aaa

src/codeforces/set1/set19/set197/set1970/e1/problem.md

@@ -0,0 +1,21 @@
+Harry Potter is hiking in the Alps surrounding Lake Geneva. In this area there are 𝑚
+ cabins, numbered 1 to 𝑚
+. Each cabin is connected, with one or more trails, to a central meeting point next to the lake. Each trail is either short or long. Cabin 𝑖
+ is connected with 𝑠𝑖
+ short trails and 𝑙𝑖
+ long trails to the lake.
+
+Each day, Harry walks a trail from the cabin where he currently is to Lake Geneva, and then from there he walks a trail to any of the 𝑚
+ cabins (including the one he started in). However, as he has to finish the hike in a day, at least one of the two trails has to be short.
+
+How many possible combinations of trails can Harry take if he starts in cabin 1 and walks for 𝑛
+ days?
+
+Give the answer modulo 109+7
+.
+
+
+### ideas
+1. 如果 n = 1? 如果他选择short, 那么有 s1, * sum(li) + l1 * sum(si)
+2. 所以，必须知道他在第i天的时候处在什么位置
+3. dp[i][j] 表示第i天的时候处在j, dp[i+1][x] = dp[i][j] * (s[j] * l[x] + l[j] * s[x])

src/codeforces/set1/set19/set197/set1970/e1/solution.go

@@ -0,0 +1,131 @@
+package main
+
+import (
+	"bufio"
+	"fmt"
+	"os"
+)
+
+func main() {
+	reader := bufio.NewReader(os.Stdin)
+
+	m, n := readTwoNums(reader)
+	s := readNNums(reader, m)
+	l := readNNums(reader, m)
+
+	res := solve(n, s, l)
+
+	fmt.Println(res)
+}
+func readString(reader *bufio.Reader) string {
+	s, _ := reader.ReadString('\n')
+	for i := 0; i < len(s); i++ {
+		if s[i] == '\n' || s[i] == '\r' {
+			return s[:i]
+		}
+	}
+	return s
+}
+
+func readInt(bytes []byte, from int, val *int) int {
+	i := from
+	sign := 1
+	if bytes[i] == '-' {
+		sign = -1
+		i++
+	}
+	tmp := 0
+	for i < len(bytes) && bytes[i] >= '0' && bytes[i] <= '9' {
+		tmp = tmp*10 + int(bytes[i]-'0')
+		i++
+	}
+	*val = tmp * sign
+	return i
+}
+
+func readNum(reader *bufio.Reader) (a int) {
+	bs, _ := reader.ReadBytes('\n')
+	readInt(bs, 0, &a)
+	return
+}
+
+func readTwoNums(reader *bufio.Reader) (a int, b int) {
+	res := readNNums(reader, 2)
+	a, b = res[0], res[1]
+	return
+}
+
+func readThreeNums(reader *bufio.Reader) (a int, b int, c int) {
+	res := readNNums(reader, 3)
+	a, b, c = res[0], res[1], res[2]
+	return
+}
+
+func readNNums(reader *bufio.Reader, n int) []int {
+	res := make([]int, n)
+	x := 0
+	bs, _ := reader.ReadBytes('\n')
+	for i := 0; i < n; i++ {
+		for x < len(bs) && (bs[x] < '0' || bs[x] > '9') && bs[x] != '-' {
+			x++
+		}
+		x = readInt(bs, x, &res[i])
+	}
+	return res
+}
+
+const mod = 1e9 + 7
+
+func add(a, b int) int {
+	a += b
+	if a >= mod {
+		a -= mod
+	}
+	return a
+}
+
+func sub(a, b int) int {
+	return add(a, mod-b)
+}
+
+func mul(a, b int) int {
+	return a * b % mod
+}
+
+func solve(n int, s []int, l []int) int {
+	m := len(s)
+
+	dp := make([]int, m)
+	// dp[i] = 在当前处于位置i时的状态数
+	dp[0] = 1
+	sp := mul(1, s[0])
+	lp := mul(1, l[0])
+
+	fp := make([]int, m)
+
+	for d := 0; d < n; d++ {
+		for i := 0; i < m; i++ {
+			// dp[i] = dp[j] * (((l[j] + s[j]) * s[i] + s[j] * (l[i] + s[i]))
+			tmp1 := mul(sp, add(l[i], s[i]))
+			tmp2 := mul(lp, s[i])
+			fp[i] = add(tmp1, tmp2)
+		}
+
+		sp = 0
+		lp = 0
+		for i := 0; i < m; i++ {
+			dp[i] = fp[i]
+			sp = add(sp, mul(dp[i], s[i]))
+			lp = add(lp, mul(dp[i], l[i]))
+			fp[i] = 0
+		}
+	}
+
+	var res int
+
+	for i := 0; i < m; i++ {
+		res = add(res, dp[i])
+	}
+
+	return res
+}

