2-B-1, 2-B-2

2026-05-11 20:23:54 +08:00
parent 7ccb2ea522
commit 459af53f27
6 changed files with 236 additions and 0 deletions
@@ -0,0 +1,4 @@
+module algo
+
+go 1.26.3
+
@@ -0,0 +1,41 @@
+package algo
+
+func DP(t1 []int, t2 []int, e1 []int, e2 []int) int {
+	Len := len(t1)
+	if len(t2) != Len || len(e1) != Len || len(e2) != Len {
+		return -1
+	}
+	dp1 := make([]int, Len)
+	dp2 := make([]int, Len)
+	dp1[0], dp2[0] = t1[0], t2[0]
+
+	for i := 1; i < Len; i++ {
+		dp1[i] = min(dp1[i-1], dp2[i-1]+e2[i-1]) + t1[i]
+		dp2[i] = min(dp2[i-1], dp1[i-1]+e1[i-1]) + t2[i]
+	}
+
+	return min(dp1[Len-1], dp2[Len-1])
+}
+
+func Rec(t1 []int, t2 []int, e1 []int, e2 []int) int {
+	Len := len(t1)
+	if len(t2) != Len || len(e1) != Len || len(e2) != Len {
+		return -1
+	}
+
+	return min(rec(t1, t2, e1, e2))
+}
+
+func rec(t1 []int, t2 []int, e1 []int, e2 []int) (int, int, int, int) {
+	Len := len(t1)
+	if Len == 1 {
+		return t1[0], 0x3f3f3f3f3f3f3f3f, 0x3f3f3f3f3f3f3f3f, t2[0]
+	}
+	mid := Len / 2
+	a11, a12, a21, a22 := rec(t1[:mid], t2[:mid], e1[:mid], e2[:mid])
+	b11, b12, b21, b22 := rec(t1[mid:], t2[mid:], e1[mid:], e2[mid:])
+	s1 := e1[mid-1]
+	s2 := e2[mid-1]
+	return min(a11+b11, a11+s1+b21, a12+s2+b11, a12+b21), min(a11+b12, a11+s1+b22, a12+s2+b12, a12+b22),
+		min(a21+b11, a21+s1+b21, a22+b21, a22+s2+b11), min(a21+b12, a21+s1+b22, a22+b22, a22+s2+b12)
+}
@@ -0,0 +1,75 @@
+package algo
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+)
+
+type testCase struct {
+	t1 []int
+	t2 []int
+	e1 []int
+	e2 []int
+}
+
+func randomCase(rng *rand.Rand, n int) testCase {
+	tc := testCase{
+		t1: make([]int, n),
+		t2: make([]int, n),
+		e1: make([]int, n),
+		e2: make([]int, n),
+	}
+
+	for i := 0; i < n; i++ {
+		tc.t1[i] = rng.Intn(1000)
+		tc.t2[i] = rng.Intn(1000)
+		tc.e1[i] = rng.Intn(1000)
+		tc.e2[i] = rng.Intn(1000)
+	}
+
+	return tc
+}
+
+func TestRecAndDPMatchOnRandomData(t *testing.T) {
+	rng := rand.New(rand.NewSource(1))
+	const casesPerLen = 200
+
+	for n := 1; n <= 128; n++ {
+		for caseIdx := 0; caseIdx < casesPerLen; caseIdx++ {
+			tc := randomCase(rng, n)
+			gotRec := Rec(tc.t1, tc.t2, tc.e1, tc.e2)
+			gotDP := DP(tc.t1, tc.t2, tc.e1, tc.e2)
+			if gotRec != gotDP {
+				t.Fatalf("mismatch for len=%d case=%d: Rec=%d DP=%d t1=%v t2=%v e1=%v e2=%v",
+					n, caseIdx, gotRec, gotDP, tc.t1, tc.t2, tc.e1, tc.e2)
+			}
+		}
+	}
+}
+
+func BenchmarkDP(b *testing.B) {
+	benchmarkByLen(b, "DP", DP)
+}
+
+func BenchmarkRec(b *testing.B) {
+	benchmarkByLen(b, "Rec", Rec)
+}
+
+func benchmarkByLen(b *testing.B, name string, fn func([]int, []int, []int, []int) int) {
+	lengths := []int{1, 10, 100, 1000, 10000, 100000, 1000000, 10000000}
+
+	for _, n := range lengths {
+		n := n
+		b.Run(fmt.Sprintf("%s/len=%d", name, n), func(b *testing.B) {
+			rng := rand.New(rand.NewSource(int64(n)))
+			tc := randomCase(rng, n)
+
+			b.ReportAllocs()
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				_ = fn(tc.t1, tc.t2, tc.e1, tc.e2)
+			}
+		})
+	}
+}
@@ -0,0 +1,3 @@
+module algo
+
+go 1.26.3
@@ -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
+}
@@ -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")
+	}
+}