p1990

Author: EndlessCheng

misc/luogu/p1990.go

@@ -0,0 +1,61 @@
+package main
+
+import (
+	. "fmt"
+	"io"
+)
+
+// https://space.bilibili.com/206214
+type matrix [][]int
+
+func newMatrix(n, m int) matrix {
+	a := make(matrix, n)
+	for i := range a {
+		a[i] = make([]int, m)
+	}
+	return a
+}
+
+func (a matrix) mul(b matrix) matrix {
+	c := newMatrix(len(a), len(b[0]))
+	for i, row := range a {
+		for k, x := range row {
+			if x == 0 {
+				continue
+			}
+			for j, y := range b[k] {
+				c[i][j] = (c[i][j] + x*y) % 10000
+			}
+		}
+	}
+	return c
+}
+
+func (a matrix) powMul(n int, f matrix) matrix {
+	res := f
+	for ; n > 0; n /= 2 {
+		if n%2 > 0 {
+			res = a.mul(res)
+		}
+		a = a.mul(a)
+	}
+	return res
+}
+
+func p1990(in io.Reader, out io.Writer) {
+	var n int
+	Fscan(in, &n)
+	if n == 1 {
+		Fprint(out, 1)
+		return
+	}
+	f2 := matrix{{2}, {1}, {1}}
+	m := matrix{
+		{2, 0, 1},
+		{1, 0, 0},
+		{0, 1, 0},
+	};
+	Fprint(out, m.powMul(n-2, f2)[0][0])
+}
+
+//func main() { p1990(bufio.NewReader(os.Stdin), os.Stdout) }