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Puzzler: Quickly tell if two absolute indices (a,b) are four connected for n x m matrix.

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function flag = isFourConnected(a,b,n,m)
%
% a,b: indices of interest a ~= b
% n,m: size of matrix of interest
%
% flag: True if indices a and b are four connected
% in a matrix of size n x m
%
%
% Your code here
Note, this code should use no toolboxes, and should be reasonably quick as this function will be called many times. Reasonably quick is up to debate as the rest of the code forms.

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Andrei Bobrov
Andrei Bobrov on 2 Sep 2011
for three-dimensional array
d = abs(a-b);
flag = d == n || d == n*m || (d == 1 && mod(min(a,b), n));

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Accepted Answer

David Young
David Young on 1 Sep 2011
function flag = isFourConnected(a,b,n,m)
%
% a,b: indices of interest a ~= b
% n,m: size of matrix of interest
%
% flag: True if indices a and b are four connected
% in a matrix of size n x m
%
d = abs(a-b);
flag = d == n || (d == 1 && mod(min(a,b), n));
end

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More Answers (5)

Fangjun Jiang
Fangjun Jiang on 1 Sep 2011
Circle-shifting neighbors are considered connected.
function flag = isFourConnected(a,b,n,m)
%
% a,b: indices of interest a ~= b
% n,m: size of matrix of interest
%
% flag: True if indices a and b are four connected
% in a matrix of size n x m
%
%
% Your code here
[x,y]=ind2sub([n,m],[a;b]);
xdiff=abs(x(1)-x(2));
ydiff=abs(y(1)-y(2));
flag = ((xdiff==0) && (ydiff==1) || (ydiff==m-1)) || ...
((ydiff==0) && (xdiff==1) || (xdiff==n-1));
A little test script. All other entries so far didn't pass this test.
clc;
TestVector={6,7,4,5
6,10,4,5
1,4,4,5
1,17,4,5};
for k=1:size(TestVector,1)
if isFourConnected(TestVector{k,:})~=true
disp(k);beep;
end
end

  1 Comment

Doug Hull
Doug Hull on 1 Sep 2011
clever, I like it! First in also! Thanks (will accept after a few hours to let more people at it!)

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Walter Roberson
Walter Roberson on 1 Sep 2011
function flag = isFourConnected(a,b,n,m)
%
% a,b: indices of interest a ~= b
% n,m: size of matrix of interest
%
% flag: True if indices a and b are four connected
% in a matrix of size n x m
%
%
flag = abs(a-b)==n || (floor(a/n)==floor(b/n) && abs(a-b)==1);

  3 Comments

Walter Roberson
Walter Roberson on 1 Sep 2011
Saving a repeated calculation to a variable isn't always faster once you take the JIT into account.
That's my excuse, and I'm sticking to it :-)

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Oleg Komarov
Oleg Komarov on 1 Sep 2011
I assume a,b,m,n always numeric and integer values > 1
function flag = isFourConnected(a,b,n,m)
% a,b : indices of interest a ~= b
% m,n : size of matrix of interest
% flag: True if indices a and b are four connected
% in a matrix of size n x m
d = a-b; flag = d == n || d == -n || (d == 1 && mod(a,n) ~= 1) || (d == -1 && mod(b,n) ~= 1);

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Oleg Komarov
Oleg Komarov on 1 Sep 2011
Can't find any other valid solution to ensure bottom vs top not 4 conn except the ones already proposed.

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Bruno Luong
Bruno Luong on 1 Sep 2011
function flag = isFourConnected(a,b,n,m)
% 10 arithmetic operations by pair
c = max(a,b);
d = min(a,b);
e = c - d;
flag = (e==1 & mod(d,n)) | (e==n & c>n);

  2 Comments

Walter Roberson
Walter Roberson on 1 Sep 2011
This might or might not be slightly faster:
c = sort([a,b]);
e = c(2)-c(1);
flag = (e==1 & mod(c(1),n)) | (e==m & c(2)>n);
Or if you prefer your original structure, then instead of max/min, you could use
c = max(a,b);
d = a + b - c;
Bruno Luong
Bruno Luong on 1 Sep 2011
I believe I had one redundant test in the earlier code:
function flag = isFourConnected(a,b,n,m)
% 8 arithmetic operations by pair
c = max(a,b);
d = min(a,b);
e = c - d;
flag = (e==1 & mod(d,n)) | (e==n);

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Daniel Shub
Daniel Shub on 2 Sep 2011
I am not sure what to do about circle-shifting neighbors so I have two answers.
function flag = isFourConnected(a,b,n,m)
%
% a,b: indices of interest a ~= b
% n,m: size of matrix of interest
%
% flag: True if indices a and b are four connected
% in a matrix of size n x m
%
%
% Your code here
% Using ind2sub might be faster.
col = mod([a(:), b(:)]-1, n)+1;
row = ceil([a(:), b(:)]/n);
%[col, row] = ind2sub([n, m], [a(:), b(:)]);
flag = reshape(mod(abs(diff(col, 1, 2)), n-2)+mod(abs(diff(row, 1, 2)), m-2) == 1, size(a));
% if circle shifted points are not connected:
% flag = reshape(abs(diff(col, 1, 2))+abs(diff(row, 1, 2)) == 1, size(a));

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