Problem:
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Single Source Shortest Path

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

$1 \leq n \leq 100$

$0 \leq c_i \leq 100,000$

$|E| \leq 10,000$

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 JavaScript (judge verdict: Accepted)

var h = [],hs = 0;
h[0] = new Array(2);
h[0][0] = -1;h[0][1] = -1;
 
function insert(key){
    h[++hs] = key;
 
    var i = hs;
 
    while(h[i][1] < h[Math.floor(i / 2)][1]){
        var ex = h[i];
        h[i] = h[Math.floor(i / 2)];
        h[Math.floor(i / 2)] = ex;
        i = Math.floor(i / 2);
    }
}
 
function extract(){
    if(hs <= 0)
        return;
 
    var ret = h[1];
 
    h[1] = h[hs--];
 
    i = 1;
    while((i * 2 <= hs && h[i][1] > h[i * 2][1]) || (i * 2 + 1 <= hs && h[i][1] > h[i * 2 + 1][1])){
        var l = i * 2;var r = i * 2;
        if(i * 2 + 1 <= hs)
            r++;
        var m = h[l][1] <= h[r][1] ? l : r;
        var ex = h[i];
        h[i] = h[m];
        h[m] = ex;
        i = m;
 
    }
    return ret;
}


function Main(input){
    input = input.split("\n");
    var n = parseInt(input[0],10);

    var graph = new Array(n);
    var k = new Array(n);

    for(var i = 0;i < n;i++){
        input[i + 1] = input[i + 1].split(" ");
        var u = parseInt(input[i + 1][0],10);
        k[u] = parseInt(input[i + 1][1],10);
        graph[u] = new Array(k[u]);
        for(var j = 0;j < k[u];j++)
            graph[u][j] = new Array(2);
        for(var j = 0;j < k[u];j++){
            graph[u][j][0] = parseInt(input[i + 1][j * 2 + 2],10);
            graph[u][j][1] = parseInt(input[i + 1][j * 2 + 3],10);
        }
    }

    var count = 1;
    var sum = Array(n);
    for(var i = 0;i < n;i++)
        sum[i] = 1000000000;
    sum[0] = 0;
    for(var i = 0;i < k[0];i++){
        insert(graph[0][i]);
    } 
    while(count < n){
        var aa = extract();
        if(sum[aa[0]] < 1000000000)
            continue;

        sum[aa[0]] = aa[1];
        count++;

        for(var i = 0;i < k[aa[0]];i++){
            graph[aa[0]][i][1] += sum[aa[0]];
            insert(graph[aa[0]][i]);
        }
    }

    for(var i = 0;i < n;i++){
        console.log(i + " " + sum[i]);
    }
}

Main(require("fs").readFileSync("/dev/stdin","utf8"));