330B - Road Construction

原创于 2022-03-26 23:32:11 发布 · 112 阅读

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本文介绍了一种解决特定图论问题的方法，通过构建菊花图确保任意两点间距离不超过2。适用于算法竞赛中类似题目。

// Problem: B. Road Construction
// Contest: Codeforces - Codeforces Round #192 (Div. 2)
// URL: https://codeforces.com/problemset/problem/330/B
// Memory Limit: 256 MB
// Time Limit: 2000 ms
// 2022-03-26 23:09:21
// 
// Powered by CP Editor (https://cpeditor.org)

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

#define rep(i,l,r) for(int i=(l);i<=(r);i++)
#define per(i,l,r) for(int i=(l);i>=(r);i--)
#define ll long long
#define mset(s,t) memset(s,t,sizeof(t))
#define mcpy(s,t) memcpy(s,t,sizeof(t))
#define fi first
#define se second
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define SZ(x) ((int)(x).size())
#define mp make_pair

typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;   
typedef vector<ll> Vll;               
typedef vector<pair<int, int> > vpii;
typedef vector<pair<ll, ll> > vpll;                        

const ll mod = 1e9 + 7;
//const ll mod = 998244353;
const double pi  = acos(-1.0);

inline ll qmi (ll a, ll b) {
	ll ans = 1;
	while (b) {
		if (b & 1) ans = ans * a%mod;
		a = a * a %mod;
		b >>= 1;
	}
	return ans;
}
inline int read () {
	int x = 0, f = 0;
	char ch = getchar();
	while (!isdigit(ch)) f |= (ch=='-'),ch= getchar();
	while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
	return f?-x:x;
}
template<typename T> void print(T x) {
	if (x < 0) putchar('-'), x = -x;
	if (x >= 10) print(x/10);
	putchar(x % 10 + '0');
}
inline ll sub (ll a, ll b) {
	return ((a - b ) %mod + mod) %mod;
}
inline ll add (ll a, ll b) {
	return (a + b) %mod;
}
inline ll inv (ll a) {
	return qmi(a, mod - 2);
}
const int N = 1e3 + 10;
int n, m;
bool vis[N][N];
int vist[N];
void solve() {
	cin >> n >> m;
	for (int i =1 ; i<= m; i ++) {
		int a, b;
		cin >> a >> b;
		vis[a][b] = vis[b][a] = 1;
		vist[a] = vist[b] = 1;
	}
	int root = 0;
	for (int i = 1; i <= n ;i ++) {
		if (!vist[i]) {
			root = i;
			break;
		}
	}
	vector<pii> ans;
	for (int i = 1; i <= n; i ++) {
		if (i != root) {
			if (!vis[i][root]) {
				ans.pb({i, root});
			}
			else {
				for (int j = 1; j < i; j ++) {
					ans.pb({i, j});
				}
			}
		}
	}
	cout << ans.size() << endl;
	for (auto t : ans) {
		cout << t.fi << ' ' << t.se << endl;
	}
}
int main () {
	// ios::sync_with_stdio(0),cin.tie(0), cout.tie(0);
    int t;
    t =1;
    //cin >> t;
    while (t --) solve();
    return 0;
}

题意构造一个符合任意一个点到其他点距离不超过2的图

题解:通过尝试小的样例可以发现最终是个菊花图