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 Kotlin (judge verdict: Accepted)

fun main(args: Array<String>) {
    Main.init()

    Main.execute()

    Main.display()
}

data class Timestamp(var findedAt: Int? = null, var endedAt: Int? = null)

class Main {

    companion object {
        private val graphMatrix = arrayListOf<ArrayList<Int>>()

        private val nodeList = arrayListOf<Node>()

        fun init() {
            val num = readLine()!!.toInt()

            // 初期化
            for (i in 1..num) {
                // ノード初期化
                nodeList.add(Node())

                // グラフ行列初期化
                graphMatrix.add(arrayListOf())
                for (j in 1..num) {
                    graphMatrix[i - 1].add(Int.MAX_VALUE)
                }
            }

            // データ投入
            for (hoge in 1..num) {

                val inputs = readLine()!!.split(" ")

                val edgeNum = inputs[1].toInt()

                for (index in 0 until edgeNum) {
                    val toIndex = inputs[(index * 2) + 2].toInt()
                    val toCost = inputs[(index * 2) + 3].toInt()
                    graphMatrix[inputs[0].toInt()][toIndex] = toCost
                }

            }
        }

        fun display() {

            nodeList.forEachIndexed{index, node->
                println("$index ${node.minCost}")
            }
        }

        /**
         * 深さ優先
         */
        fun execute() {

            nodeList[0].minCost = 0

            while (true) {
                // 黒ではなく、なおかつ最小のノードを取得
                var minCost = Int.MAX_VALUE
                var minIndex: Int? = null
                for (index in 1..nodeList.size) {
                    if (nodeList[index - 1].color != Node.Color.BLACK && minCost > nodeList[index - 1].minCost) {
                        minCost = nodeList[index - 1].minCost
                        minIndex = index
                    }
                }

                // 一つもないので終了
                if (minCost == Int.MAX_VALUE || minIndex == null) {
                    break
                }

                // ノードを取得
                val currentNode = nodeList[minIndex - 1]

                // 色を変える
                currentNode.color = Node.Color.BLACK


                graphMatrix[minIndex - 1].forEachIndexed { index, cost ->
                    // 調査対象かどうかチェック
                    if (nodeList[index].color != Node.Color.BLACK && cost != Int.MAX_VALUE) {

                        // もともとのコストより小さいかチェック
                        val originalCost = nodeList[index].minCost
                        val foundedDistanceCost = graphMatrix[minIndex!! - 1][index]
                        val foundedTotalCost = foundedDistanceCost + currentNode.minCost
                        if (originalCost > foundedTotalCost) {
                            nodeList[index].color = Node.Color.GRAY
                            nodeList[index].minCost = foundedTotalCost
                            nodeList[index].parent = minIndex!! - 1
                        }
                    }
                }
            }
        }
    }
}


open class Node {
    enum class Color {
        WHITE, GRAY, BLACK
    }

    var minCost: Int = Int.MAX_VALUE

    var color: Color = Color.WHITE

    var parent: Int? = null

    override fun toString(): String {
        return "cost: $minCost, color: $color,  parent: ${parent}"
    }
}