一本通差分约束入门题

最关键的就是找好所有的要满足的不等式条件,注意隐含的条件还有一点就是注意没有源点 建立源点

#2436. 「SCOI2011」糖果

#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int,int>;
#define int long long
const int N = 5e5+10,M = 2e6+10;
const int inf = 0x3f3f3f3f;
const int mod = 1e9+7;
int gcd(int a,int b){return b?a:gcd(b,a%b);}
int lcm(int a,int b){return a*b/gcd(a,b);}
int qmi(int a,int b,int mod){int res=1;while(b){if(b&1)res=res*a%mod;b>>=1;a=a*a%mod;}return res;}


int n,q,m;
int dist[N];
bool vis[N];
int cnt[N];
int e[M],ne[M],w[M],h[N],idx;
void add(int a,int b,int c){
	e[idx] = b,ne[idx] = h[a],w[idx] = c,h[a] = idx++;
}

void spfa()
{
	stack<int>q;
	memset(dist,-0x3f,sizeof dist);
	dist[0] = 0;
	vis[0] = true;
	q.push(0);
	
	//int count = 0;
	while(q.size()){
		auto t = q.top();
		q.pop();
		vis[t] = false;
		
		for(int i=h[t];~i;i=ne[i]){
			int j = e[i];
			if(dist[j]<dist[t]+w[i]){
				dist[j] = dist[t]+w[i];
				cnt[j]++;
				if(cnt[j]>=n){cout<<-1;return;}
				//if(++count>100000){cout<<-1;return;}
				if(!vis[j]){
					vis[j] = true;
					q.push(j);
				}
			}
		}
	}
	
	
	int res = 0;
	
	
	for(int i=1;i<=n;i++)res+=dist[i];
	cout<<res;
	
	

	
}

void solve()
{
	cin>>n>>m;
	memset(h,-1,sizeof h);
	for(int i=1;i<=m;i++){
		int a,b,c;cin>>c>>a>>b;
		if(c==1){add(a,b,0),add(b,a,0);}
		else if(c==2){add(a,b,1);}
		else if(c==3){add(b,a,0);}
		else if(c==4){add(b,a,1);}
		else add(a,b,0);
	}
	for(int i=1;i<=n;i++)add(0,i,1);
	spfa();

}

signed main()
{
	ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
	int _;
	//cin>>_;
	_ = 1;
	while(_--)solve();
	return 0;
}

#10087. 「一本通 3.4 例 1」Intervals

#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int,int>;
#define int long long
const int N = 2e5+10;
const int inf = 0x3f3f3f3f;
const int mod = 1e9+7;
int gcd(int a,int b){return b?a:gcd(b,a%b);}
int lcm(int a,int b){return a*b/gcd(a,b);}
int qmi(int a,int b,int mod){int res=1;while(b){if(b&1)res=res*a%mod;b>>=1;a=a*a%mod;}return res;}


int n,q,m;

int e[N],ne[N],w[N],h[N],idx;
void add(int a,int b,int c){
	e[idx] = b,ne[idx] = h[a],w[idx] = c,h[a] = idx++;
}

int dist[N];
bool vis[N];
int mx;
void spfa()
{
	memset(dist,-0x3f,sizeof dist);
	queue<int>q;
	q.push(0);
	dist[0] = 0;
	vis[0] = true;
	
	
	while(q.size()){
		auto t = q.front();
		q.pop();
		vis[t] = false;
		//cout<<t<<"\n";
		for(int i=h[t];~i;i=ne[i]){
			int j = e[i];
			if(dist[j]<dist[t]+w[i]){
				dist[j] = dist[t]+w[i];
				if(!vis[j]){
					vis[j] = true;
					q.push(j);
				}
			}
		}
	}
	
	
	
	cout<<dist[50001];
}



void solve()
{
	memset(h,-1,sizeof h);
	cin>>m;
	for(int i=1;i<=50001;++i){
		add(i-1,i,0),add(i,i-1,-1);
	}
	while(m--){
		int a,b,c;cin>>a>>b>>c;
		a++,b++;
		add(a-1,b,c);
	}
	
	
	
	spfa();

}

signed main()
{
	ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
	int _;
	//cin>>_;
	_ = 1;
	while(_--)solve();
	return 0;
}

#10090. 「一本通 3.4 练习 2」布局 Layout

#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int,int>;
#define int long long
const int N = 1e5+10;
const int inf = 0x3f3f3f3f;
const int mod = 1e9+7;
int gcd(int a,int b){return b?a:gcd(b,a%b);}
int lcm(int a,int b){return a*b/gcd(a,b);}
int qmi(int a,int b,int mod){int res=1;while(b){if(b&1)res=res*a%mod;b>>=1;a=a*a%mod;}return res;}


int n,q,m1,m2;
int dist[N],cnt[N];
bool vis[N];
int e[N],ne[N],w[N],h[N],idx;
void add(int a,int b,int c){
	e[idx] = b,ne[idx] = h[a],w[idx] = c,h[a] = idx++;
}


bool spfa(int sz)
{
	memset(dist,0x3,sizeof dist);
	memset(cnt,0,sizeof cnt);
	memset(vis,0,sizeof vis);
	queue<int>q;
	
	for(int i=1;i<=sz;++i){
		dist[i] = 0;
		q.push(i);
		vis[i] = true;
	}
	
	while(q.size()){
		auto t = q.front();
		q.pop();
		vis[t] = false;
		for(int i=h[t];~i;i=ne[i]){
			int j = e[i];
			if(dist[j]>dist[t]+w[i]){
				dist[j] = dist[t]+w[i];
				cnt[j]++;
				if(cnt[j]>=n)return true;
				if(!vis[j]){
					vis[j] = true;
					q.push(j);
				}
			}
		}
		
	}
	
	return false;
	
	
}


void solve()
{
	cin>>n>>m1>>m2;
	memset(h,-1,sizeof h);
	for(int i=0;i<=n;++i)add(i+1,i,0);
	while(m1--){
		int a,b,c;cin>>a>>b>>c;if(a>b)swap(a,b);
		add(a,b,c);
	}	
	
	while(m2--){
		int a,b,c;cin>>a>>b>>c;if(a>b)swap(a,b);
		add(b,a,-c);
	}
	
	if(spfa(n))cout<<-1;
	else{
		spfa(1);
		if(dist[n]>inf/2)cout<<-2;
		else cout<<dist[n];
	}
	

}

signed main()
{
	ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
	int _;
	//cin>>_;
	_ = 1;
	while(_--)solve();
	return 0;
}

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