Show that the following algorithm is correct, complete, and finite.
Input: a list of n distinct positive integers a0, ..., an-1
Output: The largest even integers in the list, or 0 if there are no even integers
Procedure:
even= 0
for (i=0, i<n, i+=1)
if ai%2 == 0 and ai > even
even = ai
return even
Show that the following algorithm is correct, complete, and finite. Input: a list of n distinct...
Explain why the following algorithm is complete, correct, and finite. Input: a list of n distinct integers a0 to an-1 ordered from least to greatest and an integer x Output: the index in the list at which x is found, or -1 if x is not found Procedure: i = 0 while (i <= n-1 and x != ai) i = i + 1 if i < n then location = i else location = -1 return location
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...
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 |...
Consider the following problem: Input: a list of n-1 integers and these integers are in the range of 1 to n. There are no duplicates in list. One of the integers from 1 to n is missing in the list. Output: find the missing integer Let the input array be [2, 4, 1, 6, 3, 7, 8]. Elements in this list are in the range of 1 to 8. There are no duplicates, and 5 is missing. Your algorithm needs...
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...
(V). Given the following algorithm, answer relevant questions. Algorithm 1 An algorithm 1: procedure WHATISTHIS(21,22,...,n: a list of n integers) for i = 2 to n do c= j=i-1 while (j > 0) do if ra; then break end if 4j+1 = a; j= j-1 end while j+1 = 1 end for 14: return 0.02. 1, 15: end procedure Answer the following questions: (1) Run the algorithm with input (41, 02, 03, 04) = (3, 0, 1,6). Record the values...
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-...
Describe an algorithm that takes as input a list of n integers and produces output the smallest integer in the list.
The following algorithm (Rosen pg. 363) is a recursive version of linear search, which has access to a global list of distinct integers a_1, a_2,..., a_n. procedure search(i, j, x : i,j, x integers, 1 < i < j < n) if a_i = x then return i else if i = j then 4. return 0 else return search(i + 1, j, x) Prove that this algorithm correctly solves the searching problem when called with parameters i = 1...