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#include <vector>
#include <array>
#include <numeric>
#include <iostream>
constexpr size_t M = 3;
constexpr size_t N = 3;
template<size_t MM, size_t NN>
using Mat = std::array<std::array<int8_t,MM*NN>,MM*NN>;
template<size_t MM, size_t NN>
using Vec = std::array<int8_t,MM*NN>;
template<size_t MM, size_t NN>
struct point {
point():x{0},y{0}{}
point(size_t x_, size_t y_):x{x_},y{y_}{}
size_t x,y;
point& inc() {
point& ret = *this;
++y;
if(y >= NN){
++x;
y -= NN;
}
return *this;
}
size_t stride() const {
return x + y*NN;
}
bool equal(const point& rhs) const {
return (x == rhs.x && y == rhs.y);
}
};
template<size_t MM, size_t NN>
void print_vec(const Vec<MM,NN>& x){
for(size_t j = 0; j < NN; ++j){
for(size_t i = 0; i < MM; ++i){
point<MM,NN> ind{i,j};
std::cout<<x[ind.stride()]<<" ";
}
std::cout<<"\n";
}
std::cout<<std::endl;
}
template<size_t MM, size_t NN>
void print_perm(const std::array<size_t,MM*NN>& x){
for(size_t j = 0; j < MM*NN; ++j){
std::cout<<x[j]<<"\n";
}
std::cout<<std::endl;
}
template<size_t MM, size_t NN>
void print_mat(const Mat<MM,NN>& x, const std::array<size_t,MM*NN>& P){
for(size_t j = 0; j < MM*NN; ++j){
for(size_t i = 0; i < MM*NN; ++i){
std::cout<<x[P[j]][i]<<" ";
}
std::cout<<"\n";
}
std::cout<<std::endl;
}
template<size_t MM, size_t NN>
bool lu_decompose_gf2(Mat<MM,NN>& R, std::array<size_t,MM*NN>& P){
for(size_t i = 0; i < MM*NN; ++i){
bool found_pivot = false;
size_t pivot_row = i;
for(size_t k = i; k < MM*NN && (not found_pivot); ++k){
if(R[P[k]][i]){
found_pivot = true;
pivot_row = k;
}
}
if(not found_pivot){
return false;
}else if ( i != pivot_row ){
std::swap(P[i],P[pivot_row]);
}
for(size_t k = i+1u; k < MM*NN; ++k){
if(R[P[k]][i]){
for(size_t j = i+1u; j < MM*NN; ++j){
R[P[k]][j] ^= (R[P[i]][j]);
}
}
}
}
return true;
}
template<uint64_t MM, uint64_t NN>
int solve_lights_out(std::array<int8_t,MM*NN>& b_raw){
Mat<M,N> A;
constexpr size_t MN = M*N;
Vec<M,N> b{
1,0,1,
1,0,1,
0,0,0
};
// Works best if we use odd N's
// even N might not be solvable in roughly half of the cases
// Init
std::cout<<"Init"<<std::endl;
for(point<M,N> i{}; i.x < M && i.y < N; i.inc()){
for(point<M,N> j{}; j.x < M && j.y < N; j.inc()){
if(
(i.equal(j)) ||
(i.x == j.x && (i.y+1) == j.y) ||
(i.x == j.x && (j.y+1) == i.y) ||
(i.y == j.y && (i.x+1) == j.x) ||
(i.y == j.y && (j.x+1) == i.x)
){
A[i.stride()][j.stride()] = true;
}else{
A[i.stride()][j.stride()] = false;
}
// std::cout<<A[i.stride()][j.stride()]<<std::endl;
}
// Populate how you like it.
//b[i.stride()] = false;
}
std::array<size_t, MN> P_ident;
std::iota(P_ident.begin(),P_ident.end(),0);
print_mat<M,N>(A,P_ident);
std::array<size_t, MN> P;
std::iota(P.begin(),P.end(),0);
// Solve it :)
std::cout<<"Solve"<<std::endl;
if(!lu_decompose_gf2<M,N>(A,P)){
return -1;
}
std::array<size_t,MN> P_inv{};
for(size_t i = 0; i < MN; ++i){
P_inv[P[i]] = i;
}
Vec<M,N> y;
for(size_t i = 0; i < MN; ++i){
y[i] = b[P[i]];
for(size_t j = 0; j < i; ++j){
y[i] ^= A[P[i]][j] & y[j];
}
}
Vec<M,N> x;
for(size_t i = MN; i > 0; --i){
x[i-1] = y[i-1];
for(size_t j = i; j < MN; ++j){
x[i-1] ^= (A[P[i-1]][j] and x[j]);
}
}
return 0;
}
extern "C"{
int solve_lights_out_3_x_3(std::array<int8_t, 3u*3u>& inp){
int rc = solve_lights_out<3u,3u>(inp);
return rc;
}
int fake_main(){
Mat<M,N> A;
constexpr size_t MN = M*N;
Vec<M,N> b{
1,0,1,
1,0,1,
0,0,0
};
// Works best if we use odd N's
// even N might not be solvable in roughly half of the cases
// Init
std::cout<<"Init"<<std::endl;
for(point<M,N> i{}; i.x < M && i.y < N; i.inc()){
for(point<M,N> j{}; j.x < M && j.y < N; j.inc()){
if(
(i.equal(j)) ||
(i.x == j.x && (i.y+1) == j.y) ||
(i.x == j.x && (j.y+1) == i.y) ||
(i.y == j.y && (i.x+1) == j.x) ||
(i.y == j.y && (j.x+1) == i.x)
){
A[i.stride()][j.stride()] = true;
}else{
A[i.stride()][j.stride()] = false;
}
// std::cout<<A[i.stride()][j.stride()]<<std::endl;
}
// Populate how you like it.
//b[i.stride()] = false;
}
std::array<size_t, MN> P_ident;
std::iota(P_ident.begin(),P_ident.end(),0);
print_mat<M,N>(A,P_ident);
std::array<size_t, MN> P;
std::iota(P.begin(),P.end(),0);
// Solve it :)
std::cout<<"Solve"<<std::endl;
if(!lu_decompose_gf2<M,N>(A,P)){
return -1;
}
std::array<size_t,MN> P_inv{};
for(size_t i = 0; i < MN; ++i){
P_inv[P[i]] = i;
}
std::cout<<"LR"<<std::endl;
print_mat<M,N>(A,P);
std::cout<<"P"<<std::endl;
print_perm<M,N>(P);
std::cout<<"Lights-Off puzzle"<<std::endl;
print_vec<M,N>(b);
Vec<M,N> y;
for(size_t i = 0; i < MN; ++i){
y[i] = b[P[i]];
for(size_t j = 0; j < i; ++j){
y[i] ^= A[P[i]][j] & y[j];
}
}
Vec<M,N> x;
for(size_t i = MN; i > 0; --i){
x[i-1] = y[i-1];
for(size_t j = i; j < MN; ++j){
x[i-1] ^= (A[P[i-1]][j] and x[j]);
}
}
std::cout<<"Solution"<<std::endl;
print_vec<M,N>(x);
return 0;
}
}
int main(){
return fake_main();
}
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