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
+}

internal/engine/educate_test.go

@@ -0,0 +1,68 @@
+package engine
+
+import (
+	"slices"
+	"testing"
+)
+
+// starGraph builds a small graph with a known degree ranking:
+// node 0 has degree 5, node 1 degree 3, nodes 2 and 3 degree 2,
+// nodes 4 and 5 degree 1.
+func starGraph() *Graph {
+	graph := NewGraph(6)
+	for leaf := 1; leaf <= 5; leaf++ {
+		graph.AddEdge(0, leaf)
+	}
+	graph.AddEdge(1, 2)
+	graph.AddEdge(1, 3)
+	return graph
+}
+
+func TestEducateMostConnected(t *testing.T) {
+	tests := []struct {
+		name   string
+		origin int
+		count  int
+		want   []int
+	}{
+		{name: "picks top degrees, skips origin", origin: 0, count: 2, want: []int{1, 2}},
+		{name: "origin can be the biggest hub", origin: 1, count: 2, want: []int{0, 2}},
+		{name: "tie breaks to lower node number", origin: 0, count: 3, want: []int{1, 2, 3}},
+		{name: "count clamps to available students", origin: 0, count: 99, want: []int{1, 2, 3, 4, 5}},
+		{name: "zero count educates nobody", origin: 0, count: 0, want: nil},
+	}
+	for _, testCase := range tests {
+		t.Run(testCase.name, func(t *testing.T) {
+			got := EducateMostConnected(starGraph(), testCase.origin, testCase.count)
+			if !slices.Equal(got, testCase.want) {
+				t.Errorf("EducateMostConnected(origin=%d, count=%d) = %v, want %v",
+					testCase.origin, testCase.count, got, testCase.want)
+			}
+		})
+	}
+}
+
+func TestEducateRandomProperties(t *testing.T) {
+	graph := starGraph()
+	const origin, count = 0, 3
+
+	educated := EducateRandom(graph, origin, count, newRand(1))
+
+	if len(educated) != count {
+		t.Fatalf("len(educated) = %d, want %d", len(educated), count)
+	}
+	if slices.Contains(educated, origin) {
+		t.Errorf("educated %v contains the origin %d", educated, origin)
+	}
+	for index := 1; index < len(educated); index++ {
+		if educated[index] == educated[index-1] {
+			t.Errorf("educated %v contains a duplicate", educated)
+		}
+	}
+
+	// Same seed, same pick; that is the determinism contract.
+	repeat := EducateRandom(graph, origin, count, newRand(1))
+	if !slices.Equal(educated, repeat) {
+		t.Errorf("same seed picked %v then %v", educated, repeat)
+	}
+}