Question

matlab( answer the question in matlab)

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W a rnction to find the largest product of adjacent number pairs in a matrix, where pair combinations can be selected the horsonal accent or vertically adjacent (but not diagonally adjacent) of numbers in a matrix are accent if they are in the same row or column and located next to each other when the 2D matrix is displayed The largest product of a pair of adjacent numbers could be located horizontally as in a below or vertically, as in below. The product is the multiplication of the two pair values Note that the largest number is not always a member of the largest product of a pair (see 96 in b) 82 9228 97 91 64 55 18 13 10 96 98 98 15 80 494396 81 92 66 4 75 85 40 94 66 68 18 76 71 4 28 5 10 83 70 39 45 32 77 65 96 8071 4 1976 44 49 28 Inputs and O ut Input Your function must accept one input argument, which will be the input matrix variable. The input matrix will definitely be numerical but there is no fixed size and your function must be able to handle any number of rows or columns. The matrix is two-dimensional - matrices of higher dimensions will not be used Output: Your function must output one number only - the largest product of any adjacent pair in the matrix. You do not have to output the location of the pair of numbers, only the product, How your function will be tested Marks will be awarded for program correctness, correct filename, enough comments and error-free execution. Your function will be automatically tested with a large variety of randomly generated matrices of random sizes and checked for correct output each time. An example of how the above two matrices would be checked is given below. >> a = randi (100, [37]); >> b - randi (100, (5 6)); >> C-maxpairs (a) 9408 >d - maxpairs (b) 7990

Answer 1

The MATLAB Code is given as follows:

function maxprod=maxpairs(a)
    [m,n]=size(a); % find the order of the matrix m-rows n-columns
    maxprod=0; % initialize maxproduct to 0
    for i=1:m
        for j=1:n
            %Find the neighbours of the given element a(i,j)
            neighbour=[0 0 0 0]; % an element in the matrix can have a maximum of 4 neighbours eliminating
            %the diagonal neighbours. So we initialize an array of size 4
            %to store the neighbours of each element in the matrix.
            % In case an element does not have a neighbour, the neigbour
            % value will be maintained as 0.
            if i-1>0 % TOP neighbour
                %top neighbour will not be available for the first row
                % elements. Hence i-1>0 condition should be verified
                % because i-1 will be 0 for top row elements
                neighbour(1)=a(i-1,j);
            end
            if i+1<=m %BOTTOM neighbour
                %bottom neighbour will not be available for the last row
                %elements. Hence i+1<=m condition should be verified
                %because i+1 will be >m for bottom row elements
                neighbour(2)=a(i+1,j);
            end
            if j+1<=n %RIGHT neighbour
                %right neighbour will not be available for the last column
                %elements. Hence j+1<=n condition should be because j+1
                %will be >n for last column elements
                neighbour(3)=a(i,j+1);
            end
            if j-1>0 %LEFT neighbour
                %left neighbour will not be available for the last column
                %elements. Hence j-1>0 condition should be verified because
                %j-1 will be 0 for first column elements
                neighbour(4)=a(i,j-1);
            end
            for k=1:4 % check the product of matrix element with every neighbour
                prod=a(i,j)*neighbour(k);
                if(prod>maxprod) %if the product is larger than maxprod, update maxprod with the value of prod
                    maxprod=prod;
                end
            end
        end
    end
end

TILL I function maxprod=maxpairs(a) [m, n]=size(a); $ find the order of the matrix m-rows n-columns maxprod=0; $initialize maxproduct to O for i=1:m for j=1:n Find the neighbours of the given element a(i,)) neighbour=[0 0 0 0]; an element in the matrix can have a maximum of 4 neighbours eliminating $the diagonal neighbours. So we initialize an array of size 4 fto store the neighbours of each element in the matrix. % In case an element does not have a neighbour, the neigbour $value will be maintained as 0. if i-l>0 & TOP neighbour Stop neighbour will not be available for the first row 4 elements. Hence i-l>o condition should be verified because i-l will be o for top row elements neighbour (1) =a (i-1,3); end if i+l<=m BOTTOM neighbour tbottom neighbour will not be available for the last row felements. Hence i+l<=m condition should be verified because i+l will be >m for bottom row elements neighbour (2) =a (i+1,1); end if j+l<=n RIGHT neighbour fright neighbour will not be available for the last column TI

felements. Hence 1+1<=n condition should be because 3+1 twill be >n for last column elements neighbour (3) =a (i, j+1); end if j-1>0 SLEFT neighbour *left neighbour will not be available for the last column felements. Hence j-1>0 condition should be verified because *j-1 will be o for first column elements neighbour (4) =a (i,j-1); end for k=1:4 & check the product of matrix element with every neighbour prod=a (i,j) *neighbour (k); if(prod>maxprod) fif the product is larger than maxprod, update maxprod with the value of prod maxprod=prod; end TITIIIIIIII end

OUTPUT:

>> a=randi (100, [37]) a = 82 80 65 38 82 54 52 88 >> c=maxpairs(a) 8272 fx >> |

>> b=randi (100, [5 6]) b = 23 93 44 27 30 27 18 44 12 613281 23 1926 72 433 44 91 41 23 51 93 32 98 60 12 9 74 >> c=maxpairs (b) 8918