engine: education strategies (random vs most-connected)

Two ways to spend the same education budget: a uniform random sample
(spray and pray) vs the highest-degree hubs, ties broken stably towards
lower node numbers so the pick is deterministic. The origin is never
educated; they post the fake. rng.Shuffle does a seeded Fisher-Yates,
so the random pick is reproducible too. min() is a builtin since
Go 1.21.

internal/engine/educate.go

@@ -0,0 +1,52 @@
+package engine
+
+import (
+	"math/rand/v2"
+	"slices"
+)
+
+// Education strategies pick which students the program educates. The origin
+// is never educated (they post the fake in the first place). Returned
+// slices are sorted by node number for readable, stable output; the order
+// carries no meaning.
+
+// EducateRandom educates count students drawn uniformly from everyone but
+// the origin. This is the "spray and pray" baseline.
+func EducateRandom(graph *Graph, origin, count int, rng *rand.Rand) []int {
+	if count <= 0 {
+		return nil
+	}
+	candidates := make([]int, 0, graph.NumNodes()-1)
+	for student := range graph.NumNodes() {
+		if student != origin {
+			candidates = append(candidates, student)
+		}
+	}
+	rng.Shuffle(len(candidates), func(i, j int) {
+		candidates[i], candidates[j] = candidates[j], candidates[i]
+	})
+	educated := candidates[:min(count, len(candidates))]
+	slices.Sort(educated)
+	return educated
+}
+
+// EducateMostConnected educates the count students with the highest degree:
+// the hubs whose forwarding keeps the network connected. Ties break towards
+// the lower node number (stable sort) so the choice is deterministic.
+func EducateMostConnected(graph *Graph, origin, count int) []int {
+	if count <= 0 {
+		return nil
+	}
+	candidates := make([]int, 0, graph.NumNodes()-1)
+	for student := range graph.NumNodes() {
+		if student != origin {
+			candidates = append(candidates, student)
+		}
+	}
+	slices.SortStableFunc(candidates, func(first, second int) int {
+		return graph.Degree(second) - graph.Degree(first) // descending by degree
+	})
+	educated := candidates[:min(count, len(candidates))]
+	slices.Sort(educated)
+	return educated
+}