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)

(function(stdin) {
  var lines = stdin.trim().split('\n');
  var n = parseInt(lines.shift(), 10);
  var m = [];
  for (var i = 0; i < n; i++) {
    m[i] = [];
    for (var j = 0; j < n; j++) {
      m[i][j] = Infinity;
    }
  }
  lines.map(function(row) {
    var nums = row.trim().split(' ').map(Number);
    var u = nums.shift();
    var k = nums.shift();
    for (var i = 0; i < k; i++) {
      var v = nums.shift();
      var c = nums.shift();
      m[u][v] = c;
    }
  });
  var d = [], p = [], color = [];
  for (var i = 0; i < n; i++) {
    color[i] = 'WHITE';
    d[i] = Infinity;
  }
  d[0] = 0;
  p[0] = -1;
  var minv, u;
  while (1) {
    minv = Infinity;
    for (var i = 0; i < n; i++) {
      if (color[i] != 'BLACK' && d[i] < minv) {
        minv = d[i];
        u = i;
      }
    }
    if (minv == Infinity) {
      break;
    }
    color[u] = 'BLACK';
    for (var v = 0; v < n; v++) {
      if (color[v] != 'BLACK' && m[u][v] != Infinity) {
        if (d[u] + m[u][v] < d[v]) {
          d[v] = d[u] + m[u][v];
          p[v] = u;
          color[v] = 'GRAY';
        }
      }
    }
  }
  console.log(d.map(function(c, i) {return [i, c].join(' ');}).join('\n'));
})(require('fs').readFileSync('/dev/stdin', 'utf8'));