#include "bits/stdc++.h"
using namespace std;
void abc() {cout << endl;}
template <typename T, typename ...U> void abc(T a, U ...b) {
cout << a << ' ', abc(b...);
}
template <typename T> void printv(T l, T r) {
while (l != r) cout << *l << " \n"[++l == r];
}
template <typename A, typename B> istream& operator >> (istream& o, pair<A, B> &a) {
return o >> a.first >> a.second;
}
template <typename A, typename B> ostream& operator << (ostream& o, pair<A, B> a) {
return o << '(' << a.first << ", " << a.second << ')';
}
template <typename T> ostream& operator << (ostream& o, vector<T> a) {
bool is = false;
for (T i : a) {o << (is ? ' ' : '{'), is = true, o << i;}
return o << '}';
}
#ifdef local
#define test(args...) abc("[" + string(#args) + "]", args)
#else
#define test(args...) void(0)
#endif
using ll = long long;
struct wire {
int l, r, len, idx;
};
vector<wire> wires;
const int MAXT = 555555;
struct bit {
pair<int, int> tree[MAXT];
void init() {
fill(tree, tree+MAXT, pair<int, int> {0, 0});
}
void upd(int x, pair<int, int> v) {
for (; x < MAXT; x += x & (-x)) tree[x] = max(tree[x], v);
}
pair<int, int> query(int x) {
pair<int, int> res = {0, 0};
for (; x; x -= x & (-x)) {
res = max(res, tree[x]);
}
return res;
}
} bt;
struct segtree {
int tree[MAXT];
int lazy[MAXT];
void init() {
fill(tree, tree+MAXT, 0);
fill(lazy, lazy+MAXT, 0);
}
void pushdown(int x, int l, int r) {
if (l == r) return;
int mid = (l + r) / 2;
tree[2 * x] += lazy[x];
tree[2 * x + 1] += lazy[x];
lazy[2 * x] += lazy[x];
lazy[2 * x + 1] += lazy[x];
lazy[x] = 0;
return;
}
void update(int x, int l, int r, int ql, int qr, int v) {
pushdown(x, l, r);
if (ql <= l && r <= qr) {
lazy[x] += v;
tree[x] += v;
return;
}
if (l > qr || ql > r) return;
int mid = (l + r) / 2;
update(2 * x, l, mid, ql, qr, v);
update(2* x + 1, mid + 1, r, ql, qr, v);
tree[x] = min(tree[ 2 * x], tree[2 * x + 1]);
}
} segs[2];
int par[200005];
vector<int> adj[200005];
int col[200005];
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
// freopen("", "r", stdin);
// freopen("", "w", stdout);
int n, m; cin >> n >> m;
bt.init();
segs[0].init(); segs[1].init();
for (int i = 0; i < m; i++) {
int a, b; cin >> a >> b;
if (b < a) {
wires.push_back({a, b, b + (n - a) + 1, i});
} else wires.push_back({a, b, b - a + 1, i});
}
sort(wires.begin(), wires.end(), [](wire a, wire b) {
return a.len < b.len;
});
vector<wire> doms;
for (int i = m - 1; i >= 0; i--) {
int st = wires[i].l, en = wires[i].r;
if (en < st) en += n;
auto q = bt.query(st);
int dom = -1;
if (q.first >= en) {
dom = q.second;
}
if (dom == -1 && wires[i].l <= wires[i].r) {
q = bt.query(wires[i].l + n);
if (q.first >= wires[i].r + n) {
dom = q.second;
}
}
par[wires[i].idx] = dom;
if (dom != -1) {
adj[dom].push_back(wires[i].idx);
}
if (par[wires[i].idx] == -1) {
doms.push_back(wires[i]);
bt.upd(st, {en, wires[i].idx});
if (wires[i].l <= wires[i].r) {
bt.upd(st + n, {en + n, wires[i].idx});
}
}
}
sort(doms.begin(), doms.end(), [](wire a, wire b) {
return a.l < b.l;
});
sort(wires.begin(), wires.end(), [](wire a, wire b) {
return a.idx < b.idx;
});
