Data Structure Questions and Answers-Maximum Sum Rectangle in a 2D Matrix

 

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Data Structure Questions and Answers-Maximum Sum Rectangle in a 2D Matrix

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Question 1
Given a 2D matri, x find a submatrix that has the maximum sum. Which of the following methods can be used to solve this problem?
A
Brute force
B
Recursion
C
Dynamic programming
D
All of the mentioned
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Question 1 Explanation: 
All of the mentioned methods can be used to solve the above problem.

Question 2
In which of the following cases, the maximum sum rectangle is the 2D matrix itself?
A
When all the elements are negative
B
When all the elements are positive
C
When some elements are positive and some negative
D
None of the mentioned
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Question 2 Explanation: 
When all the elements of a matrix are positive, the maximum sum rectangle is the 2D matrix itself.

Question 3
In which of the following cases, the maximum sum rectangle can be a 1 x 1 matrix containing the largest element?
A
When the matrix is a 1×1 matrix
B
When all the elements of a matrix are zero
C
When all the elements of the matrix are negative
D
All of the mentioned
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Question 3 Explanation: 
In all of the above cases, the maximum sum rectangle is a 1×1 matrix containing the largest element.

For the case, when all elements are zero, any submatrix can be chosen and 1×1 submatrix is a possible solution.

Question 4
Consider a matrix in which all the elements are non-zero(at least one positive and at least one negative element). In this case, the sum of the elements of the maximum sum rectangle cannot be zero.
A
True
B
False
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Question 4 Explanation: 
If a matrix contains all non-zero elements with at least one positive and at least on negative element, then the sum of elements of the maximum sum rectangle cannot be zero.

Question 5
Consider the 2×3 matrix {{1, 2, 3}, {1, 2, 3}}. What is the sum of elements of the maximum sum rectangle?
A
3
B
6
C
12
D
18
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Question 5 Explanation: 
Since all the elements of the 2×3 matrix are positive, the maximum sum rectangle is the matrix itself and the sum of elements is 12.

There are 5 questions to complete.

 

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