day8, example3 new approach

day8/dayEight.go

@@ -18,8 +18,7 @@ func Run() int {
 	return result
 }
 
-func GhostTraverse(net Network, path Path) int {
-	stepsNum := 0
+func getGhostStartNodes(net Network) []Node {
 	simultaneousPaths := make([]Node, 0)
 	for nodeName, node := range net.Nodes {
 		if strings.HasSuffix(nodeName, "A") {
@@ -27,28 +26,94 @@ func GhostTraverse(net Network, path Path) int {
 		}
 	}
 	log.Printf("collected start points: %+v\n", simultaneousPaths)
-
-	// concurrent iteraction
-	for !isGhostWayDone(simultaneousPaths) {
-		direction := path.next()
-		for i, curNode := range simultaneousPaths {
-			simultaneousPaths[i] = getNextNode(net, curNode, direction)
-		}
-		// log.Printf("done step into %+v\n", simultaneousPaths)
-		stepsNum += 1
-	}
-
-	return stepsNum
+	return simultaneousPaths
 }
 
-func isGhostWayDone(simulaneousPath []Node) bool {
-	containsNonZEnding := slices.ContainsFunc(simulaneousPath, func(curNode Node) bool {
-		name := curNode.Name
-		last := name[len(name) - 1]
-		return last != 'Z'
-	})
-	// log.Printf("checking if done for %+v : %t", simulaneousPath, !containsNonZEnding)
-	return !containsNonZEnding
+type GhostPathInfo struct {
+	InitialSteps, CycleLen int
+}
+
+func getGhostPathInfo(startNode Node, net Network, pathString string) GhostPathInfo {
+	path := Path {Instruction: pathString}
+	initialSteps, cycleLen := 0, 1
+	runnerNode := startNode
+
+	for !strings.HasSuffix(runnerNode.Name, "Z") {
+		direction := path.next()
+		runnerNode = getNextNode(net, runnerNode, direction)
+		initialSteps += 1
+	}
+	// one more step for starting to check for cycle
+	oneDirection := path.next()
+	runnerNode = getNextNode(net, runnerNode, oneDirection)
+
+	for !strings.HasSuffix(runnerNode.Name, "Z") {
+		direction := path.next()
+		runnerNode = getNextNode(net, runnerNode, direction)
+		cycleLen += 1
+	}
+
+	return GhostPathInfo{
+		InitialSteps: initialSteps,
+		CycleLen: cycleLen,
+	}
+}
+
+func GhostTraverse(net Network, path Path) int {
+	simultaneousPaths := getGhostStartNodes(net)
+	pathInfos := make([]GhostPathInfo, 0, len(simultaneousPaths))
+	for _, pathStart := range simultaneousPaths {
+		pathInfos = append(pathInfos, getGhostPathInfo(pathStart, net, path.Instruction))
+	}
+	log.Printf("path infos are %+v\n", pathInfos)
+
+	// and now the algo.
+	// if initial paths equal - that's answer
+	// if not - seed round, +1 cycle to each
+	// if equal - that the answer
+	// if not - here's the main loop
+	// find biggest.
+	// then iterate all but that one.
+	// calculate diff % curCycle. if == 0, just add to where they stand together
+	// if not - add cycles to this with one overhopping
+	// and check whether they are all equeal
+
+	stepCounts := make([]int, len(pathInfos))
+	for i, pathInfo := range pathInfos {
+		stepCounts[i] = pathInfo.InitialSteps
+	}
+
+	// oh, i don't need to seed the cycle, they are already not equal
+	for !allEqual(stepCounts) {
+		max := slices.Max(stepCounts)
+		for i, pathInfo := range pathInfos {
+			steps := stepCounts[i]
+			if steps == max {
+				continue
+			}
+			diff := max - steps
+			isCatchingUp := diff % pathInfo.CycleLen == 0
+			if isCatchingUp {
+				stepCounts[i] = max
+			} else {
+				overJump := (diff / pathInfo.CycleLen + 1) * pathInfo.CycleLen
+				stepCounts[i] += overJump
+			}
+		}
+		log.Printf("done one cycle iteration, results : %+v", stepCounts)
+	}
+
+	return stepCounts[0]
+}
+
+func allEqual(nums []int) bool {
+	head := nums[0]
+	for _, num := range nums {
+		if num != head {
+			return false
+		}
+	}
+	return true
 }
 
 func getNextNode(net Network, curNode Node, direction rune) Node {

day8/notes.org

@@ -0,0 +1,29 @@
+#+title: Notes
+* ok, for part 2 i think i'm supposed to find cicles.
+so for each starting point?
+calculate how long it takes to get to first Z, let's call is initialN
+and then how long it takes to get to Z again, call it cicleN
+
+i have initial0 + n0 * cicle0 = k
+
+now i need to find minimal number K ( steps ), so that exists solution for each starting point
+
+(k - initial0) % cycle0 == 0
+
+so. get both these numbers for each starting point.
+if initialN are equal, that's the answer.
+
+if they are not equal?
+then i have what? huh
+
+i guess then i need to add 1 cycle length to all.
+if they are equal, nice.
+
+but if they are not equal?
+i guess i have one that's longest?
+then i need to advance all paths, up to and overshoot if necessary by their cycle lengths.
+so take the difference, if divisible by cycle - yay. just multiply, if not divisible - overshoot with +1 cycle
+
+if all are same, that's solution.
+if one is farthest, repeat
+* i stopped bruteforce at 4080000000