[Johnson + barrel Maintenance Dij] Codeforces #843D. Dynamic Shortest path__ graph theory-

This is the idea of the Johnson Johnson algorithm, which is to first go to the shortest circuit brush out dis (i) dis (i) and then transform the diagram. The power of the Edge (X,y) (x,y) is changed to W (x,y) +dis (x) −dis (y) W (x,y) +dis (x)-dis (y).
After this, the edge right is not negative, the new map to do the shortest line of things and the original image is completely equivalent, the new map from 1 1 to v V of the length of a path is the corresponding length of the original and Dis (v) dis (v) difference. Delta Delta deltas in dis dis may be useful in some questions related to weights and sizes.
This problem, we first rebuilt the map, when 1 to n δdis \delta dis are 0 0, when the weight of K K Edge plus 1 1, it is clear that the shortest possible length of the maximum increase min (k,n−1) min (k,n-1).
The shortest length has an upper bound, we can force the use of drums to maintain Dij dij, that is, the bucket instead of the priority queue, the shortest value of each point removed is not dropped log log, each o (n+m) O (n+m), the total complexity O (n+m) q) O ((n+m) q).

#include <cstdio> #include <queue> #include <algorithm> using namespace std;
typedef long Long LL;
const int maxn=100005,maxe=100005,maxd=100005;
int n,m,q;
LL Dis[maxn],f[maxn],inf=1e16;
int Fir[maxn],nxt[maxe],son[maxe],w[maxe],tot; void Add (int x,int y,int z) {son[++tot]=y; w[tot]=z; nxt[tot]=fir[x]; fir[x]=tot;} struct data{int x;
    LL D;
    Data (int t1=1,ll t2=1) {x=t1;d=t2;}
BOOL operator < (const data &b) const{return d<b.d;}};
Priority_queue <data> Heap; 
    inline void Dij () {for (int i=1;i<=n;i++) dis[i]=inf; dis[1]=0;
    Heap.push (data (1,dis[1])); while (! Heap.empty ()) {int x=heap.top (). x; 
        Heap.pop (); for (int j=fir[x];j;j=nxt[j]) if (Dis[x]+w[j]<dis[son[j]]) dis[son[j]]=dis[x]+w[j], Heap.push (Data (son[j],dis[so
    N[J]));
}} queue<int> Bk[maxd];
    int main () {freopen ("cf843d.in", "R", stdin);
    Freopen ("Cf843d.out", "w", stdout);
    scanf ("%d%d%d", &n,&m,&q); for (int i=1;i<=m;i++) {int x,y,z; scanf ("%d%d%d", &x,&y,&z); 
    Add (x,y,z);
    } dij ();
        while (q--) {int _type,k,x; scanf ("%d%d", &_type,&k); if (_type==1) printf ("%i64d\n", dis[k]<inf?dis[k]:-1);
            else{for (int i=1;i<=k;i++) scanf ("%d", &x), w[x]++; for (int i=1;i<=n;i++) F[i]=inf; f[1]=0;
            Bk[0].push (1); for (int i=0,_max=0;i<=_max;i++) while (! Bk[i].empty ()) {int X=bk[i].front ();
                Bk[i].pop ();
                if (f[x]<i) continue;
                    for (int j=fir[x];j;j=nxt[j]) {int t=f[x]+ (w[j]+dis[x]-dis[son[j]]);
                        if (T<f[son[j]]) {f[son[j]]=t;
                    if (T<=min (k,n-1)) Bk[t].push (Son[j]), _max=max (_max,t);   
        for (int i=1;i<=n;i++) dis[i]=min (Inf,dis[i]+f[i]);
} return 0;

 }