Write an efficient algorithm (to the best of your knowledge) for the following probler describe why it is a correct algorithm, and analyze the time complexity. If you cannot polynomial-time algorithm, then give a backtracking algorithm. Problem: Array Sum Input: A 2D array A[1...n][1..n] of integers with n rows and n columns. No number in this array.

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Please help with this algorithm problem

Write an efficient algorithm (to the best of your knowledge) for the following problem, briefly
describe why it is a correct algorithm, and analyze the time complexity. If you cannot find any
polynomial-time algorithm, then give a backtracking algorithm.
Problem: Array Sum
Input: A 2D array A[1...n][1...n] of integers withn rows and n columns. No number is repeated
in this array.
• Output: Return true - if there are exactly n numbers, one from each row, such that the sum of
the numbers is 0. Otherwise, return false.
Example: Input: A = [5,7,-2; 3,-4,1; 20, 10, 30]. Here we have n = 3. Output: False
Example: Input: A = [-2,4,1; 3,10,5; -8,12,-9]. Here we have n = 3. Output: True (because we have
4 from the first row, 5 from the second row, and -9 from the third row).
Transcribed Image Text:Write an efficient algorithm (to the best of your knowledge) for the following problem, briefly describe why it is a correct algorithm, and analyze the time complexity. If you cannot find any polynomial-time algorithm, then give a backtracking algorithm. Problem: Array Sum Input: A 2D array A[1...n][1...n] of integers withn rows and n columns. No number is repeated in this array. • Output: Return true - if there are exactly n numbers, one from each row, such that the sum of the numbers is 0. Otherwise, return false. Example: Input: A = [5,7,-2; 3,-4,1; 20, 10, 30]. Here we have n = 3. Output: False Example: Input: A = [-2,4,1; 3,10,5; -8,12,-9]. Here we have n = 3. Output: True (because we have 4 from the first row, 5 from the second row, and -9 from the third row).
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