package dijkstra

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

// Edge is a directed, weighted edge to another vertex.
type Edge struct {
	To     int
	Weight int
}

// Dijkstra returns distances and predecessors for shortest paths from source.
// Unreachable vertices have distance math.MaxInt and predecessor -1.
func Dijkstra(graph [][]Edge, source int) ([]int, []int, error) {
	if source < 0 || source >= len(graph) {
		return nil, nil, fmt.Errorf("source vertex %d is out of range", source)
	}

	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{{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 from %d targets invalid vertex %d", current.vertex, edge.To)
			}
			if edge.Weight < 0 {
				return nil, nil, fmt.Errorf("edge from %d to %d has negative weight", current.vertex, edge.To)
			}
			if current.distance > math.MaxInt-edge.Weight {
				continue // This path cannot be represented by int.
			}

			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 int
}

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
}

func TestDijkstra(t *testing.T) {
	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 {
		t.Fatal(err)
	}

	wantDist := []int{0, 3, 1, 4}
	wantPrev := []int{-1, 2, 0, 1}
	for i := range wantDist {
		if dist[i] != wantDist[i] || prev[i] != wantPrev[i] {
			t.Fatalf("vertex %d: got distance=%d predecessor=%d; want distance=%d predecessor=%d",
				i, dist[i], prev[i], wantDist[i], wantPrev[i])
		}
	}
}

func TestDijkstraUnreachableVertex(t *testing.T) {
	graph := [][]Edge{
		{{To: 1, Weight: 7}},
		nil,
		nil,
	}

	dist, prev, err := Dijkstra(graph, 0)
	if err != nil {
		t.Fatal(err)
	}
	if dist[2] != math.MaxInt || prev[2] != -1 {
		t.Fatalf("unreachable vertex: got distance=%d predecessor=%d", dist[2], prev[2])
	}
}