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 Go (judge verdict: Accepted)

package main

import (
	"bufio"
	"container/heap"
	"fmt"
	"os"
	"strconv"
)

func getScanner(fp *os.File) *bufio.Scanner {
	scanner := bufio.NewScanner(fp)
	scanner.Split(bufio.ScanWords)
	scanner.Buffer(make([]byte, 500001), 500000)
	return scanner
}

func getNextString(scanner *bufio.Scanner) string {
	scanner.Scan()
	return scanner.Text()
}

func getNextInt(scanner *bufio.Scanner) int {
	i, _ := strconv.Atoi(getNextString(scanner))
	return i
}

func main() {
	fp := os.Stdin
	if len(os.Args) > 1 {
		fp, _ = os.Open(os.Args[1])
	}

	scanner := getScanner(fp)
	writer := bufio.NewWriter(os.Stdout)

	n := getNextInt(scanner)
	list := make([]Nodes, n)

	for i := 0; i < n; i++ {
		heap.Init(&list[i])
	}

	for i := 0; i < n; i++ {
		u := getNextInt(scanner)
		k := getNextInt(scanner)
		for ii := 0; ii < k; ii++ {
			v := getNextInt(scanner)
			c := getNextInt(scanner)
			heap.Push(&list[u], &Node{
				id:   v,
				cost: c,
			})
		}
	}

	ans := make([]int, n)
	for i := 0; i < n; i++ {
		ans[i] = 1 << 30
	}
	h := make(Nodes, 0)
	heap.Init(&h)
	heap.Push(&h, &Node{
		id:   0,
		cost: 0,
	})

	im := make(IntMap, 1)

	for len(h) > 0 {
		node := heap.Pop(&h).(*Node)
		u := node.id
		if ans[u] < node.cost {
			continue
		}
		ans[node.id] = node.cost
		im.increment(u)
		for l := list[u].Len(); l > 0; l-- {
			p := heap.Pop(&list[u]).(*Node)
			v := p.id
			c := p.cost
			if im.get(v) != 0 {
				continue
			}
			if ans[v] > ans[u]+c {
				ans[v] = ans[u] + c
				heap.Push(&h, &Node{
					id:   v,
					cost: ans[v],
				})
			}
		}
	}

	for i := 0; i < n; i++ {
		fmt.Fprintln(writer, fmt.Sprintf("%d %d", i, ans[i]))
	}
	writer.Flush()
}

// Node ...
type Node struct {
	id   int
	cost int
}

// Nodes ...
type Nodes []*Node

func (a Nodes) Len() int           { return len(a) }
func (a Nodes) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }
func (a Nodes) Less(i, j int) bool { return a[i].cost < a[j].cost }

// Push ...
func (a *Nodes) Push(x interface{}) {
	*a = append(*a, x.(*Node))
}

// Pop ...
func (a *Nodes) Pop() interface{} {
	old := *a
	n := len(old)
	x := old[n-1]
	*a = old[0 : n-1]
	return x
}

// IntMap ...
type IntMap map[int]int

func (m IntMap) get(key int) int {
	if _, ok := m[key]; ok {
		return m[key]
	}
	return 0
}
func (m IntMap) increment(key int) {
	if _, ok := m[key]; ok == false {
		m[key] = 0
	}
	m[key]++
}