Advent of Code 2021 Day 12: Passage Pathing
By Andreas Røssland
https://adventofcode.com/2021/day/12 https://github.com/roessland/advent-of-code
Finally a graph problem. This turns out to be a variation of DFS (depth-first search), that I solved using recursion. Since the path search must be exhaustive (find all paths) we can use DFS instead of BFS (breadth-first search) which is slightly easier to implement. In addition there is no need to keep passing down copies of the visited state since each step of DFS can effectively “undo” what it did before recursing, making it possible to use a single shared map for storing this.
For part 2 any single small cave can be visited twice instead of just once, drastically increasing the number of possible paths. I solved this by giving the search a “token”. If a small cave is already visited, the token can be used to visit the cave again. The token can only be used once for each path from start to end, and is optional to use.
Finally, I optimized the solution by returning the number of paths instead of the entire list of paths. This reduced the runtime from 0.9 seconds to around 0.05 seconds.
package main
import (
"bufio"
"fmt"
"log"
"os"
"strings"
"time"
)
func main() {
t0 := time.Now()
g := ReadInput()
part1(g)
part2(g)
fmt.Println(time.Since(t0))
}
func part1(g Graph) {
visited := map[string]int{}
paths := search(g, "start", visited, false)
fmt.Println("Part 1:", paths)
}
func part2(g Graph) {
visited := map[string]int{}
paths := search(g, "start", visited, true)
fmt.Println("Part 2:", paths)
}
func search(g Graph, fromId string, visited map[string]int, token bool) int {
if fromId == "end" {
return 1
}
if IsSmall(fromId) {
visited[fromId]++
}
var paths int
for _, neighborId := range g[fromId] {
if neighborId == "start" {
continue
}
if visited[neighborId] == 0 {
// Visit without using token
paths += search(g, neighborId, visited, token)
} else if IsSmall(neighborId) && token {
// Visit using token
paths += search(g, neighborId, visited, false)
}
}
if IsSmall(fromId) {
visited[fromId]--
}
return paths
}
type Graph map[string][]string
func (g Graph) AddNode(id string) {
if g[id] == nil {
g[id] = make([]string, 0)
}
}
func (g Graph) AddEdge(nodeId1 string, nodeId2 string) {
g[nodeId1] = append(g[nodeId1], nodeId2)
g[nodeId2] = append(g[nodeId2], nodeId1)
}
func IsSmall(nodeId string) bool {
return strings.ToLower(nodeId) == nodeId
}
func ReadInput() Graph {
f, err := os.Open("input.txt")
if err != nil {
log.Fatal(err)
}
scanner := bufio.NewScanner(f)
g := make(Graph)
for scanner.Scan() {
nodes := strings.Split(scanner.Text(), "-")
g.AddNode(nodes[0])
g.AddNode(nodes[1])
g.AddEdge(nodes[0], nodes[1])
}
return g
}