Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > In the above question, which entry of the arr...
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In the above question, which entry of the array X, if TRUE, implies that there is a subset whose elements sum to W?
- a)X[1, W]
- b)X[n ,0]
- c)X[n, W]
- d)X[n -1, n]
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In the above question, which entry of the array X, if TRUE, implies th...
If we get the entry X[n, W] as true then there is a subset of {a1, a2, .. an} that has sum as W.
Most Upvoted Answer
In the above question, which entry of the array X, if TRUE, implies th...
Understanding the Problem
The question revolves around the subset sum problem, a classic problem in computer science where the goal is to determine whether there's a subset of a given set of integers that adds up to a specific target sum, W.
Dynamic Programming Approach
In a dynamic programming table (often denoted as X), the entries represent whether a certain sum can be achieved using the first 'n' items. The table is structured such that:
- Rows correspond to the items (0 to n).
- Columns correspond to possible sums (0 to W).
Key Entry of Interest
- X[n, W]: This entry indicates whether a sum of W can be achieved using all 'n' items.
Why X[n, W] is the Correct Answer
- If X[n, W] is TRUE, it means that it is possible to form the sum W using any of the items available (from 1 to n).
- This signifies that there exists at least one subset composed of the given integers that sums up to W.
Analysis of Other Options
- X[1, W]: This entry only considers the first item. It cannot confirm the existence of a subset across all items.
- X[n, 0]: This entry will always be TRUE since a sum of 0 can always be achieved by choosing an empty subset.
- X[n - 1, n]: This entry does not relate to the specific sum W but rather compares a sum to the count of items, which is irrelevant in this context.
Conclusion
In summary, X[n, W] is the definitive indicator that a subset exists with the desired sum W. Thus, option 'C' is the correct answer.
The question revolves around the subset sum problem, a classic problem in computer science where the goal is to determine whether there's a subset of a given set of integers that adds up to a specific target sum, W.
Dynamic Programming Approach
In a dynamic programming table (often denoted as X), the entries represent whether a certain sum can be achieved using the first 'n' items. The table is structured such that:
- Rows correspond to the items (0 to n).
- Columns correspond to possible sums (0 to W).
Key Entry of Interest
- X[n, W]: This entry indicates whether a sum of W can be achieved using all 'n' items.
Why X[n, W] is the Correct Answer
- If X[n, W] is TRUE, it means that it is possible to form the sum W using any of the items available (from 1 to n).
- This signifies that there exists at least one subset composed of the given integers that sums up to W.
Analysis of Other Options
- X[1, W]: This entry only considers the first item. It cannot confirm the existence of a subset across all items.
- X[n, 0]: This entry will always be TRUE since a sum of 0 can always be achieved by choosing an empty subset.
- X[n - 1, n]: This entry does not relate to the specific sum W but rather compares a sum to the count of items, which is irrelevant in this context.
Conclusion
In summary, X[n, W] is the definitive indicator that a subset exists with the desired sum W. Thus, option 'C' is the correct answer.
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In the above question, which entry of the array X, if TRUE, implies that there is a subset whose elements sum to W?a)X[1, W]b)X[n ,0]c)X[n, W]d)X[n -1, n]Correct answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 In the above question, which entry of the array X, if TRUE, implies that there is a subset whose elements sum to W?a)X[1, W]b)X[n ,0]c)X[n, W]d)X[n -1, n]Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the above question, which entry of the array X, if TRUE, implies that there is a subset whose elements sum to W?a)X[1, W]b)X[n ,0]c)X[n, W]d)X[n -1, n]Correct answer is option 'C'. Can you explain this answer?.
In the above question, which entry of the array X, if TRUE, implies that there is a subset whose elements sum to W?a)X[1, W]b)X[n ,0]c)X[n, W]d)X[n -1, n]Correct answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 In the above question, which entry of the array X, if TRUE, implies that there is a subset whose elements sum to W?a)X[1, W]b)X[n ,0]c)X[n, W]d)X[n -1, n]Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the above question, which entry of the array X, if TRUE, implies that there is a subset whose elements sum to W?a)X[1, W]b)X[n ,0]c)X[n, W]d)X[n -1, n]Correct answer is option 'C'. Can you explain this answer?.
Solutions for In the above question, which entry of the array X, if TRUE, implies that there is a subset whose elements sum to W?a)X[1, W]b)X[n ,0]c)X[n, W]d)X[n -1, n]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).
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