Problem:
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Single Source Shortest Path II

For a given weighted graph $G = (V, E)$, find the shortest path from a source to each vertex. For each vertex $u$, print the total weight of edges on the shortest path from vertex $0$ to $u$.

Input

In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, adjacency lists for each vertex $u$ are respectively given in the following format:

$u$ $k$ $v_1$ $c_1$ $v_2$ $c_2$ ... $v_k$ $c_k$

Vertices in $G$ are named with IDs $0, 1, ..., n-1$. $u$ is ID of the target vertex and $k$ denotes its degree. $v_i (i = 1, 2, ... k)$ denote IDs of vertices adjacent to $u$ and $c_i$ denotes the weight of a directed edge connecting $u$ and $v_i$ (from $u$ to $v_i$).

Output

For each vertex, print its ID and the distance separated by a space character in a line respectively. Print in order of vertex IDs.

Constraints

$1 \leq n \leq 10,000$

$0 \leq c_i \leq 100,000$

$|E| < 500,000$

All vertices are reachable from vertex $0$

Sample Input 1

5
0 3 2 3 3 1 1 2
1 2 0 2 3 4
2 3 0 3 3 1 4 1
3 4 2 1 0 1 1 4 4 3
4 2 2 1 3 3

Sample Output 1

0 0
1 2
2 2
3 1
4 3

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in C++14 (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef pair<LL,LL> P;
const LL mod=1e9+7;
const LL LINF=1LL<<62;
string u="abcdefghijklmnopqrstuvwxyz";

struct edge {int to;LL cost;};

const int M_N=10000;

vector<edge> G[M_N+1];
LL d[M_N+1];

struct Dijkstra{

    void dijkstra(int s){
        priority_queue<P,vector<P>,greater<P>> que;
        que.push(P(0,s));
        while(!que.empty()){
            P p=que.top();
            que.pop();
            int v=p.second;
            if(d[v]<p.first) continue;
            for(int i=0;i<G[v].size();i++){
                edge e=G[v][i];
                if(d[e.to]>d[v]+e.cost){
                    d[e.to]=d[v]+e.cost;
                    que.push(P(d[e.to],e.to));
                }
            }
        }
    }

};

int main(){
    Dijkstra Ds;
    fill(d,d+M_N+1,LINF);
    d[0]=0;
    int N;
    cin >> N;
    int u,k,v,c;
    while(cin >> u >> k){
        for(int i=0;i<k;i++){
            cin >> v >> c;
            G[u].push_back({v,c});
        }
    }
    Ds.dijkstra(0);
    for(int i=0;i<N;i++){
        cout << i <<" "<< d[i] << endl;
    }
    return 0;
}