package main

import (
	"container/heap"
	"fmt"
	"math"
)

// Edge represents a directed, non-negative weighted edge.
type Edge struct {
	To     int
	Weight int
}

type item struct {
	node int
	dist int
}

type priorityQueue []item

func (pq priorityQueue) Len() int            { return len(pq) }
func (pq priorityQueue) Less(i, j int) bool  { return pq[i].dist < pq[j].dist }
func (pq priorityQueue) Swap(i, j int)       { pq[i], pq[j] = pq[j], pq[i] }
func (pq *priorityQueue) Push(x any)         { *pq = append(*pq, x.(item)) }
func (pq *priorityQueue) Pop() any {
	old := *pq
	n := len(old)
	x := old[n-1]
	*pq = old[:n-1]
	return x
}

// Dijkstra returns distances and predecessors from source.
// Unreachable vertices have distance math.MaxInt and predecessor -1.
func Dijkstra(graph [][]Edge, source int) ([]int, []int) {
	if source < 0 || source >= len(graph) {
		panic("source vertex out of range")
	}

	dist := make([]int, len(graph))
	prev := make([]int, len(graph))
	for i := range graph {
		dist[i] = math.MaxInt
		prev[i] = -1
	}
	dist[source] = 0

	pq := &priorityQueue{{node: source, dist: 0}}
	heap.Init(pq)

	for pq.Len() > 0 {
		current := heap.Pop(pq).(item)
		if current.dist != dist[current.node] {
			continue // Ignore stale queue entries.
		}

		for _, edge := range graph[current.node] {
			if edge.To < 0 || edge.To >= len(graph) {
				panic("edge destination out of range")
			}
			if edge.Weight < 0 {
				panic("Dijkstra requires non-negative edge weights")
			}
			if current.dist > math.MaxInt-edge.Weight {
				continue // Avoid integer overflow.
			}

			candidate := current.dist + edge.Weight
			if candidate < dist[edge.To] {
				dist[edge.To] = candidate
				prev[edge.To] = current.node
				heap.Push(pq, item{node: edge.To, dist: candidate})
			}
		}
	}

	return dist, prev
}

// Path reconstructs the path from source to target using Dijkstra's predecessors.
func Path(prev []int, source, target int) []int {
	if source < 0 || source >= len(prev) || target < 0 || target >= len(prev) {
		return nil
	}

	var reversed []int
	for node := target; node != -1; node = prev[node] {
		reversed = append(reversed, node)
		if node == source {
			path := make([]int, len(reversed))
			for i := range reversed {
				path[len(reversed)-1-i] = reversed[i]
			}
			return path
		}
	}
	return nil
}

func main() {
	// Test a graph with multiple possible routes.
	graph := [][]Edge{
		{{To: 1, Weight: 4}, {To: 2, Weight: 1}},
		{{To: 3, Weight: 1}},
		{{To: 1, Weight: 2}, {To: 3, Weight: 5}},
		{},
	}
	dist, prev := Dijkstra(graph, 0)
	if dist[3] != 4 || fmt.Sprint(Path(prev, 0, 3)) != "[0 2 1 3]" {
		panic("shortest-path test failed")
	}

	// Test an unreachable vertex.
	disconnected := [][]Edge{
		{{To: 1, Weight: 7}},
		{},
		{},
	}
	dist, prev = Dijkstra(disconnected, 0)
	if dist[2] != math.MaxInt || Path(prev, 0, 2) != nil {
		panic("unreachable-vertex test failed")
	}
}