[2400] CF626F 计数 DP

Author: EndlessCheng

main/600-699/626F.go

@@ -0,0 +1,59 @@
+package main
+
+import (
+	"bufio"
+	. "fmt"
+	"io"
+	"sort"
+)
+
+// https://space.bilibili.com/206214
+func CF626F(_r io.Reader, out io.Writer) {
+	in := bufio.NewReader(_r)
+	const mod = 1_000_000_007
+	var n, k int
+	Fscan(in, &n, &k)
+	a := make([]int, n, n+1)
+	for i := range a {
+		Fscan(in, &a[i])
+	}
+	sort.Ints(a)
+	a = append(a, 0) // 避免越界
+
+	memo := [200][101][1001]int{}
+	for i := range memo {
+		for j := range memo[i] {
+			for k := range memo[i][j] {
+				memo[i][j][k] = -1
+			}
+		}
+	}
+	var dfs func(int, int, int) int64
+	dfs = func(i, groups, leftK int) (res int64) {
+		if leftK < 0 || groups > i+1 { // groups > i+1 说明剩余数字不够组成最小值
+			return
+		}
+		if i < 0 {
+			if groups == 0 {
+				return 1
+			}
+			return
+		}
+		p := &memo[i][groups][leftK]
+		if *p != -1 {
+			return int64(*p)
+		}
+		leftK -= (a[i+1] - a[i]) * groups
+		res = dfs(i-1, groups+1, leftK) // a[i] 作为最大值
+		res += dfs(i-1, groups, leftK) * int64(groups+1) // 不参与最大最小：从 groups 中选一个组   这里 +1 是只有一个数的组的方案数
+		if groups > 0 {
+			res += dfs(i-1, groups-1, leftK) * int64(groups) // a[i] 作为最小值：从 groups 中选一个组
+		}
+		res %= mod
+		*p = int(res) // 记忆化
+		return
+	}
+	Fprint(out, dfs(n-1, 0, k))
+}
+
+//func main() { CF626F(os.Stdin, os.Stdout) }

main/600-699/626F_test.go

@@ -0,0 +1,34 @@
+package main
+
+import (
+	"github.com/EndlessCheng/codeforces-go/main/testutil"
+	"testing"
+)
+
+// https://codeforces.com/contest/626/problem/F
+// https://codeforces.com/problemset/status/626/problem/F
+func TestCF626F(t *testing.T) {
+	// just copy from website
+	rawText := `
+inputCopy
+3 2
+2 4 5
+outputCopy
+3
+inputCopy
+4 3
+7 8 9 10
+outputCopy
+13
+inputCopy
+4 0
+5 10 20 21
+outputCopy
+1
+inputCopy
+20 1000
+50 50 100 100 150 150 200 200 250 250 300 300 350 350 400 400 450 450 500 500
+outputCopy
+97456952`
+	testutil.AssertEqualCase(t, rawText, 0, CF626F)
+}