Bellman-Ford(贝尔曼—福特)
时间复杂度O(nm)
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define endl "\n"
#define sf scanf
#define pf printf
#define fi first
#define se second
#define pb push_back
#define pll pair<ll,ll>
const int mod=1e9+7;
const int N=1e3+9,M=1e4+9;
int a[N],x[M],y[M],z[M];
int n,m;
void f0(int T)
{
sf("%d%d",&n,&m);
for(int i=1;i<=m;i++)
sf("%d%d%d",&x[i],&y[i],&z[i]);
for(int i=1;i<=n;i++)
a[i]=1e9;
a[1]=0;
for(int j=1;j<n;j++)
for(int i=1;i<=m;i++)
{
a[y[i]]=min(a[y[i]],a[x[i]]+z[i]);//从x到y
a[x[i]]=min(a[x[i]],a[y[i]]+z[i]);//从y到x
}
pf("%d\n",a[n]);
}
int main()
{
int T=1;
// sf("%d",&T);
for(int i=1;i<=T;i++)
f0(i);
return 0;
}
SPFA(Bellman-Ford队列优化)
时间复杂度O(km),最大O(nm)
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define endl "\n"
#define sf scanf
#define pf printf
#define fi first
#define se second
#define pb push_back
#define pll pair<ll,ll>
const int mod=1e9+7;
const int N=1e3+9,M=2e4+9;
struct pp
{
int x,y,z;
}p[M];
bool book[N];
int h[M],b[N];
int n,m,k;
void SPFA()
{
queue<int>q;
for(int i=1;i<=n;i++)
{
b[i]=1e9;
book[i]=false;
}
b[1]=0;
book[1]=true;
q.push(1);
while(q.size())
{
int x=q.front();
q.pop();
book[x]=false;
for(int i=h[x];i!=-1;i=p[i].x)
{
int y=p[i].y;
if(b[y]>b[x]+p[i].z)
{
b[y]=b[x]+p[i].z;
if(!book[y])
{
q.push(y);
book[y]=true;
}
}
}
}
}
void add(int x,int y,int z)
{
p[k].x=h[x];
p[k].y=y;
p[k].z=z;
h[x]=k++;
}
void f0(int T)
{
k=0;
memset(h,-1,sizeof h);
sf("%d%d",&n,&m);
for(int i=1;i<=m;i++)
{
int x,y,z;
sf("%d%d%d",&x,&y,&z);
add(x,y,z);
add(y,x,z);
}
SPFA();
pf("%d\n",b[n]);
}
int main()
{
int T=1;
// sf("%d",&T);
for(int i=1;i<=T;i++)
f0(i);
return 0;
}
SPFA(Bellman-Ford队列优化)判断负环
时间复杂度O(nm)
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define endl "\n"
#define sf scanf
#define pf printf
#define fi first
#define se second
#define pb push_back
#define pll pair<ll,ll>
const int mod=1e9+7;
const int N=1e4+9,M=1e5+9;
struct pp
{
int x,y,z;
}p[M];
bool book[N];
int h[M],b[N],c[N];
int n,m,k;
bool SPFA()
{
queue<int>q;
for(int i=1;i<=n;i++)
{
b[i]=1e9;
c[i]=0;
book[i]=false;
}
b[1]=0;
book[1]=true;
q.push(1);
while(q.size())
{
int x=q.front();
q.pop();
book[x]=false;
for(int i=h[x];i!=-1;i=p[i].x)
{
int y=p[i].y;
if(b[y]>b[x]+p[i].z)
{
b[y]=b[x]+p[i].z;
c[y]=c[x]+1;
if(c[y]>=n)
return true;
if(!book[y])
{
q.push(y);
book[y]=true;
}
}
}
}
return false;
}
void add(int x,int y,int z)
{
p[k].x=h[x];
p[k].y=y;
p[k].z=z;
h[x]=k++;
}
void f0(int T)
{
k=0;
memset(h,-1,sizeof h);
sf("%d%d",&n,&m);
for(int i=1;i<=m;i++)
{
int x,y,z;
sf("%d%d%d",&x,&y,&z);
add(x,y,z);
if(z>=0)
add(y,x,z);
}
if(SPFA())
pf("YES\n");
else
pf("NO\n");
}
int main()
{
int T=1;
// sf("%d",&T);
for(int i=1;i<=T;i++)
f0(i);
return 0;
}
标签:const,int,Bellman,Ford,book,long,贝尔曼,sf,define From: https://www.cnblogs.com/2021sgy/p/16601659.html