Computer Science Engineering (CSE) Exam  >  Computer Science Engineering (CSE) Questions  >  A sub-sequence of a given sequence is just th... Start Learning for Free
A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences X[m] and Y[n] of lengths m and n respectively, with indexes of X and Y starting from 0. We wish to find the length of the longest common sub-sequence(LCS) of X[m] and Y[n] as l(m,n), where an incomplete recursive definition for the function l(i,j) to compute the length of The LCS of X[m] and Y[n] is given below:
l(i,j) = 0, if either i=0 or j=0
       = expr1, if i,j > 0 and X[i-1] = Y[j-1]
       = expr2, if i,j > 0 and X[i-1] != Y[j-1]
  • a)
    expr1 ≡ l(i-1, j) + 1
  • b)
    expr1 ≡ l(i, j-1)
  • c)
    expr2 ≡ max(l(i-1, j), l(i, j-1))
  • d)
    expr2 ≡ max(l(i-1,j-1),l(i,j))
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A sub-sequence of a given sequence is just the given sequence with som...
In Longest common subsequence problem, there are two cases for X[0..i] and Y[0..j]
1) The last characters of two strings match.
The length of lcs is length of lcs of X[0..i-1] and Y[0..j-1]
2) The last characters don't match.
The length of lcs is max of following two lcs values
a) LCS of X[0..i-1] and Y[0..j]
b) LCS of X[0..i] and Y[0..j-1]
View all questions of this test
Most Upvoted Answer
A sub-sequence of a given sequence is just the given sequence with som...
Explanation:

Longest Common Subsequence (LCS):
- LCS is a dynamic programming problem where we find the longest subsequence that is common in two given sequences.

Recursive Definition:
- The given incomplete recursive definition helps in finding the length of the LCS of two sequences X[m] and Y[n].

Explanation of Options:
- Option 'C' is correct as it states that if the elements at the current positions in X and Y are not the same, the length of the LCS is the maximum of the LCS without the last element of X and Y (l(i-1, j) and l(i, j-1)).
- Option 'C' captures the essence of finding the common subsequence length by considering all possibilities.
- Options 'A' and 'B' are incorrect as they only consider adding the last element to the LCS without checking if the elements at the current positions match or not.
- Option 'D' is incorrect as it directly compares the LCS lengths without considering the elements at the current positions.

Conclusion:
- The correct option 'C' is essential for finding the length of the LCS by considering all possible cases and recursive calls.
Explore Courses for Computer Science Engineering (CSE) exam

Top Courses for Computer Science Engineering (CSE)

