USACO Section 2.2: Party Lamps

/*
ID: yingzho1
LANG: C++
TASK: lamps
*/
#include <iostream>
#include <fstream>
#include <string>
#include <map>
#include <vector>
#include <set>
#include <algorithm>
#include <stdio.h>
#include <queue>
#include <cstring>

using namespace std;

ifstream fin("lamps.in");
ofstream fout("lamps.out");

int N, depsum;

bool check(string s, vector<int> &on, vector<int> &off) {
for (int i = 0; i < on.size(); i++) {
if (s[on[i]] != '1') return false;
}
for (int i = 0; i < off.size(); i++) {
if (s[off[i]] != '0') return false;
}
return s.size();
}

void dfs(set<string> &res, int c1, int c2, int c3, int c4, string s, vector<int> &on, vector<int> &off, int dep) {
if (check(s, on, off)) {
if (dep <= depsum && (depsum-dep)%2 == 0) {
res.insert(s);
//return;
}
}
if (dep == 4 || dep > depsum) return;
string pre = s;
if (c1 < 1) {
dfs(res, c1+1, c2, c3, c4, s, on, off, dep+1);
for (int i = 0; i < s.size(); i++) {
if (s[i] == '0') s[i] = '1';
else s[i] = '0';
}
dfs(res, c1+1, c2, c3, c4, s, on, off, dep+1);
}

s = pre;

if (c2 < 1) {
dfs(res, c1, c2+1, c3, c4, s, on, off, dep+1);
for (int i = 0; i < s.size(); i++) {
if (i % 2 == 1) {
if (s[i] == '1') s[i] = '0';
else s[i] = '1';
}
}
dfs(res, c1, c2+1, c3, c4, s, on, off, dep+1);
}

s = pre;
if (c3 < 1) {
dfs(res, c1, c2, c3+1, c4, s, on, off, dep+1);
for (int i = 0; i < s.size(); i++) {
if (i % 2 == 0) {
if (s[i] == '1') s[i] = '0';
else s[i] = '1';
}
}
dfs(res, c1, c2, c3+1, c4, s, on, off, dep+1);
}

s = pre;
if (c4 < 1) {
dfs(res, c1, c2, c3, c4+1, s, on, off, dep+1);
for (int i = 0; i < s.size(); i++) {
if (i % 3 == 0) {
if (s[i] == '1') s[i] = '0';
else s[i] = '1';
}
}
dfs(res, c1, c2, c3, c4+1, s, on, off, dep+1);
}

s = pre;
}

int main()
{
fin >> N >> depsum;
string s(N, '1');
int n;
vector<int> on, off;
//cout << N << " " << depsum << endl;
while (fin >> n && n != -1) on.push_back(n-1);
while (fin >> n && n != -1) off.push_back(n-1);
//for (int i = 0; i < on.size(); i++) cout << on[i] << endl;
//for (int i = 0; i < off.size(); i++) cout << off[i] << endl;
set<string> res;
dfs(res, 0, 0, 0, 0, s, on, off, 0);
vector<string> ret;
for (set<string>::iterator it = res.begin(); it != res.end(); it++) ret.push_back(*it);
sort(ret.begin(), ret.end());
if (ret.size() == 0) {
fout << "IMPOSSIBLE" << endl;
return 0;
}
for (int i = 0; i < ret.size(); i++) {
fout << ret[i] << endl;
}

return 0;
}