Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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++14 (judge verdict: Accepted)

// ダイクストラ法
// Dijkstra's Algorithm
// priority_queue
// Single Source Shortest Path 2 単一始点最短経路
#include <iostream>
#include <cstring>
#include <algorithm>
#include <queue>
#include <stack>
#include <cstdio>
#include <cstdlib>
#include <vector>
using namespace std;

static const int MAX = 10000;
static const int INF = (1 << 21);
static const int WHITE = 0;
static const int GRAY = 1;
static const int BLACK = 2;

int n;
vector<pair<int, int>> adj[MAX]; //重み付き有向グラフ

void dijkstra() {

    priority_queue<pair<int, int>> PQ;
    int d[MAX], color[MAX];

    for(int i = 0; i < n; i++) {
        d[i] = INF;
        color[i] = WHITE;
    }

    d[0] = 0;
    PQ.push(make_pair(0, 0));
    color[0] = BLACK;

    while (!PQ.empty()) {
        
        pair<int, int> f = PQ.top();
        PQ.pop();
        int u = f.second;

        color[u] = BLACK;

        // 最小値を取り出し、それが最短でなければ無視
        if (d[u] < f.first * (-1)) continue;

        for(int j = 0; j < adj[u].size(); j++) {
            int v = adj[u][j].first;
            
            if (color[v] == BLACK) continue;

            if (d[v] > d[u] + adj[u][j].second) {
                d[v] = d[u] + adj[u][j].second;
                // priority_queueのため-1を掛ける
                PQ.push(make_pair(d[v]*(-1), v));
                color[v] = GRAY;
            }
        }
    }

    for(int i = 0; i < n; i++) {
        cout << i << " " << (d[i] == INF ? -1 : d[i]) << endl;
    }
}

int main() {

    cin >> n;
    int k, c, u, v;

    for(int i = 0; i < n; i++) {
        cin >> u >> k;
        for(int j = 0; j < k; j++) {
            cin >> v >> c;
            adj[u].push_back(make_pair(v, c));
        }
    }


    dijkstra();

    return 0;
}