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2022.4.3澳门赛区补题

辰鑫chenxin 2022-04-04 阅读 24
算法

A.So I’ll Max Out My Constructive Algorithm Skills

思路:任意找一条路径,正着不满足的话,反过来必然满足

#include<iostream>
#include<cstring>
#include<algorithm>
#include<vector>
using namespace std;
#define int long long
void solve()
{
	int n;cin>>n;
    int a[100][100];
    for(int i=1;i<=n;i++)
        for(int j=1;j<=n;j++)
            cin>>a[i][j];
    vector<int>b;
    for(int i=1;i<=n;i++)
    {
        if(i&1)for(int j=1;j<=n;j++)b.push_back(a[i][j]);
        else for(int j=n;j>=1;j--)b.push_back(a[i][j]);
    }
    int cnt1=0,cnt2=0;
    for(int i=1;i<b.size();i++)if(b[i]>b[i-1])cnt1++;else cnt2++;
    if(cnt1>cnt2)reverse(b.begin(),b.end());
    for(auto x : b)cout<<x<<" ";
    cout<<'\n';
}

signed main()
{
	int T;cin>>T;
	while(T--)solve(); 
}

K.Link-Cut Tree—并查集判环+贪心

贪心,按下标从最小路径开始找环,找到就结束输出路径

#include<iostream>
#include<cstring>
#include<algorithm>
#include<vector>
#include<functional>
using namespace std;
#define int long long
const int N = 100010;
int a[N],b[N],p[N];
int n,m;
vector<pair<int,int>>g[N];
vector<int>res;
void solve()
{
	res.clear();
	cin>>n>>m;
    for(int i=1;i<=m;i++)cin>>a[i]>>b[i];
    
    function<int(int)> find = [&](int x)
    {
    	if(p[x]!=x)p[x]=find(p[x]);
    	return p[x];
	};
	
	for(int i=0;i<=n;i++)p[i]=i,g[i].clear();
	
	 function<bool(int,int,int)> dfs = [&](int u,int fa,int ed)->bool
	{
		if(u==ed)return true;
		for(auto [v,i] : g[u])
		{
			if(v==fa)continue;
			if(dfs(v,u,ed))
            {
                res.push_back(i);
                return true;
            }
		}
        return false;
	};
	
	for(int i=1;i<=m;i++)
	{
		int pa=find(a[i]),pb=find(b[i]);
		if(pa!=pb)
		{
			p[pb]=pa;
			g[a[i]].push_back({b[i],i});
			g[b[i]].push_back({a[i],i});
		}
		else
		{
			res.push_back(i);
			dfs(a[i],-1,b[i]);
			break;
		}
	}
	
	sort(res.begin(),res.end());
	if(res.empty())
	{
		cout<<-1<<'\n';
		return ;
	}
	for(auto x : res)cout<<x<<' ';
	cout<<'\n';
	
}

signed main()
{
	ios::sync_with_stdio(0);
    cin.tie(0);cout.tie(0);
	int T;cin>>T;
	while(T--)solve(); 
}

F.Sandpile on Clique—数学+思维

#include<iostream>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<vector>
using namespace std;
#define int long long
const int N = 500010;
int a[N],b[N],cnt[N];
int n,ps=0,s=0;
signed main()
{
	cin>>n;
    for(int i=0;i<n;i++)
    {
        cin>>a[i];
        ps+=a[i];
        a[i]%=n;
        s+=a[i];
    }
    for(int i=0;i<n;i++)cnt[a[i]]++;
    for(int i=n;i>=0;i--)cnt[i]+=cnt[i+1];
    vector<int>res;
    for(int i=0;i<n;i++)
    {
        int qs=s+i*n-(cnt[max(n-i-1,0ll)]*n);
        if(qs==ps)
        {
            res.push_back(i);
        }
    }
    if(res.size()!=1)cout<<"Recurrent"<<'\n';
    else 
    {
        for(int i=0;i<n;i++)
            cout<<(a[i]+res[0])%n<<' ';
        cout<<'\n';
    }
}
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