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
In the context of the subset sum problem, you are tasked with determining if there exists a subset of a given set of integers that sums to a specified value, W. This problem can be approached using dynamic programming, which builds a table (array X) to keep track of achievable sums.
Dynamic Programming Table Structure
- The table X is typically structured such that:
- Rows represent the first 'n' elements of the set.
- Columns represent possible sums from 0 to W.
Key Entries in the Table
- X[i, j] indicates whether a sum of 'j' can be achieved using the first 'i' elements of the array.
Why X[n, W] Implies a Subset Exists
- The entry X[n, W] represents whether it is possible to form the sum W using all 'n' elements of the array.
- If X[n, W] is TRUE, it means that there exists at least one subset of the given set that sums to W.
Other Options Explained
- X[1, W]: This only considers the first element. It cannot determine the overall possibility for 'n' elements.
- X[n, 0]: This indicates that a sum of 0 can always be achieved by taking an empty subset, which does not provide information about achieving the sum W.
- X[n - 1, n]: This does not relate directly to the target sum W and is not a valid entry for checking the subset sum condition.
Conclusion
Thus, the correct answer is option C: X[n, W], as it conclusively indicates the existence of a subset that sums to W when TRUE.
In the context of the subset sum problem, you are tasked with determining if there exists a subset of a given set of integers that sums to a specified value, W. This problem can be approached using dynamic programming, which builds a table (array X) to keep track of achievable sums.
Dynamic Programming Table Structure
- The table X is typically structured such that:
- Rows represent the first 'n' elements of the set.
- Columns represent possible sums from 0 to W.
Key Entries in the Table
- X[i, j] indicates whether a sum of 'j' can be achieved using the first 'i' elements of the array.
Why X[n, W] Implies a Subset Exists
- The entry X[n, W] represents whether it is possible to form the sum W using all 'n' elements of the array.
- If X[n, W] is TRUE, it means that there exists at least one subset of the given set that sums to W.
Other Options Explained
- X[1, W]: This only considers the first element. It cannot determine the overall possibility for 'n' elements.
- X[n, 0]: This indicates that a sum of 0 can always be achieved by taking an empty subset, which does not provide information about achieving the sum W.
- X[n - 1, n]: This does not relate directly to the target sum W and is not a valid entry for checking the subset sum condition.
Conclusion
Thus, the correct answer is option C: X[n, W], as it conclusively indicates the existence of a subset that sums to W when TRUE.
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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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