2-B-1, 2-B-2

2-B-2/go.mod

@@ -0,0 +1,3 @@
+module algo
+
+go 1.26.3

2-B-2/main.go

@@ -0,0 +1,52 @@
+package algo
+
+func DP(arr []int) int {
+	n := len(arr) - 1
+	if n <= 0 {
+		return 0
+	}
+
+	const inf = int(^uint(0) >> 1)
+	dp := make([][]int, n)
+	for i := range dp {
+		dp[i] = make([]int, n)
+	}
+
+	for length := 2; length <= n; length++ {
+		for l := 0; l+length-1 < n; l++ {
+			r := l + length - 1
+			dp[l][r] = inf
+			for k := l; k < r; k++ {
+				cost := dp[l][k] + dp[k+1][r] + arr[l]*arr[k+1]*arr[r+1]
+				if cost < dp[l][r] {
+					dp[l][r] = cost
+				}
+			}
+		}
+	}
+
+	return dp[0][n-1]
+}
+
+func Greedy(arr []int) int {
+	if len(arr) <= 2 {
+		return 0
+	}
+
+	dims := append([]int(nil), arr...)
+	cost := 0
+
+	for len(dims) > 2 {
+		best := 1
+		for i := 2; i < len(dims)-1; i++ {
+			if dims[i] > dims[best] {
+				best = i
+			}
+		}
+
+		cost += dims[best-1] * dims[best] * dims[best+1]
+		dims = append(dims[:best], dims[best+1:]...)
+	}
+
+	return cost
+}

2-B-2/main_test.go

@@ -0,0 +1,61 @@
+package algo
+
+import (
+	"math/rand"
+	"testing"
+)
+
+func TestDPKnownCase(t *testing.T) {
+	arr := []int{30, 35, 15, 5, 10, 20, 25}
+	want := 15125
+
+	if got := DP(arr); got != want {
+		t.Fatalf("DP(%v) = %d, want %d", arr, got, want)
+	}
+}
+
+func TestGreedyRandomCompare(t *testing.T) {
+	r := rand.New(rand.NewSource(1))
+
+	for tc := 0; tc < 500; tc++ {
+		matrixCount := r.Intn(5) + 3
+		arr := make([]int, matrixCount+1)
+		for i := range arr {
+			arr[i] = r.Intn(9) + 2
+		}
+
+		greedy := Greedy(arr)
+		dp := DP(arr)
+		if greedy < dp {
+			t.Fatalf("greedy beat dp unexpectedly: arr=%v greedy=%d dp=%d", arr, greedy, dp)
+		}
+	}
+}
+
+func TestGreedyIsNotAlwaysOptimal(t *testing.T) {
+	r := rand.New(rand.NewSource(2))
+	found := false
+
+	for tc := 0; tc < 500; tc++ {
+		matrixCount := r.Intn(5) + 3
+		arr := make([]int, matrixCount+1)
+		for i := range arr {
+			arr[i] = r.Intn(9) + 2
+		}
+
+		greedy := Greedy(arr)
+		dp := DP(arr)
+		if dp < greedy {
+			t.Logf("found counterexample: arr=%v greedy=%d dp=%d", arr, greedy, dp)
+			found = true
+		}
+
+		if dp > greedy {
+			t.Fatalf("why greedy < dp???")
+		}
+	}
+
+	if !found {
+		t.Fatal("expected to find at least one case where dp < greedy")
+	}
+}