package main

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

// Edge is a directed, non-negative weighted edge.
type Edge struct {
	To     int
	Weight int64
}

// Dijkstra returns distances and predecessors 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 %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: %d", edge.Weight)
			}
			if current.distance > math.MaxInt64-edge.Weight {
				continue // The candidate distance would overflow.
			}

			candidate := current.distance + 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
}

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(value any) {
	*pq = append(*pq, value.(item))
}

func (pq *priorityQueue) Pop() any {
	old := *pq
	last := old[len(old)-1]
	*pq = old[:len(old)-1]
	return last
}

// Lightweight tests keep this example self-contained in one source file.
func main() {
	graph := [][]Edge{
		{{To: 1, Weight: 4}, {To: 2, Weight: 1}},
		{{To: 3, Weight: 1}},
		{{To: 1, Weight: 2}, {To: 3, Weight: 5}},
		nil,
		nil,
	}

	dist, prev, err := Dijkstra(graph, 0)
	if err != nil {
		panic(err)
	}
	assertEqual(dist, []int64{0, 3, 1, 4, math.MaxInt64})
	assertEqual(prev, []int{-1, 2, 0, 1, -1})

	_, _, err = Dijkstra([][]Edge{{{To: 0, Weight: -1}}}, 0)
	if err == nil {
		panic("expected negative-weight error")
	}
}

func assertEqual[T comparable](got, want []T) {
	if len(got) != len(want) {
		panic(fmt.Sprintf("length mismatch: got %d, want %d", len(got), len(want)))
	}
	for i := range got {
		if got[i] != want[i] {
			panic(fmt.Sprintf("index %d: got %v, want %v", i, got[i], want[i]))
		}
	}
}