Design an efficient algorithm that, given an N x M matrix A of (positive, zero and negative) integers, finds the maximum sum of a contiguous submatrix A. More precisely, a contiguous submatrix consist of the elements A, of A where i

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Design an efficient algorithm that, given an N x M matrix A of (positive, zero and
negative) integers, finds the maximum sum of a contiguous submatrix A. More
precisely, a contiguous submatrix consist of the elements A, of A where i<k ,
k<j, i'<k' , k' <j' for some i,j € [1,N] and i',j' e [1,M]. The corresponding
submatrix is B = A+k-1,i'+*-1 ·
a) Write the pseudo code of the algorithm.
b) Prove its correctness.
c) Prove an asymptotically tight bound for its time complexity.
Transcribed Image Text:Design an efficient algorithm that, given an N x M matrix A of (positive, zero and negative) integers, finds the maximum sum of a contiguous submatrix A. More precisely, a contiguous submatrix consist of the elements A, of A where i<k , k<j, i'<k' , k' <j' for some i,j € [1,N] and i',j' e [1,M]. The corresponding submatrix is B = A+k-1,i'+*-1 · a) Write the pseudo code of the algorithm. b) Prove its correctness. c) Prove an asymptotically tight bound for its time complexity.
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