index ị such that l 〈 i 〈 n . Assume that a...
10 pts Question 2 Let A[1.n] and B[1.m] be two arrays, where n 2 mz 1. Use pseudocode to write an algorithm which prints TRUE if the array A contains the sequence B, and FALSE otherwise. The elements from B must appear in order, but they do not have to occur as a contiguous sequence in A. The running time of the algorithm must be O(n). some examples: Here are <5,6,8> then the algorithm prints TRUE - if A =...
Let A = [A[1], A[2],…..,A[n]] be an array of n distinct integers. For 1 <= j <= n, the index j is a happy index if A[i] < A[j] for all 1 <= i < j. Describe an O(n)- time algorithm that finds all the happy indices in the array A. Partial credit will be given for an O(n log(n))-time algorithm and a minimal credit will be given for an O(n^2) –time algorithm. What is the running time of your...
Suppose we are given two sorted arrays (nondecreasing from index 1 to index n) X[1] · · · X[n] and Y [1] · · · Y [n] of integers. For simplicity, assume that n is a power of 2. Problem is to design an algorithm that determines if there is a number p in X and a number q in Y such that p + q is zero. If such numbers exist, the algorithm returns true; otherwise, it returns false....
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...
urgent
L. Consider the following pseudocode for finding binomial coefficients: Binom(n, r) Input: integers n and r Output: n choose r if r-0 or r-n thern return 1 end else return Binom(n-1, r-1) Binom(n-1, r); end running time of this algorithm. Prove your bound for the upper bound. (5 points) Rewrite the above algorithm so that it is efficient. (You have 2 choices!) Analyze the worst case time of your new algorithm. (5 points) Find the edit distance between "SPOKE...
Consider n indivisible objects with distinct types i = 1, 2, 3,…, n. We are given positive integer weights W = {w1,w2...wn} and positive integer prices V = {v1,v2...vn} for the objects and a knapsack of weight capacity (m). Our problem is to find the maximum profit possible by including a subset of the objects into the knapsack with total weight of at most m. This form of the 0/1 Knapsack Problem can be solved by a Decrease and Conquer...
9. [10 points) Consider the following algorithm: procedure Algorithm(n: positive integer; ddd: distinet integers) for k:=1 to n-1 for 1-1 to n-k print(k, I, di,da...-1,dn) if ds dti then interchange dy and d (a) Assume that this algorithm receives as input the integer n 6 and the input sequence 하하하하하하, Miss ^-ruteae rehen i12|3141516 Fill out the table below: ds ds (b) Assume that the algorithm receives the same input values as in part a). Once the algorithm finishes, what...
17. Consider the following algorithm: procedure Algorithm(n: positive integer; di,d2.. ,dn: distinct integers) for 1 to n-1 for 1 to n-k if ddi+ then interchange di and di+ print(k, I, d,ddn-1, dn) (a) |3 points Assume that this algorithm receives as input the integer-6 and the corresponding input sequence 41 36 27 31 17 20 Fill out the table below ds (b) 1 point Assume that the algorithm receives the same input values as in part a). Once the algo-...
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Question 3. (30 Pts) Let LU is the Crout LU decomposition of the nx n tridiagonal matrix 01. 1012 02.1 222 223 03.2 23,3 43,4 Gr-1,-2 -1,-1 On-1,60 BIL 332/532 - Numerical methods Homework 2 Note that the Crout decomposition implies that the diagonal of U consists of 1s. Besides, ky 0 if j < (i-1) and j>i and wij = 0 ifj<i and j> (i+1) because of the nonzero structure of A. Write...
Write a C program that computes Pi with the approximation algorithm that I introduced in class. I want you to write the program in two different ways: The first version will add up the first 28284277 elements of the approximation series in a simple for loop. I ask you to put the code into a function with this signature: float get_pi_for(void); The second version will break out of a while loop depending on whether a pair of adjacent elements (remember...