Find the rth "0" in specific columns in a matrix

Hello,

In the code below, thanks to the solution by Cedric Wannaz posted here , I am able to efficiently find the first and last "0" in an n x m matrix.

n = 10;
m = 20;
M = randi([0 1], n,m);

%%Start and Goal Points
[r1,c1] = ind2sub( size( M ), find( M(:) == 0, 1, 'first' )); % Start Point
[r2,c2] = ind2sub( size( M ), find( M(:) == 0, 1, 'last' ));  % Goal Point

How do I go about finding the 3rd or 4th or the rth "0" in any column. For example, how to find the index of the 3rd "0" in the 6th column?

Thanks.

Answer 1

[Andrei Bobrov]

cols = [1 3 4 6 7]; % selected columns.
num_zeros = [3,4];% The ordinal number "0" in each selected column.

M_nozeros = cumsum(~M).*~M;
[~,ii] = ismember(M_nozeros(:,cols),num_zeros);
[k,jj] = ndgrid(1:size(M,1),cols);
idx = [k(:),jj(:)];
out = accumarray(ii(:) + 1,1:numel(ii),[],@(x){idx(x,:)});
out = out(2:end);

out - cell array, here each cell corresponds to the ordinal number "0" ( num_zeros), each cell contains a double matrix: rows are the ordinal number of the row containing zero, the columns correspond to cols.

Use:

>> cols = [1 3 4 6 7]; % selected columns.
num_zeros = [3,4];% The ordinal number "0" in each selected column.
M = rand(15,10) < .25
M =
  15×10 logical array
   0   0   0   0   1   0   0   0   0   0
   0   0   0   0   0   0   1   0   0   1
   1   0   0   1   1   0   0   0   0   1
   0   0   0   1   0   0   1   0   0   0
   0   0   0   0   1   0   0   0   0   0
   0   0   0   1   1   0   0   0   0   0
   0   1   0   0   0   1   0   0   0   0
   0   1   0   0   0   0   0   0   1   1
   1   0   1   0   0   1   0   0   0   0
   0   0   0   0   0   0   0   0   0   0
   1   0   0   0   0   0   1   0   0   0
   0   0   0   1   1   1   1   1   0   1
   0   0   0   0   0   0   1   0   0   0
   0   0   1   0   0   1   1   0   0   0
   1   0   0   0   0   0   1   0   0   0
>> 
>> M_nozeros = cumsum(~M).*~M;
[~,ii] = ismember(M_nozeros(:,cols),num_zeros);
[k,jj] = ndgrid(1:size(M,1),cols);
idx = [k(:),jj(:)];
out = accumarray(ii(:) + 1,1:numel(ii),[],@(x){idx(x,:)});
out = out(2:end);
>> 
>> out{:}
ans =
     4     1
     3     3
     3     6
     5     4
     5     7
ans =
     4     6
     5     1
     6     7
     4     3
     7     4
>>

Answer 2

[Image Analyst]

In general:

rows = 10;
columns = 16;
M = randi([0 1], rows,columns)
r = 2  % Whatever...
% Start and Goal Points
linearIndexes = find( M(:) == 0, r, 'first' )
[r1,c1] = ind2sub( size( M ), linearIndexes(end)) % Start Point
linearIndexes = find( M(:) == 0, r, 'last' )
[r2,c2] = ind2sub( size( M ), linearIndexes(1))  % Goal Point