package main

import (
	"fmt"
	"math"
)

func calcMin(maps []Map) float64 {
	var minDist float64 = math.MaxFloat64
	for _, m := range maps {
		for _, path := range m.paths {
			minDist = math.Min(minDist, calcMinPath(path, m.ponds))
		}
	}
	return minDist
}

func calcMinPath(path Path, ponds []Pond) float64 {
	var minDist float64 = math.MaxFloat64
	for _, pond := range ponds {
		for _, vertex := range pond.vertices {
			cinitial := path.start.distance(path.end)
			ainitial := path.end.distance(vertex)
			c := path.start.distance(vertex)
			alpha := math.Acos((ainitial*ainitial - cinitial*cinitial - c*c) / (-2 * cinitial * c))
			height := math.Sin(alpha) * c
			minDist = math.Min(minDist, height)
			fmt.Printf("alpha: %f, c: %f, cinital: %f, ainitial: %F, h: %f\n", alpha, c, cinitial, ainitial, height)
		}
	}
	return minDist
}