package main

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

type Edge struct {
	To     int
	Weight int64
}

type item struct {
	vertex   int
	distance int64
}

type priorityQueue []item

func (pq priorityQueue) Len() int           { return len(pq) }
func (pq priorityQueue) Less(i, j int) bool { return pq[i].distance < pq[j].distance }
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 predecessor vertices from source.
// Unreachable vertices have distance math.MaxInt64 and predecessor -1.
func Dijkstra(graph [][]Edge, source int) ([]int64, []int, error) {
	if source < 0 || source >= len(graph) {
		return nil, nil, fmt.Errorf("source vertex %d is out of range", source)
	}

	dist := make([]int64, len(graph))
	prev := make([]int, len(graph))
	for i := range graph {
		dist[i] = math.MaxInt64
		prev[i] = -1
	}

	dist[source] = 0
	pq := &priorityQueue{{vertex: source, distance: 0}}
	heap.Init(pq)

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

		for _, edge := range graph[current.vertex] {
			if edge.To < 0 || edge.To >= len(graph) {
				return nil, nil, fmt.Errorf("edge destination %d is out of range", edge.To)
			}
			if edge.Weight < 0 {
				return nil, nil, fmt.Errorf("negative edge weight from %d to %d", current.vertex, edge.To)
			}
			if dist[current.vertex] > math.MaxInt64-edge.Weight {
				continue // This path would overflow.
			}

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

	return dist, prev, nil
}

// Path reconstructs a source-to-target path from 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 vertex := target; vertex != -1; vertex = prev[vertex] {
		reversed = append(reversed, vertex)
		if vertex == source {
			path := make([]int, len(reversed))
			for i := range reversed {
				path[len(reversed)-1-i] = reversed[i]
			}
			return path
		}
	}
	return nil
}

func main() {
	// Basic shortest-path test.
	graph := [][]Edge{
		{{To: 1, Weight: 4}, {To: 2, Weight: 1}},
		{{To: 3, Weight: 1}},
		{{To: 1, Weight: 2}, {To: 3, Weight: 5}},
		nil,
	}
	dist, prev, err := Dijkstra(graph, 0)
	if err != nil || dist[3] != 4 || !equal(Path(prev, 0, 3), []int{0, 2, 1, 3}) {
		panic("shortest-path test failed")
	}

	// Unreachable-vertex test.
	dist, prev, err = Dijkstra([][]Edge{{{To: 1, Weight: 2}}, nil, nil}, 0)
	if err != nil || dist[2] != math.MaxInt64 || Path(prev, 0, 2) != nil {
		panic("unreachable-vertex test failed")
	}
}

func equal(a, b []int) bool {
	if len(a) != len(b) {
		return false
	}
	for i := range a {
		if a[i] != b[i] {
			return false
		}
	}
	return true
}