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 (judge verdict: Memory Limit Exceeded)

#include<stdio.h>

#define WHITE 0
#define BLACK 1
#define N 10000
#define INF 1000000

int d[N];
int color[N];
int w[N][N];
int pi[N];


void difkstra(int,int);

int main()
{
    int i,n,j,k,c,u,v;
    
    scanf("%d",&n);
    for(i=0;i<n;i++)
    {
        for(j=0;j<n;j++)
        {
            w[i][j]=-1;
        }
    }
    for(i=0;i<n;i++)
    {
        scanf("%d%d",&u,&k);
        for(j=0;j<k;j++)
        {
            scanf("%d%d",&v,&c);
            w[u][v]=c;
        }
    }
    difkstra(n,0);
    
    for(i=0;i<n;i++)
    {
        printf("%d %d\n",i,d[i]);
    }
    
    return 0;
}

void difkstra(int n,int s)
{
    int i,j,u,v;
    int mincost;
    for(v=0; v<n; v++)
    {
        d[v] = INF;
        pi[v]=-1;
        color[v]=WHITE;
    }
    d[s]=0;
    
    while(1)
    {
        mincost=INF;
        for(i=0;i<n;i++)
        {
            if(color[i]!=BLACK && d[i]<mincost)
            {
                mincost=d[i];
                u=i;
            }
        }
        if(mincost==INF)
            break;
        
        color[u]=BLACK;
        
        for(v=0;v<n;v++)
        {
            if(color[v]!=BLACK && w[u][v]+d[u]<d[v] && w[u][v]>=0)
            {
                pi[v]=u;
                d[v]=w[u][v]+d[u];
            }
        }
        
        
    }
    
}