A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences X[m] and Y[n] of lengths m and n respectively, with indexes of X and Y starting from 0. We wish to find the length of the longest common sub-sequence(LCS) of X[m] and Y[n] as l(m,n), where an incomplete recursive definition for the function l(i,j) to compute the length of The LCS of X[m] and Y[n] is given below:l(i,j) = 0, if either i=0 or j=0 = expr1, if i,j > 0 and X[i-1] = Y[j-1] = expr2, if i,j > 0 and X[i-1] != Y[j-1]a)expr1 ≡ l(i-1, j) + 1b)expr1 ≡ l(i, j-1)c)expr2 ≡ max(l(i-1, j), l(i, j-1))d)expr2 ≡ max(l(i-1,j-1),l(i,j))Correct answer is option 'C'. Can you explain this answer?
Question Description
A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences X[m] and Y[n] of lengths m and n respectively, with indexes of X and Y starting from 0. We wish to find the length of the longest common sub-sequence(LCS) of X[m] and Y[n] as l(m,n), where an incomplete recursive definition for the function l(i,j) to compute the length of The LCS of X[m] and Y[n] is given below:l(i,j) = 0, if either i=0 or j=0 = expr1, if i,j > 0 and X[i-1] = Y[j-1] = expr2, if i,j > 0 and X[i-1] != Y[j-1]a)expr1 ≡ l(i-1, j) + 1b)expr1 ≡ l(i, j-1)c)expr2 ≡ max(l(i-1, j), l(i, j-1))d)expr2 ≡ max(l(i-1,j-1),l(i,j))Correct answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences X[m] and Y[n] of lengths m and n respectively, with indexes of X and Y starting from 0. We wish to find the length of the longest common sub-sequence(LCS) of X[m] and Y[n] as l(m,n), where an incomplete recursive definition for the function l(i,j) to compute the length of The LCS of X[m] and Y[n] is given below:l(i,j) = 0, if either i=0 or j=0 = expr1, if i,j > 0 and X[i-1] = Y[j-1] = expr2, if i,j > 0 and X[i-1] != Y[j-1]a)expr1 ≡ l(i-1, j) + 1b)expr1 ≡ l(i, j-1)c)expr2 ≡ max(l(i-1, j), l(i, j-1))d)expr2 ≡ max(l(i-1,j-1),l(i,j))Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences X[m] and Y[n] of lengths m and n respectively, with indexes of X and Y starting from 0. We wish to find the length of the longest common sub-sequence(LCS) of X[m] and Y[n] as l(m,n), where an incomplete recursive definition for the function l(i,j) to compute the length of The LCS of X[m] and Y[n] is given below:l(i,j) = 0, if either i=0 or j=0 = expr1, if i,j > 0 and X[i-1] = Y[j-1] = expr2, if i,j > 0 and X[i-1] != Y[j-1]a)expr1 ≡ l(i-1, j) + 1b)expr1 ≡ l(i, j-1)c)expr2 ≡ max(l(i-1, j), l(i, j-1))d)expr2 ≡ max(l(i-1,j-1),l(i,j))Correct answer is option 'C'. Can you explain this answer?.
Solutions for A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences X[m] and Y[n] of lengths m and n respectively, with indexes of X and Y starting from 0. We wish to find the length of the longest common sub-sequence(LCS) of X[m] and Y[n] as l(m,n), where an incomplete recursive definition for the function l(i,j) to compute the length of The LCS of X[m] and Y[n] is given below:l(i,j) = 0, if either i=0 or j=0 = expr1, if i,j > 0 and X[i-1] = Y[j-1] = expr2, if i,j > 0 and X[i-1] != Y[j-1]a)expr1 ≡ l(i-1, j) + 1b)expr1 ≡ l(i, j-1)c)expr2 ≡ max(l(i-1, j), l(i, j-1))d)expr2 ≡ max(l(i-1,j-1),l(i,j))Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE). Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences X[m] and Y[n] of lengths m and n respectively, with indexes of X and Y starting from 0. We wish to find the length of the longest common sub-sequence(LCS) of X[m] and Y[n] as l(m,n), where an incomplete recursive definition for the function l(i,j) to compute the length of The LCS of X[m] and Y[n] is given below:l(i,j) = 0, if either i=0 or j=0 = expr1, if i,j > 0 and X[i-1] = Y[j-1] = expr2, if i,j > 0 and X[i-1] != Y[j-1]a)expr1 ≡ l(i-1, j) + 1b)expr1 ≡ l(i, j-1)c)expr2 ≡ max(l(i-1, j), l(i, j-1))d)expr2 ≡ max(l(i-1,j-1),l(i,j))Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences X[m] and Y[n] of lengths m and n respectively, with indexes of X and Y starting from 0. We wish to find the length of the longest common sub-sequence(LCS) of X[m] and Y[n] as l(m,n), where an incomplete recursive definition for the function l(i,j) to compute the length of The LCS of X[m] and Y[n] is given below:l(i,j) = 0, if either i=0 or j=0 = expr1, if i,j > 0 and X[i-1] = Y[j-1] = expr2, if i,j > 0 and X[i-1] != Y[j-1]a)expr1 ≡ l(i-1, j) + 1b)expr1 ≡ l(i, j-1)c)expr2 ≡ max(l(i-1, j), l(i, j-1))d)expr2 ≡ max(l(i-1,j-1),l(i,j))Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences X[m] and Y[n] of lengths m and n respectively, with indexes of X and Y starting from 0. We wish to find the length of the longest common sub-sequence(LCS) of X[m] and Y[n] as l(m,n), where an incomplete recursive definition for the function l(i,j) to compute the length of The LCS of X[m] and Y[n] is given below:l(i,j) = 0, if either i=0 or j=0 = expr1, if i,j > 0 and X[i-1] = Y[j-1] = expr2, if i,j > 0 and X[i-1] != Y[j-1]a)expr1 ≡ l(i-1, j) + 1b)expr1 ≡ l(i, j-1)c)expr2 ≡ max(l(i-1, j), l(i, j-1))d)expr2 ≡ max(l(i-1,j-1),l(i,j))Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences X[m] and Y[n] of lengths m and n respectively, with indexes of X and Y starting from 0. We wish to find the length of the longest common sub-sequence(LCS) of X[m] and Y[n] as l(m,n), where an incomplete recursive definition for the function l(i,j) to compute the length of The LCS of X[m] and Y[n] is given below:l(i,j) = 0, if either i=0 or j=0 = expr1, if i,j > 0 and X[i-1] = Y[j-1] = expr2, if i,j > 0 and X[i-1] != Y[j-1]a)expr1 ≡ l(i-1, j) + 1b)expr1 ≡ l(i, j-1)c)expr2 ≡ max(l(i-1, j), l(i, j-1))d)expr2 ≡ max(l(i-1,j-1),l(i,j))Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences X[m] and Y[n] of lengths m and n respectively, with indexes of X and Y starting from 0. We wish to find the length of the longest common sub-sequence(LCS) of X[m] and Y[n] as l(m,n), where an incomplete recursive definition for the function l(i,j) to compute the length of The LCS of X[m] and Y[n] is given below:l(i,j) = 0, if either i=0 or j=0 = expr1, if i,j > 0 and X[i-1] = Y[j-1] = expr2, if i,j > 0 and X[i-1] != Y[j-1]a)expr1 ≡ l(i-1, j) + 1b)expr1 ≡ l(i, j-1)c)expr2 ≡ max(l(i-1, j), l(i, j-1))d)expr2 ≡ max(l(i-1,j-1),l(i,j))Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
Explore Courses for Computer Science Engineering (CSE) exam

Top Courses for Computer Science Engineering (CSE)

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev