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

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monkey_matlab on 27 Oct 2017
Edited: Andrei Bobrov on 27 Oct 2017
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.

Andrei Bobrov on 27 Oct 2017
Edited: Andrei Bobrov on 27 Oct 2017
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
>>

Image Analyst on 27 Oct 2017
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

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