// cout << segs[0].query(1, 1, n, 1, n) << endl;
auto upd = [&](int idx, int v) {
if (wires[idx].l <= wires[idx].r) {
segs[col[idx] - 1].update(1, 1, n, wires[idx].l, wires[idx].r, v);
} else {
segs[col[idx] - 1].update(1, 1, n, 1, wires[idx].r, v);
segs[col[idx] - 1].update(1, 1, n, wires[idx].l, n, v);
}
};
int ct = 0;
for (int i = 0; i < m; i++) {
if (par[i] == -1) {
col[i] = 1 + (ct % 2);
ct++;
}
}
for (int i = 0; i < m; i++) {
if (par[i] != -1) {
col[i] = 3 - col[par[i]];
}
}
for (int i = 0; i < m; i++) {
upd(i, 1);
}
if (segs[0].tree[1] > 0 && segs[1].tree[1] > 0) {
for (int i = 0; i < m; i++) {
cout << col[i] - 1;
}
return 0;
}
if (doms.size() % 2 == 0 || doms.size() <= 1) {
cout << "impossible";
return 0;
}
for (int i = 0; i < doms.size(); i++) {
upd(doms[i].idx, -1);
col[doms[i].idx] = 3 - col[doms[i].idx];
upd(doms[i].idx, 1);
for (auto nxt : adj[doms[i].idx]) {
upd(nxt, -1);
col[nxt] = 3 - col[nxt];
upd(nxt, 1);
}
if (segs[0].tree[1] > 0 && segs[1].tree[1] > 0) {
for (int i = 0; i < m; i++) {
cout << col[i] - 1;
}
return 0;
}
}
cout << "impossible";
}
Compilation message
alternating.cpp: In member function 'void segtree::pushdown(int, int, int)':
alternating.cpp:73:13: warning: unused variable 'mid' [-Wunused-variable]
73 | int mid = (l + r) / 2;
| ^~~
alternating.cpp: In function 'int main()':
alternating.cpp:218:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<wire>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
218 | for (int i = 0; i < doms.size(); i++) {
| ~~^~~~~~~~~~~~~
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
9 ms |
18004 KB |
Output is correct |
2 |
Correct |
9 ms |
18004 KB |
Output is correct |
3 |
Correct |
9 ms |
17956 KB |
Output is correct |
4 |
Incorrect |
9 ms |
17964 KB |
'impossible' claimed, but there is a solution |
5 |
Halted |
0 ms |
0 KB |
- |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
9 ms |
18004 KB |
Output is correct |
2 |
Correct |
9 ms |
18004 KB |
Output is correct |
3 |
Correct |
9 ms |
17956 KB |
Output is correct |
4 |
Incorrect |
9 ms |
17964 KB |
'impossible' claimed, but there is a solution |
5 |
Halted |
0 ms |
0 KB |
- |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
9 ms |
18004 KB |
Output is correct |
2 |
Correct |
9 ms |
18004 KB |
Output is correct |
3 |
Correct |
9 ms |
17956 KB |
Output is correct |
4 |
Incorrect |
9 ms |
17964 KB |
'impossible' claimed, but there is a solution |
5 |
Halted |
0 ms |
0 KB |
- |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
34 ms |
22308 KB |
Output is correct |
2 |
Correct |
10 ms |
17984 KB |
Output is correct |
3 |
Correct |
44 ms |
20228 KB |
Output is correct |
4 |
Correct |
40 ms |
20304 KB |
Output is correct |
5 |
Incorrect |
73 ms |
23104 KB |
'impossible' claimed, but there is a solution |
6 |
Halted |
0 ms |
0 KB |
- |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
9 ms |
18004 KB |
Output is correct |
2 |
Correct |
9 ms |
18004 KB |
Output is correct |
3 |
Correct |
9 ms |
17956 KB |
Output is correct |
4 |
Incorrect |
9 ms |
17964 KB |
'impossible' claimed, but there is a solution |
5 |
Halted |
0 ms |
0 KB |
- |