a) This will correct solution because atleast LCS of 3 strings will be obtained by applying for any 2 also, and then we can apply LCS for third and this string, to get for LCS of all three.
b)
The idea is to take a 3D array to store the length of common subsequence in all 3 given sequences i. e., L[m + 1][n + 1][o + 1] 1- If any of the string is empty then there is no common subsequence at all then L[i][j][k] = 0 2- If the characters of all sequences match (or X[i] == Y[j] ==Z[k]) then L[i][j][k] = 1 + L[i-1][j-1][k-1] 3- If the characters of both sequences do not match (or X[i] != Y[j] || X[i] != Z[k] || Y[j] !=Z[k]) then L[i][j][k] = max(L[i-1][j][k], L[i][j-1][k], L[i][j][k-1])
2. (40 pts) Let A, B, and C be three strings each n characters long. We want to compute the longest subsequence th...
2. (40 pts) Let A, B, and C be three strings each n characters long. We want to compute the longest subsequence that is common to all three strings. (a) Let us first consider the following greedy algorithm for this problem. Find the longest common subsequence between any pair of strings, namely, LCS(A, B) LCS(B, C), LCS(A, C). Then, find the longest common subsequence between this LCS and the 3rd string. That is, supposing that the longest common pair wise...
need the answer to b not a. thanks! 2. (40 pts) Let A, B, and C be three strings each n characters long. We want to compute the longest subsequence that is common to all three strings. (a) Let us first consider the following greedy algorithm for this problem. Find the longest common subsequence between any pair of strings, namely, LCS(A, B). LCS(B,C), LCS(A, C). Then, find the longest common subsequence between this LCS and the 3rd string. That is,...
Longest common subsequence (LCS) algorithms give a way to decide how similar two given strings are. However, sometimes, we have to filter away some common subsequences that are in some pattern. Here is a problem for you to solve. Given two strings alpha and beta, let gamma to be the longest word satisfying all of the following conditions: gamma is a subsequence of alpha. gamma is a subsequence of beta. gamma does not contain abb. Design an algorithm that finds...
Question 2 (2.5 points) Longest common subsequence Consider the procedure to determine the length of the longest common subsequence, LCS- LENGTH(X, Y). It solves the LCS problem in a bottom-up manner, by filling out a 2-D tabular LCS-LENGTH(X, Y) m = X.length 2. n-Y.length 3. let cO.m, 0n] be a new array 4, for i = 0 to m for/ = 0 to n else if ATY ci,ci ,j-1 +1 10 else 12. return clm, n] For example, X (B,...
C. 7. True/False Questions. (2 points each) a. Applying Horner's Rule, an n-degree polynomial can be evaluated at a given point using only n multiplications and n additions. b. Quick Sort and Merge Sort are comparison-based sorting algorithms. Heap Sort and Distribution Counting Sort are not comparison-based sorting algorithms. An AVL tree applies four types of rotations: RIGHT, LEFT, RIGHT-LEFT, and LEFT-RIGHT. d. When an AVL tree's left sub-tree is left-heavy, a LEFT rotation is needed. e. When an AVL...
We are given four items, namely A, B, C, and D. Their corresponding unit profits are pA, pB, pC, and pD. The following shows five transactions with these items. Each row corresponds to a transaction where a non-negative integer shown in the row corresponds to the total number of occurrences of the correspondence item present in the transaction. T A B C D t1 0 0 3 2 t2 3 4 0 0 t3 0 0 1 3 t4 1...