P2294 [HNOI2005] 狡猾的商人 五种做法

贪心

#include<bits/stdc++.h>
#define int long long

using namespace std;

const int N=1e3+100;

int n,m;

struct NODE{
	int l,r,val;
	bool operator < (const NODE &h)const
	{
		if(l!=h.l)	return l>h.l;
		return r>h.r;
	}
};

priority_queue<NODE> q;

signed main()
{
	int T;
	cin>>T;
	while(T--)
	{
		while(q.size())	q.pop();
		cin>>n>>m;
		for(int i=1;i<=m;i++)
		{
			int l,r,val;
			cin>>l>>r>>val;
			q.push({l,r,val});
		}
		
		bool sg=false;
		
		auto tmp=q.top();
		q.pop();
		while(q.size())
		{
			auto tmp1=q.top();q.pop();
			if(tmp.l==tmp1.l)
			{
				if(tmp.r==tmp1.r)
				{
					if(tmp.val!=tmp1.val)
					{
						sg=true;
						break;
					}
				}
				else
					if(tmp.r<tmp1.r)
						q.push({tmp.r+1,tmp1.r,tmp1.val-tmp.val});
			}
			tmp=tmp1;
		}
		if(sg)	cout<<"false"<<endl;
		else	cout<<"true"<<endl;
	}
	
	return 0;
}

带权并查集

#include<bits/stdc++.h>
#define int long long

using namespace std;

const int N=110;

int n,m;
int f[N],cha[N];

int find(int x)
{
	if(x!=f[x])
	{
		int t=find(f[x]);
		cha[x]+=cha[f[x]];
		f[x]=t;
	}
	return f[x];
}

signed main()
{
	int T;
	cin>>T;
	while(T--)
	{
		bool sg=false;
		cin>>n>>m;
		for(int i=0;i<=n;i++)	f[i]=i,cha[i]=0;
		for(int i=1;i<=m;i++)
		{
			int x,y,z;
			cin>>x>>y>>z;
			x--;
			if(find(x)!=find(y))
			{
				cha[f[y]]=cha[x]-cha[y]-z;
				f[f[y]]=f[x];
			}
			else
				if(cha[x]-cha[y]!=z)
				{
					sg=true;
					break;
				}
		}
		if(sg)	cout<<"false";
		else	cout<<"true";
		cout<<endl; 
	}
	return 0;
}

区间DP

#include<bits/stdc++.h>
#define int long long

using namespace std;

const int N=110;

int n,m;
int f[N][N];

signed main()
{
	int T;
	cin>>T;
	while(T--)
	{
		memset(f,0,sizeof f);
		cin>>n>>m;
		for(int i=1;i<=m;i++)
		{
			int x,y,z;
			cin>>x>>y>>z;
			f[x][y]=z;
		}
		bool sg=true;
		for(int i=2;i<=n;i++)
			if(sg)//加速
				for(int j=i-1;j>=1;j--)
					if(sg)//加速*2
						for(int k=j;k<i;k++)
							if(f[j][k] && f[k+1][i]) 
							{
								if(f[j][i])
								{
									if(f[j][i]!=f[j][k]+f[k+1][i])
									{
										sg=false;
										break;
									}
								}
								else
									f[j][i]=f[j][k]+f[k+1][i];
							}
		if(sg)	cout<<"true";
		else	cout<<"false";
		cout<<endl; 
	}
	return 0;
}

高斯消元

#include<bits/stdc++.h>
#define int long long

using namespace std;

int n,m;
double d[1100][110];

bool Guass()
{
	int start=1;
	for(int i=1;i<=n;i++)
	{
		int now=start;
		while(now<=m && d[now][i]==0)	now++;
		if(now>m)	continue;
		for(int j=1;j<=n+1;j++)	
			swap(d[start][j],d[now][j]);
		for(int j=start+1;j<=m;j++)
		{
			if(d[j][i]==0)	continue;
			double tmp=d[j][i]/d[start][i];
			for(int k=i;k<=n+1;k++)
				d[j][k]-=d[start][k]*tmp;
		}
		start++;
	}
	for(int i=1;i<=m;i++)
	{
		bool sg=true;
		for(int j=1;j<=n;j++)
			if(d[i][j]!=0)
				sg=false;
		if(d[i][n+1]!=0 && sg)
			return false;
	}
	return true;
}

signed main()
{
	int T;
	cin>>T;
	while(T--)
	{
		memset(d,0,sizeof d);
		cin>>n>>m;
		for(int i=1;i<=m;i++)
		{
			int x,y,z;
			cin>>x>>y>>z;
			
			for(int j=x;j<=y;j++)	d[i][j]=1;
			d[i][n+1]=z;//建立方程 
		}
		if(Guass())	cout<<"true";
		else		cout<<"false";
		cout<<endl; 
	}
	return 0;
}

差分约束

#include<bits/stdc++.h>
#define int long long
#define pb push_back
#define pa pair<int,int>
#define x first
#define y second

using namespace std;

const int N=120;

int n,m;
int dis[N];
int vis[N];
bool inq[N];
vector<pa> G[N];

signed main()
{
	int T;
	cin>>T;
	while(T--)
	{
		bool sg=false;
		cin>>n>>m;
		for(int i=0;i<=n+1;i++)	G[i].clear();
		for(int i=1;i<=m;i++)
		{
			int u,v,z;
			cin>>u>>v>>z;
			G[u-1].pb({v,z});
			G[v].pb({u-1,-z});
		}
		for(int i=0;i<=n;i++)
			G[n+1].pb({i,0});
			
		queue<int> q;
		q.push(n+1);
		memset(dis,0xcf,sizeof dis);
		memset(vis,0,sizeof vis);
		memset(inq,0,sizeof inq);
		dis[n+1]=0;
		while(q.size())
		{
			if(sg) break;
			int t=q.front();
			q.pop();
			inq[t]=0;
			for(auto i:G[t])
			{
				if(dis[i.x]<dis[t]+i.y)
				{
					dis[i.x]=dis[t]+i.y;
					if(!inq[i.x])
					{
						vis[i.x]++;
						if(vis[i.x]>n)
						{
							sg=true;
							break;
						}
						inq[i.x]=true;
						q.push(i.x);
					}
				}
			}
		}
		if(sg)	cout<<"false";
		else	cout<<"true";
		cout<<endl;
	}

	return 0;
}