Spfa + SLF&LLL优化

Posted 2022-05-30 mb61c049ad36458

tags:

篇首语：本文由小常识网(cha138.com)小编为大家整理，主要介绍了Spfa + SLF&LLL优化相关的知识，希望对你有一定的参考价值。

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
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 Edgell 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;