This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define ll long long
#define pii pair<int, int>
#define pll pair<ll, ll>
#define F first
#define S second
using namespace std;
ll N, M;
vector<pair<int, pii>> v;
int side[100005];
signed main()
{
ios::sync_with_stdio(0), cin.tie(0);
cin >> N >> M;
for (int i = 1; i <= M; i++)
{
int a, b;
cin >> a >> b;
v.emplace_back(make_pair(i, pii{a, b}));
}
if (N <= 15)
{
for (int mask = 0; mask < (1 << M); mask++)
{
bool valid[2] = {1, 1};
for (int i = 1; i <= N; i++)
{
bool exist[2] = {0, 0};
for (int j = 0; j < M; j++)
{
pii p = v[j].S;
if ((p.F <= p.S && p.F <= i && i <= p.S) || (p.F > p.S && !(p.S < i && i < p.F)))
exist[(mask >> j) & 1] = 1;
}
valid[0] &= exist[0];
valid[1] &= exist[1];
}
if (valid[0] && valid[1])
{
for (int j = 0; j < M; j++)
cout << ((mask >> j) & 1);
cout << '\n';
return 0;
}
}
cout << "impossible\n";
}
else
{
int top[3] = {}, idx[3] = {};
priority_queue<pii> pq[3];
sort(v.begin(), v.end(), [](pair<int, pii> p1, pair<int, pii> p2)
{ return p1.S.F < p2.S.F; });
while(top[1] < N || top[2] < N)
{
int cur = (top[1] <= top[2] ? 1 : 2);
while(idx[cur] < M && v[idx[cur]].S.F <= top[cur] + 1)
{
pq[cur].push(make_pair(v[idx[cur]].S.S, v[idx[cur]].F));
idx[cur]++;
}
while(!pq[cur].empty() && side[pq[cur].top().S] != 0)
pq[cur].pop();
if(pq[cur].empty() || pq[cur].top().F <= top[cur])
{
cout << "impossible\n";
return 0;
}
else
{
top[cur] = pq[cur].top().F;
//cout << cur << "use " << pq[cur].top().S << '\n';
side[pq[cur].top().S] = cur;
pq[cur].pop();
}
}
for (int i = 1; i <= M; i++)
cout << side[i] % 2;
cout << '\n';
}
}
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