package main

import (
	"bufio"
	"container/heap"
	"fmt"
	"log"
	"os"
	"strings"
)

func die(err error) {
	log.Fatal(err)
}

func check(err error) {
	if err != nil {
		die(err)
	}
}

func main() {
	solve("sample")
	solve("input")
}

func solve(filename string) {
	input, err := os.Open(filename + ".x")
	check(err)

	scanner := bufio.NewScanner(input)
	scanner.Split(bufio.ScanLines)
	total := 0
	for scanner.Scan() {
		line := scanner.Text()
		parts := strings.Fields(line)
		var nums []uint32
		for _, p := range parts {
			var x uint32
			fmt.Sscanf(p, "0x%x", &x)
			nums = append(nums, x)
		}
		//fmt.Printf("%b %v\n", nums, parts)
		n := best(nums[0], nums[1:])
		fmt.Printf("%b %v\n", nums, n)
		total += n
		//fmt.Println(n)
	}
	check(scanner.Err())
	fmt.Println(total)

}

// An CostHeap is a min-heap of ints.
type CostHeap struct {
	heap []uint32
	cost map[uint32]int
}

func (h *CostHeap) Len() int           { return len(h.heap) }
func (h *CostHeap) Less(i, j int) bool { return h.cost[h.heap[i]] < h.cost[h.heap[j]] }
func (h *CostHeap) Swap(i, j int)      { h.heap[i], h.heap[j] = h.heap[j], h.heap[i] }

func (h *CostHeap) Push(x any) {
	// Push and Pop use pointer receivers because they modify the slice's length,
	// not just its contents.
	h.heap = append(h.heap, x.(uint32))
}

func (h *CostHeap) Pop() any {
	old := h.heap
	n := len(old)
	x := old[n-1]
	h.heap = old[0 : n-1]
	return x
}

func best(target uint32, pool []uint32) int {
	//var states = []uint32{}
	var cost = make(map[uint32]int)
	h := &CostHeap{nil, cost}
	heap.Push(h, uint32(0))
	for h.Len() > 0 {
		s := heap.Pop(h).(uint32)
		if s == target {
			break
		}
		// enumerate all the states that can be reached by toggling button p
		for _, p := range pool {
			t := s ^ p
			if cost_t, ok := cost[t]; ok {
				if cost[s]+1 < cost_t {
					cost[t] = cost[s] + 1
					for i, x := range h.heap {
						if x == t {
							heap.Fix(h, i)
							break
						}
					}
				}
			} else {
				cost[t] = cost[s] + 1
				//states = append(states, t)
				heap.Push(h, t)
			}
		}
	}

	return cost[target]
}