M = zeros(P_size); for ii = 1:P_size for jj = 1:P_size

if P_cond(ii,jj) == 0 && r_cov(ii) == 0 && c_cov(jj) == 0 M(ii,jj) = 1; r_cov(ii) = 1; c_cov(jj) = 1; end end end

r_cov = zeros(P_size,1); % A vector that shows if a row is covered c_cov = zeros(P_size,1); % A vector that shows if a column is covered stepnum = 3;

function [c_cov,stepnum] = step3(M,P_size) c_cov = sum(M,1);

if sum(c_cov) == P_size stepnum = 7; else

stepnum = 4; end

function [M,r_cov,c_cov,Z_r,Z_c,stepnum] = step4(P_cond,r_cov,c_cov,M) P_size = length(P_cond); zflag = 1; while zflag

row = 0; col = 0; exit_flag = 1; ii = 1; jj = 1; while exit_flag

if P_cond(ii,jj) == 0 && r_cov(ii) == 0 && c_cov(jj) == 0 row = ii; col = jj;

exit_flag = 0; end

jj = jj + 1;

if jj > P_size; jj = 1; ii = ii+1; end if ii > P_size; exit_flag = 0; end end

if row == 0 stepnum = 6; zflag = 0; Z_r = 0; Z_c = 0; else

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M(row,col) = 2;

if sum(find(M(row,:)==1)) ~= 0 r_cov(row) = 1;

zcol = find(M(row,:)==1); c_cov(zcol) = 0; else

stepnum = 5; zflag = 0; Z_r = row; Z_c = col; end end end

function [M,r_cov,c_cov,stepnum] = step5(M,Z_r,Z_c,r_cov,c_cov) zflag = 1; ii = 1;

while zflag

rindex = find(M(:,Z_c(ii))==1); if rindex > 0 ii = ii+1;

Z_r(ii,1) = rindex;

Z_c(ii,1) = Z_c(ii-1); else

zflag = 0; end

if zflag == 1;

cindex = find(M(Z_r(ii),:)==2); ii = ii+1;

Z_r(ii,1) = Z_r(ii-1); Z_c(ii,1) = cindex; end end

for ii = 1:length(Z_r)

if M(Z_r(ii),Z_c(ii)) == 1 M(Z_r(ii),Z_c(ii)) = 0; else

M(Z_r(ii),Z_c(ii)) = 1; end end

r_cov = r_cov.*0; c_cov = c_cov.*0; M(M==2) = 0;

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stepnum = 3;

function [P_cond,stepnum] = step6(P_cond,r_cov,c_cov) a = find(r_cov == 0); b = find(c_cov == 0);

minval = min(min(P_cond(a,b)));

P_cond(find(r_cov == 1),:) = P_cond(find(r_cov == 1),:) + minval; P_cond(:,find(c_cov == 0)) = P_cond(:,find(c_cov == 0)) - minval; stepnum = 4;

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