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#include

#include

#define null NULL

#define enter putchar(10)

#define space putchar(32)

#define rg(i, a, b, s) for(auto i = a; (b > a)?(i < b):(i > b); i += s)

#define INF USHRT_MAX

#define END LONG_LONG_MIN

#define var_name(x) #x

#define print_container(c) printf("Elements in container %s: \n", var_name(c)); for(auto x: c) {cout << to_string(x) << endl;}

using namespace std;

typedef long long ll;

typedef unsigned short int usi;

typedef unsigned int ui;

inline string to_string(string _s){

return(_s);

}

template

string to_string(pair p){

string _r = "

_r += to_string(p.first);

_r += ", ";

_r += to_string(p.second);

_r += ">";

return(_r);

}

HANDLE handle = GetStdHandle(STD_OUTPUT_HANDLE);

usi sum = 0;

usi Matrix[9][9] = {0};

size_t _Hash(const pair &p){

return(2 * pow(p.first, 2) + 3 * pow(p.second, 3));

}

/*初始化时的点坐标集合*/

unordered_set, decltype(&_Hash)> s(0, _Hash);

/*后续填入的点坐标集合*/

unordered_set, decltype(&_Hash)> has_filled(0, _Hash);

ll num_of_solutions = 0;

inline void insert_pair(usi a, usi b){

s.insert(make_pair(a, b));

}

void Initiation(){

Matrix[5][2] = Matrix[0][8] = 1;

insert_pair(5, 2);

insert_pair(0, 8);

Matrix[0][5] = Matrix[4][1] = Matrix[1][8] = 2;

insert_pair(0, 5);

insert_pair(4, 1);

insert_pair(1, 8);

Matrix[6][0] = 3;

insert_pair(6, 0);

Matrix[2][6] = Matrix[5][5] = 4;

insert_pair(2, 6);

insert_pair(5, 5);

Matrix[8][1] = Matrix[7][6] = 5;

insert_pair(8, 1);

insert_pair(7, 6);

Matrix[3][0] = Matrix[1][4] = Matrix[6][1] = 6;

insert_pair(3, 0);

insert_pair(1, 4);

insert_pair(6, 1);

Matrix[7][2] = Matrix[8][5] = Matrix[5][3] = 7;

insert_pair(7, 2);

insert_pair(8, 5);

insert_pair(5, 3);

Matrix[3][4] = Matrix[8][8] = 8;

insert_pair(3, 4);

insert_pair(8, 8);

Matrix[0][1] = Matrix[8][0] = 9;

insert_pair(0, 1);

insert_pair(8, 0);

}

inline void print_matrix(){

rg(i, 0, 9, 1){

rg(j, 0, 9, 1){

if(s.find(make_pair(i, j)) != s.end()){

SetConsoleTextAttribute(handle, FOREGROUND_RED);

}else{

SetConsoleTextAttribute(handle, FOREGROUND_GREEN);

}

printf("%hu", Matrix[i][j]);

if(j < 8){

space;

}

}

enter;

}

SetConsoleTextAttribute(handle, FOREGROUND_BLUE | FOREGROUND_GREEN | FOREGROUND_RED);

}

/*获取a行b列位置的度，返回的是这个位置“附近”的数字集合，度就是该集合的size，显然在这个位置填入的数字不能在此集合中*/

inline unordered_set get_cnt(usi a, usi b){

unordered_set _s;

rg(i, a / 3 * 3, (a + 3) / 3 * 3, 1){

rg(j, b / 3 * 3, (b + 3) / 3 * 3, 1){

if(Matrix[i][j] != 0){

_s.insert(Matrix[i][j]);

}

}

}

rg(i, 0, 9, 1){

if(Matrix[a][i] != 0){

_s.insert(Matrix[a][i]);

}

if(Matrix[i][b] != 0){

_s.insert(Matrix[i][b]);

}

}

return(_s);

}

void do_fill(){

if(sum == 81 - s.size()){

printf("第%lld组解：\n", ++num_of_solutions);

print_matrix();

system("pause");

return;

}

/*index表示接下来找到的度最大(或之一)的位置坐标*/

pair index;

unordered_set t;

usi max_cnt = 0;

rg(i, 0, 9, 1){

rg(j, 0, 9, 1){

if(has_filled.find(make_pair(i, j)) != has_filled.end() || s.find(make_pair(i, j)) != s.end()){

continue;

}

unordered_set _t = get_cnt(i, j);

if(_t.size() > max_cnt){

max_cnt = _t.size();

index.first = i;

index.second = j;

t = _t;

}

}

}

//printf("row: %hu, column: %hu\n", index.first, index.second);

//print_container(t);

rg(i, 0, 9, 1){

/*剪枝：在集合t中的数或者与此位置同行同列，或者在同一3*3区域内，不在此集合中的数可被选填*/

if(t.find(i + 1) == t.end()){

Matrix[index.first][index.second] = i + 1;

sum++;

has_filled.insert(index);

do_fill();

/*加上break就没有回溯搜索，只使用贪心策略求出一组解*/

//break;

Matrix[index.first][index.second] = 0;

sum--;

has_filled.erase(index);

}

}

}

int main(){

Initiation();

//print_container(s);

do_fill();

return 0;

}