Spfa + SLF&LLL优化

Spfa + SLF&LLL优化

基本原理

效率分析

核心代码

SLF

deque<ll>q;
void Spfa()
{
    for(ll i=1;i<=n;i++)dis[i]=INF;
    dis[s]=0;
    q.push_back(s);
    vis[s]=1;
    while(!q.empty())
    {
        ll u=q.front();
        q.pop_front();
        vis[u]=0;
        for(ll i=head[u];i;i=edge[i].next)
        {
            ll v=edge[i].v,w=edge[i].w;
            if(dis[v]>dis[u]+w)
            {
                dis[v]=dis[u]+w;
                if(!vis[v])
                {
                    if(dis[v]<=dis[q.front()])q.push_front(v);
                    else q.push_back(v);
                    vis[v]=1;
                }
            }
        }
    }
}

LLL

ll tot=1,sum;
queue<ll>q;
void Spfa()
{
    for(ll i=1;i<=n;i++)dis[i]=INF;
    dis[s]=0;
    q.push(s);
    vis[s]=1;
    while(!q.empty())
    {
        ll u=q.front();
        while(tot*dis[u]>sum)
        {
            q.pop();
            q.push(u);
            u=q.front();
        }
        q.pop();
        tot--;
        sum-=dis[u];
        vis[u]=0;
        for(ll i=head[u];i;i=edge[i].next)
        {
            ll v=edge[i].v,w=edge[i].w;
            if(dis[v]>dis[u]+w)
            {
                dis[v]=dis[u]+w;
                if(!vis[v])
                {
                    q.push(v);
                    vis[v]=1;
                    sum+=dis[v];
                    tot++;
                }
            }
        }
    }
}

SLF + LLL

ll tot=1,sum;
deque<ll>q;
void Spfa()
{
    for(ll i=1;i<=n;i++)dis[i]=INF;
    dis[s]=0;
    q.push_back(s);
    vis[s]=1;
    while(!q.empty())
    {
        ll u=q.front();
        while(tot*dis[u]>sum)
        {
            q.pop_front();
            q.push_back(u);
            u=q.front();
        }
        q.pop_front();
        tot--;
        sum-=dis[u];
        vis[u]=0;
        for(ll i=head[u];i;i=edge[i].next)
        {
            ll v=edge[i].v,w=edge[i].w;
            if(dis[v]>dis[u]+w)
            {
                dis[v]=dis[u]+w;
                if(!vis[v])
                {
                    if(q.size()&&dis[v]<=dis[q.front()])q.push_front(v);
                    else q.push_back(v);
                    vis[v]=1;
                    sum+=dis[v];
                    tot++;
                }
            }
        }
    }
}

例题解析

洛谷 P3371 【模板】单源最短路径（弱化版）

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define maxn 10005
#define maxm 500005
#define INF 2147483647
template<class T>inline bool read(T &x)
{
    x=0;register char c=getchar();register bool f=0;
    while(!isdigit(c)){if(c==EOF)return false;f^=c=='-',c=getchar();}
    while(isdigit(c))x=(x<<3)+(x<<1)+(c^48),c=getchar();
    if(f)x=-x;
    return true;
}
template<class T>inline void print(T x)
{
    if(x<0)putchar('-'),x=-x;
    if(x>9)print(x/10);
    putchar(x%10^48);
}
template<class T>inline void print(T x,char c){print(x),putchar(c);}
ll n,m,s,cnt,head[maxn],dis[maxn],tot=1,sum;
bool vis[maxn];
struct Edge{ll u,v,w,next;}edge[maxm];
void add(ll u,ll v,ll w)
{
    edge[++cnt].u=u;
    edge[cnt].v=v;
    edge[cnt].w=w;
    edge[cnt].next=head[u];
    head[u]=cnt;
}
deque<ll>q;
void Spfa()
{
    for(ll i=1;i<=n;i++)dis[i]=INF;
    dis[s]=0;
    q.push_back(s);
    vis[s]=1;
    while(!q.empty())
    {
        ll u=q.front();
        while(tot*dis[u]>sum)
        {
            q.pop_front();
            q.push_back(u);
            u=q.front();
        }
        q.pop_front();
        tot--;
        sum-=dis[u];
        vis[u]=0;
        for(ll i=head[u];i;i=edge[i].next)
        {
            ll v=edge[i].v,w=edge[i].w;
            if(dis[v]>dis[u]+w)
            {
                dis[v]=dis[u]+w;
                if(!vis[v])
                {
                    if(q.size()&&dis[v]<=dis[q.front()])q.push_front(v);
                    else q.push_back(v);
                    vis[v]=1;
                    sum+=dis[v];
                    tot++;
                }
            }
        }
    }
}
int main()
{
    read(n),read(m),read(s);
    ll u,v,w;
    for(ll i=1;i<=m;i++)
    {
        read(u),read(v),read(w);
        add(u,v,w);
    }
    Spfa();
    for(ll i=1;i<=n;i++)print(dis[i],' ');
    return 0;
}