結果

問題 No.3104 Simple Graph Problem
ユーザー shobonvip
提出日時 2025-02-01 01:24:15
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 137 ms / 2,000 ms
コード長 4,292 bytes
コンパイル時間 5,055 ms
コンパイル使用メモリ 262,432 KB
実行使用メモリ 18,028 KB
最終ジャッジ日時 2025-02-01 01:24:30
合計ジャッジ時間 13,405 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 65
権限があれば一括ダウンロードができます

ソースコード

diff # 

/**
	author:  shobonvip
	created: 2025.02.01 00:32:28
**/

#include<bits/stdc++.h>
using namespace std;

//* ATCODER
#include<atcoder/all>
using namespace atcoder;
typedef modint998244353 mint;
//*/

/* BOOST MULTIPRECISION
#include<boost/multiprecision/cpp_int.hpp>
using namespace boost::multiprecision;
//*/

typedef long long ll;

#define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--)
#define all(v) v.begin(), v.end()

template <typename T> bool chmin(T &a, const T &b) {
	if (a <= b) return false;
	a = b;
	return true;
}

template <typename T> bool chmax(T &a, const T &b) {
	if (a >= b) return false;
	a = b;
	return true;
}

template <typename T> T max(vector<T> &a){
	assert(!a.empty());
	T ret = a[0];
	for (int i=0; i<(int)a.size(); i++) chmax(ret, a[i]);
	return ret;
}

template <typename T> T min(vector<T> &a){
	assert(!a.empty());
	T ret = a[0];
	for (int i=0; i<(int)a.size(); i++) chmin(ret, a[i]);
	return ret;
}

template <typename T> T sum(vector<T> &a){
	T ret = 0;
	for (int i=0; i<(int)a.size(); i++) ret += a[i];
	return ret;
}

int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	
	int n, m; cin >> n >> m;
	vector<mint> b(n);
	rep(i,0,n) {
		int x; cin >> x;
		b[i] = x;
	}
	vector<int> u(m), v(m);
	vector ikeru(n, vector<pair<int,int>>(0));
	rep(i,0,m) {
		cin >> u[i] >> v[i];
		u[i]--;
		v[i]--;
		ikeru[u[i]].push_back(pair(v[i],i));
		ikeru[v[i]].push_back(pair(u[i],i));
	}

	vector<int> color(n);
	vector<int> mada;
	vector<bool> tansaku(n);
	tansaku[0] = 1;
	mada.push_back(0);
	while(!mada.empty()){
		int i = mada.back();
		mada.pop_back();
		for (auto [j,c]:ikeru[i]){
			if (!tansaku[j]){
				tansaku[j] = 1;
				color[j] = color[i] ^ 1;
				mada.push_back(j);
			}
		}
	}

	int cycle_ind = -1;
	vector<int> cycle_v;
	vector<int> cycle_e;
	rep(i,0,m) {
		if (color[u[i]] == color[v[i]]) {
			cycle_ind = i;
			break;
		}
	}

	bool is_bipartite = 1;
	if (cycle_ind >= 0) {
		is_bipartite = 0;
		int x = u[cycle_ind];
		int y = v[cycle_ind];
		vector<int> cf(n, -1);
		fill(all(tansaku), 0);
		tansaku[x] = 1;
		mada.push_back(x);
		while(!mada.empty()){
			int i = mada.back();
			mada.pop_back();
			for (auto [j,c]: ikeru[i]) {
				if (tansaku[j]) continue;
				if (color[j] == color[i]) continue;
				tansaku[j] = 1;
				cf[j] = c;
				mada.push_back(j);
			}
		}
		int i = y;
		cycle_e.push_back(cycle_ind);
		cycle_v.push_back(i);
		while(cf[i] != -1) {
			cycle_e.push_back(cf[i]);
			i = i ^ u[cf[i]] ^ v[cf[i]];			
			cycle_v.push_back(i);
		}
		reverse(all(cycle_e));
		reverse(all(cycle_v));
	}

	vector new_ikeru(n, vector<pair<int,int>>(0));
	for (int i: cycle_e) {
		new_ikeru[u[i]].push_back(pair(v[i], i));
		new_ikeru[v[i]].push_back(pair(u[i], i));
	}

	fill(all(tansaku), 0);
	if (is_bipartite) {
		tansaku[0] = 1;
		mada.push_back(0);
	}else{
		for (int i: cycle_v) {
			tansaku[i] = 1;
			mada.push_back(i);
		}
	}

	while(!mada.empty()) {
		int i = mada.back();
		mada.pop_back();
		for (auto [j,c]: ikeru[i]) {
			if (tansaku[j]) continue;
			new_ikeru[i].push_back(pair(j, c));
			new_ikeru[j].push_back(pair(i, c));
			tansaku[j] = 1;
			mada.push_back(j);
		}
	}

	fill(all(tansaku), 0);
	vector<int> deg(n);
	rep(i,0,n) {
		deg[i] = (int)new_ikeru[i].size();
	}

	rep(i,0,n) {
		if (deg[i] == 1) {
			mada.push_back(i);
		}
	}

	vector<mint> ans(m);
	while(!mada.empty()) {
		int i = mada.back();
		mada.pop_back();
		tansaku[i] = 1;
		for (auto [j,c]: new_ikeru[i]) {
			if (tansaku[j]) continue;
			ans[c] = b[i];
			b[i] -= ans[c];
			b[j] -= ans[c];
			deg[j] -= 1;
			if (deg[j] == 1) {
				mada.push_back(j);
			}
		}
	}

	if (!is_bipartite) {
		mint total = 0;
		for (ll i: cycle_v) {
			total += b[i];
		}
		total /= 2;
		mint tmp = total;
		for (int i=2; i<(int)cycle_v.size(); i+=2){
			tmp -= b[cycle_v[i]];
		}
		ans[cycle_e[0]] = tmp;
		rep(i,1,(int)cycle_e.size()) {
			ans[cycle_e[i]] = b[cycle_v[i]] - ans[cycle_e[i-1]];
		}
		for (int i: cycle_e) {
			b[u[i]] -= ans[i];
			b[v[i]] -= ans[i];
		}
	}

	rep(i,0,n) {
		//cout << i << ' ' << b[i].val() << endl;
		if (b[i].val() != 0) {
			cout << -1 << '\n';
			return 0;
		}
	}
	rep(i,0,m) {
		cout << ans[i].val();
		if (i==m-1) cout << '\n';
		else cout << ' ';
	}


}
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