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

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 C (judge verdict: Accepted)

#include <stdio.h>
#define N 100

int size[N], m[N][N], count[N][N], d[N], n;

void DFS(int, int);

int main(){
	int i, j, a;
	
	scanf("%d", &n);
	
	for(i = 0; i < n; i++){
		scanf("%d", &a);
		scanf("%d", &size[a]);
		
		for(j = 0; j < size[a]; j++){
			scanf("%d", &m[a][j]);
			scanf("%d", &count[a][j]);
		}
	}
	for(i = 0; i < n; i++)
		d[i] = 1000000;
	
	DFS(0, 0);
	
	for(i = 0; i < n; i++)
		printf("%d %d\n", i, d[i]);
	
	return 0;
}

void DFS(int a, int b){
	int i;
	
	d[a] = b;
	
	for(i = 0; i < size[a]; i++){
		if(d[m[a][i]] > b + count[a][i])
			DFS(m[a][i], b + count[a][i]);
	}
}