package q1466

import "math"

func walk(connections [][2][]int, minFlips []int32, node int) {
	mf := minFlips[node]

	// Walk no-flip-needed
	for _, n := range connections[node][1] {
		if mf < minFlips[n] {
			minFlips[n] = mf
			walk(connections, minFlips, n)
		}
	}

	// Walk flip-needed
	for _, n := range connections[node][0] {
		if mf+1 < minFlips[n] {
			minFlips[n] = mf + 1
			walk(connections, minFlips, n)
		}
	}
}

func collect(connections [][2][]int, minFlips []int32, node int, visited []bool) int32 {
	mf := minFlips[node]
	var sum int32

	for _, n := range connections[node][1] {
		if !visited[n] && mf == minFlips[n] {
			visited[n] = true
			sum += collect(connections, minFlips, n, visited) - mf
		}
	}

	for _, n := range connections[node][0] {
		if !visited[n] && mf+1 == minFlips[n] {
			visited[n] = true
			sum += collect(connections, minFlips, n, visited) - mf
		}
	}

	return sum + mf
}

func minReorder(n int, connections [][]int) int {
	conns := make([][2][]int, n)
	for i := range connections {
		from, to := connections[i][0], connections[i][1]
		conns[from][0] = append(conns[from][0], to)
		conns[to][1] = append(conns[to][1], from)
	}

	minFlips := make([]int32, n) // minimum flips to reach node n
	minFlips[0] = math.MaxInt32
	for i := 1; i < len(minFlips); i *= 2 {
		copy(minFlips[i:], minFlips[:i])
	}
	minFlips[0] = 0

	walk(conns, minFlips, 0)

	visited := make([]bool, n)
	return int(collect(conns, minFlips, 0, visited))
}

var _ = minReorder