Go: // ダイクストラのアルゴリズム
package main

import (
	"bufio"
	"fmt"
	"log"
	"math"
	"os"
	"strconv"
	"strings"
)

type color int

const (
	white color = iota // 未訪問
	mst                // MSTとして確定
)

// 頂点
type node struct {
	num     int         // 頂点の番号
	weights map[int]int // 重みMAP
	parent  *node       // MSTへの重み最小の親
	sum     int         // 始点からの距離
	color   color
}

func (p *node) getMinToMst() int {
	if p.parent == nil {
		return math.MaxInt32
	}
	return p.weights[p.parent.num]
}

func main() {
	scanner := bufio.NewScanner(os.Stdin)
	n := eGetInt(scanner)

	nodes := make([]*node, n)
	for i := 0; i < n; i++ {
		weights := eAtoi((strings.Fields(eGetline(scanner))))
		v := &node{weights[0], make(map[int]int, weights[1]), nil, 0, white}
		for j := 0; j < weights[1]; j++ {
			k := weights[j*2+2] // 相手の頂点名
			w := weights[j*2+3] // 重み
			v.weights[k] = w
		}
		nodes[i] = v
	}

	// 初回はnode[0]がMSTに入るように
	nodes[0].parent = nodes[0]

	for { // 全部チェックするまで

		// どの頂点を新たにMSTに取り込むか

		var minNode *node
		min := math.MaxInt32
		for _, v := range nodes {
			if v.color == mst {
				continue
			}
			if v.getMinToMst() < min {
				min = v.getMinToMst()
				minNode = v
			}
		}
		if minNode == nil {
			// すべて完了している.
			break
		}

		// MSTに追加する頂点決定
		minNode.color = mst
		// 自分の親の合計値と合算する
		minNode.sum = minNode.parent.sum + min

		// MSTに属していない頂点それぞれについて,MSTとの最小の重みの距離を加算
		for _, v := range nodes {
			if v.color == mst {
				continue
			}
			w, ok := v.weights[minNode.num]
			if !ok {
				// minNodeと接してない
				continue
			}

			if w < v.getMinToMst() {
				// minNodeへの距離がもっとも重みが少ないので親を変更
				v.parent = minNode
			}
		}
	}

	for i, v := range nodes {
		fmt.Printf("%d %d\n", i, v.sum)
	}
}

func eGetInt(scanner *bufio.Scanner) int {
	t := eAtoi(strings.Fields(eGetline(scanner)))
	return t[0]
}

func eGetline(p *bufio.Scanner) string {
	if !p.Scan() {
		if err := p.Err(); err != nil {
			log.Fatal(err.Error())
		}
		return ""
	}
	return p.Text()
}

func eAtoi(s []string) []int {
	ints := make([]int, len(s))
	var err error
	for i, e := range s {
		ints[i], err = strconv.Atoi(e)
		if err != nil {
			log.Fatal(err.Error())
		}
	}
	return ints
}

C++: #include <iostream>
#include <cstdio>
#include <climits>
#include <cstring>

using namespace std;

#define SWAP(type, a, b) do { type t = a; a = b; b = t; } while(0)

typedef struct {
    int* verIdx;
    int num;
} Heap;

int* d; 
int* weight;
int n;

void makeMinHeap(Heap *heap, int idx);
void insert(Heap *heap, int key);
int extract(Heap *heap);

static inline int getParent(int idx) { return idx / 2; }
static inline int getLeft(int idx) { return idx * 2; }
static inline int getRight(int idx) { return idx * 2 + 1; }
static inline bool isCorrectHeapIdx(int idx, int heapSize) { return idx <= heapSize && 1 <= idx; }
static inline bool isEmpty(Heap *heap) { return heap->num <= 0; }

static inline int getMinCost(int idx) {
    return d[idx];
}

void makeMinHeap(Heap *heap, int idx) {
    int left = getLeft(idx);
    int right = getRight(idx);

    int minIdx = idx;
    if(isCorrectHeapIdx(left, heap->num) && getMinCost(heap->verIdx[minIdx]) > getMinCost(heap->verIdx[left])) {
        minIdx = left;
    } if(isCorrectHeapIdx(right, heap->num) && getMinCost(heap->verIdx[minIdx]) > getMinCost(heap->verIdx[right])) {
        minIdx = right;
    }

    if(minIdx != idx) {
        SWAP(int, heap->verIdx[minIdx], heap->verIdx[idx]);
        makeMinHeap(heap, minIdx);
    }
}

void insert(Heap *heap, int* key) {
    heap->verIdx[++heap->num] = *key;
    for(int i = getParent(heap->num); i >= 1; i = getParent(i)) {
        makeMinHeap(heap, i);
    }
}

void extract(Heap *heap, int* key) {
    *key = heap->verIdx[1];
    heap->verIdx[1] = heap->verIdx[heap->num--];
    makeMinHeap(heap, 1);
}

static inline bool isConnected(int s, int t) {
    return weight[s * n + t] != INT_MAX;
}

static inline int getWeight(int s, int t) {
    return weight[s * n + t];
}

void solve(int s) {
    Heap que;
    bool* isAddS = new bool[n]();

    que.verIdx = new int[n * n];
    que.num = 0;

    d = new int[n];
    d[s] = 0;
    for(int i = 0; i < n; i++) {
        if(s != i) {
            d[i] = INT_MAX;
        }
    }
    
    insert(&que, &s);

    while(1) {
        int u;
        while(1) {
            if(isEmpty(&que)) {
                return;
            } 

            extract(&que, &u);
            if(!isAddS[u]) {
                break;
            }
        }

        isAddS[u] = true;

        for(int i = 0; i < n; i++) {
            if(isConnected(u, i) && !isAddS[i]) {
                if(d[u] + getWeight(u, i) < d[i]) {
                    d[i] = d[u] + getWeight(u, i);
                }
                insert(&que, &i);
            }
        }
    }

    return;
}

int main() {

    scanf("%d", &n);

    weight = new int[n * n];

    for(int i = 0; i < n * n; i++) {
        weight[i] = INT_MAX;
    }
    

    for(int i = 0; i < n; i++) {
        int s;
        int deg;

        scanf("%d %d", &s, &deg);
        for(int j = 0; j < deg; j++) {
            int t;
            int w;

            scanf("%d %d", &t, &w);

            weight[s * n + t] = w;
        }
    }

    solve(0);

    for(int i = 0; i < n; i++) {
        cout << i << " " << d[i] << endl;
        
    }
}