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unfairplay.cc
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unfairplay.cc
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// https://open.kattis.com/problems/unfairplay
#include <bits/stdc++.h>
using namespace std;
using ii = tuple<int, int>;
using qi = queue<int>;
using vi = vector<int>;
using vii = vector<ii>;
using vvi = vector<vi>;
using mii = map<int, int>;
int k, flow;
vi l, p;
vvi c;
bool dfs(int u, int f) {
if (u == k - 1) {
flow += f;
while (u != k - 2) {
c[p[u]][u] -= f;
c[u][p[u]] += f;
u = p[u];
}
return 1;
}
for (int v = 0; v < k; v++) {
if (l[v] == l[u] + 1 && c[u][v] > 0) {
p[v] = u;
if (dfs(v, min(c[u][v], f))) return 1;
}
}
return 0;
}
int main() {
cin.tie(0), ios::sync_with_stdio(0);
while (1) {
int n, m, u, v, C = 0;
cin >> n;
if (n < 0) break;
cin >> m;
vi ps(n);
for (int i = 0; i < n; i++) cin >> ps[i];
mii gxy, ei;
vi rei(m, -1);
vii e;
for (int i = 0; i < m; i++) {
cin >> u >> v, u--, v--;
e.push_back({u, v});
if (v < u) swap(u, v);
if (v == n - 1) ps[n - 1] += 2;
else {
int j = u * n + v;
gxy[j]++;
if (!ei.count(j)) ei[j] = ei.size();
rei[i] = ei[j];
}
}
k = n + gxy.size() + 1;
c = vvi(k, vi(k));
for (int i = 0; i < m; i++) {
int j = rei[i];
if (j < 0) continue;
tie(u, v) = e[i];
C += 2;
c[k - 2][n + j - 1] += 2;
c[n + j - 1][u] += 2;
c[n + j - 1][v] += 2;
}
bool ok = 1;
for (int i = 0; i < n - 1; i++) {
int w = ps[n - 1] - ps[i] - 1;
if (w < 0) {
ok = 0;
break;
}
c[i][k - 1] = w;
}
if (!ok) {
cout << "NO\n";
continue;
}
flow = 0;
while (1) {
l = vi(k, -1);
qi q;
q.push(k - 2);
l[k - 2] = 0;
while (!q.empty()) {
u = q.front();
if (u == k - 1) break;
q.pop();
for (int v = 0; v < k; v++)
if (l[v] < 0 && c[u][v] > 0) l[v] = l[u] + 1, q.push(v);
}
if (q.empty()) break;
p = vi(k);
while (dfs(k - 2, 1e9))
;
}
if (C > flow) {
cout << "NO\n";
continue;
}
for (int i = 0; i < m; i++) {
tie(u, v) = e[i];
if (u == n - 1) cout << 0;
else if (v == n - 1)
cout << 2;
else {
int w = n + rei[i] - 1;
if (c[u][w] >= 2) c[u][w] -= 2, cout << 0;
else if (c[u][w])
c[u][w]--, cout << 1;
else
cout << 2;
}
cout << " \n"[i == m - 1];
}
}
}