[2300] CF1204E 组合数学 推式子（除了 DP 外还可以线性做）

Author: EndlessCheng

main/1200-1299/1204E.go

@@ -0,0 +1,46 @@
+package main
+
+import (
+	. "fmt"
+	"io"
+)
+
+// github.com/EndlessCheng/codeforces-go
+func CF1204E(in io.Reader, out io.Writer) {
+	const mod = 998244853
+	pow := func(x, n int64) (res int64) {
+		res = 1
+		for ; n > 0; n >>= 1 {
+			if n&1 > 0 {
+				res = res * x % mod
+			}
+			x = x * x % mod
+		}
+		return res
+	}
+
+	var n, m int
+	Fscan(in, &n, &m)
+	F := make([]int64, n+m+1)
+	F[0] = 1
+	for i := 1; i <= n+m; i++ {
+		F[i] = F[i-1] * int64(i) % mod
+	}
+	invF := make([]int64, n+m+1)
+	invF[n+m] = pow(F[n+m], mod-2)
+	for i := n + m; i > 0; i-- {
+		invF[i-1] = invF[i] * int64(i) % mod
+	}
+	C := func(n, k int) int64 { return F[n] * invF[k] % mod * invF[n-k] % mod }
+	ans := int64(0)
+	for i := 1; i <= n; i++ {
+		if i > n-m {
+			ans += C(n+m, n-i)
+		} else {
+			ans += C(n+m, n)
+		}
+	}
+	Fprint(out, ans%mod)
+}
+
+//func main() { CF1204E(os.Stdin, os.Stdout) }

main/1200-1299/1204E_test.go

@@ -0,0 +1,30 @@
+package main
+
+import (
+	"github.com/EndlessCheng/codeforces-go/main/testutil"
+	"testing"
+)
+
+// https://codeforces.com/problemset/problem/1204/E
+// https://codeforces.com/problemset/status/1204/problem/E
+func TestCF1204E(t *testing.T) {
+	// just copy from website
+	rawText := `
+inputCopy
+0 2
+outputCopy
+0
+inputCopy
+2 0
+outputCopy
+2
+inputCopy
+2 2
+outputCopy
+5
+inputCopy
+2000 2000
+outputCopy
+674532367`
+	testutil.AssertEqualCase(t, rawText, 0, CF1204E)
+}