Discussion 07a: Mar 2 (Wed) Version: 1.0 CS/ECE 374 A, Spring 2022

A subsequence of a sequence (for example, an array, linked list, or string), obtained by removing zero or more elements and keeping the rest in the same sequence order. A subsequence is called a substring if its elements are contiguous in the original sequence. For example:

SUBSEQUENCE, UBSEQU, and the empty string ε are all substrings (and therefore subsequences) of the string SUBSEQUENCE;

SBSQNC, SQUEE, and EEE are all subsequences of SUBSEQUENCE but not substrings;

Copyright By cscodehelp代写 加微信 cscodehelp

QUEUE, EQUUS, and DIMAGGIO are not subsequences (and therefore not substrings) of SUBSEQUENCE.

Describe recursive backtracking algorithms for the following problems. Don’t worry about running times.

1 Given an array A[1 .. n] of integers, compute the length of a longest increasing subsequence . A sequence

B[1 .. l] is increasing if B[i] > B[i − 1] for every index i ≥ 2. For example, given the array

⟨3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6,2,7⟩

your algorithm should return the integer 6, because ⟨1, 4, 5, 6, 8, 9⟩ is a longest increasing subsequence (one

2 Given an array A[1 .. n] of integers, compute the length of a longest decreasing subsequence . A sequence

B[1 .. l] is decreasing if B[i] < B[i − 1] for every index i ≥ 2. For example, given the array
⟨3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6,2,7⟩
your algorithm should return the integer 5, because ⟨9, 6, 5, 4, 2⟩ is a longest decreasing subsequence (one
3 Given an array A[1 .. n] of integers, compute the length of a longest alternating subsequence . A sequence B[1 .. l] is alternating if B[i] < B[i − 1] for every even index i ≥ 2, and B[i] > B[i − 1] for every odd index i ≥ 3.

For example, given the array

⟨3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6,2,7⟩

your algorithm should return the integer 17, because ⟨3,1,4,1,5,2,6,5,8,7,9,3,8,4,6,2,7⟩ is a longest

alternating subsequence (one of many).

To think about later:

4 Given an array A[1 .. n] of integers, compute the length of a longest convex subsequence of A. A sequence B[1..l]isconvex ifB[i]−B[i−1]>B[i−1]−B[i−2]foreveryindexi≥3.

For example, given the array

⟨3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6,2,7⟩

your algorithm should return the integer 6, because ⟨3, 1, 1, 2, 5, 9⟩ is a longest convex subsequence (one of many).

5 Given an array A[1..n], compute the length of a longest palindrome subsequence of A. Recall that a sequence B[1 .. l] is a palindrome if B[i] = B[l − i + 1] for every index i.

For example, given the array

⟨3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6,2,7⟩

your algorithm should return the integer 7, because ⟨4, 9, 5, 3, 5, 9, 4⟩ is a longest palindrome subsequence (one of many).

程序代写 CS代考 加微信: cscodehelp QQ: 2235208643 Email: kyit630461@163.com