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Maximum Subarray Problem -- Classic Algorithms in Matlab

Asked by Matlab2010 on 13 Mar 2014
Latest activity Commented on by Salaheddin Hosseinzadeh on 13 Mar 2014
Trying to implement some forms of this classic algorithm
Not quite there; anyone fancy having a look at the O(n log n) and O(n) attempts -- working from the PDF above.
function MaxSubArrayProblem()
clc;
A = randn(100,1);
tic;
B1=MaxSubArray_BruteForce(A); %O(n^3)
t1=toc;
tic;
B2=MaxSubArray_reUseData(A); %O(n^2)
t2=toc;
tic;
B3=MaxSubArray_divideAndConquer(A); %O(n log n)
t3=toc;
tic;
B4=MaxSubArray_revisualizing(A); %O(n)
t4=toc;
isequaln(B1,B2,B3,B4)
bar([t1 t2 t3 t4]);
end
function B= MaxSubArray_BruteForce(A)
B= NaN(length(A),3);
VMAX = -inf;
for i = 1 : length(A)
for j = i: length(A)
V = sum(A(i:j));
if(V>VMAX)
VMAX = V;
from = i;
to = j;
end
end
disp(['Largest Sum: ' num2str(VMAX) ' from ' num2str(from) ' to ' num2str(to)]);
B(i,:) = [VMAX from to];
end
end
function B= MaxSubArray_reUseData(A)
B= NaN(length(A),3);
VMAX = -inf;
for i = 1 : length(A)
V = 0;
for j = i: length(A)
V = V + A(j);
if(V>VMAX)
VMAX = V;
from = i;
to = j;
end
end
disp(['Largest Sum: ' num2str(VMAX) ' from ' num2str(from) ' to ' num2str(to)]);
B(i,:) = [VMAX from to];
end
end
function B= MaxSubArray_divideAndConquer(A)
B= NaN(length(A),3);
for i = 1: length(A)
for j = 1: length(A)
myMax = MCS(A,i,j);
end
B(i,:) = [myMax i j];
end
end
function myMax = MCS(A,i,j)
if(i==j)
myMax = A(i:j);
else
myMax1 = MCS(A,i,floor(0.5*(i+j)));
myMax2 = MCS(A,floor(0.5*(i+j))+1,j);
myMax3 = MCS(A,i,j);
myMax = max([myMax1 myMax2 myMax3]);
end
end
function B= MaxSubArray_revisualizing(A)
B= NaN(length(A),3);
VMAX = -inf;
from = 1;
T = A(1);
V = A(1);
Tmin = min(0,T);
for j = 2: length(A)
T = T + A(j);
if((T-Tmin)>V)
V = T - Tmin;
%
VMAX = V;
to = j;
end
if(T<Tmin)
Tmin = T;
from = j;
end
disp(['Largest Sum: ' num2str(VMAX) ' from ' num2str(from) ' to ' num2str(to)]);
B(j,:) = [VMAX from to];
end
end

  1 Comment

Is there a problem with this code? If there is then let us know about it plz, I don't have the beloved MATLAB to run this code ATM!

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