src/codeforces/set1/set19/set197/set1970/e1/solution_test.go

@@ -0,0 +1,19 @@
+package main
+
+import "testing"
+
+func runSample(t *testing.T, n int, s []int, l []int, expect int) {
+	res := solve(n, s, l)
+
+	if res != expect {
+		t.Fatalf("Sample expect %d, but got %d", expect, res)
+	}
+}
+
+func TestSample1(t *testing.T) {
+	n := 2
+	s := []int{1, 0, 1}
+	l := []int{0, 1, 1}
+	expect := 18
+	runSample(t, n, s, l, expect)
+}

src/codeforces/set1/set19/set197/set1970/e2/solution.go

@@ -0,0 +1,163 @@
+package main
+
+import (
+	"bufio"
+	"fmt"
+	"os"
+)
+
+func main() {
+	reader := bufio.NewReader(os.Stdin)
+
+	m, n := readTwoNums(reader)
+	s := readNNums(reader, m)
+	l := readNNums(reader, m)
+
+	res := solve(n, s, l)
+
+	fmt.Println(res)
+}
+func readString(reader *bufio.Reader) string {
+	s, _ := reader.ReadString('\n')
+	for i := 0; i < len(s); i++ {
+		if s[i] == '\n' || s[i] == '\r' {
+			return s[:i]
+		}
+	}
+	return s
+}
+
+func readInt(bytes []byte, from int, val *int) int {
+	i := from
+	sign := 1
+	if bytes[i] == '-' {
+		sign = -1
+		i++
+	}
+	tmp := 0
+	for i < len(bytes) && bytes[i] >= '0' && bytes[i] <= '9' {
+		tmp = tmp*10 + int(bytes[i]-'0')
+		i++
+	}
+	*val = tmp * sign
+	return i
+}
+
+func readNum(reader *bufio.Reader) (a int) {
+	bs, _ := reader.ReadBytes('\n')
+	readInt(bs, 0, &a)
+	return
+}
+
+func readTwoNums(reader *bufio.Reader) (a int, b int) {
+	res := readNNums(reader, 2)
+	a, b = res[0], res[1]
+	return
+}
+
+func readThreeNums(reader *bufio.Reader) (a int, b int, c int) {
+	res := readNNums(reader, 3)
+	a, b, c = res[0], res[1], res[2]
+	return
+}
+
+func readNNums(reader *bufio.Reader, n int) []int {
+	res := make([]int, n)
+	x := 0
+	bs, _ := reader.ReadBytes('\n')
+	for i := 0; i < n; i++ {
+		for x < len(bs) && (bs[x] < '0' || bs[x] > '9') && bs[x] != '-' {
+			x++
+		}
+		x = readInt(bs, x, &res[i])
+	}
+	return res
+}
+
+const mod = 1e9 + 7
+
+func add(a, b int) int {
+	a += b
+	if a >= mod {
+		a -= mod
+	}
+	return a
+}
+
+func sub(a, b int) int {
+	return add(a, mod-b)
+}
+
+func mul(a, b int) int {
+	return a * b % mod
+}
+
+type Mat [][]int
+
+func NewMat(n, m int) Mat {
+	res := make([][]int, n)
+	for i := 0; i < n; i++ {
+		res[i] = make([]int, m)
+	}
+	return res
+}
+
+func (this Mat) Mul(that Mat) Mat {
+	n := len(this)
+	res := NewMat(n, len(that[0]))
+
+	for i := 0; i < n; i++ {
+		for j := 0; j < len(that[0]); j++ {
+			for k := 0; k < len(that); k++ {
+				res[i][j] = add(res[i][j], mul(this[i][k], that[k][j]))
+			}
+		}
+	}
+	return res
+}
+
+func pow(m Mat, n int) Mat {
+	res := NewMat(len(m), len(m))
+	for i := 0; i < len(res); i++ {
+		res[i][i] = 1
+	}
+
+	for n > 0 {
+		if n&1 == 1 {
+			res = res.Mul(m)
+		}
+		m = m.Mul(m)
+		n >>= 1
+	}
+	return res
+}
+
+func solve(n int, s []int, l []int) int {
+	m := len(s)
+
+	mat := NewMat(m, m)
+
+	t := make([]int, m)
+	for i := 0; i < m; i++ {
+		t[i] = add(s[i], l[i])
+	}
+
+	for i := 0; i < m; i++ {
+		for j := 0; j < m; j++ {
+			mat[i][j] = sub(mul(t[i], t[j]), mul(l[i], l[j]))
+		}
+	}
+
+	res := pow(mat, n)
+
+	v := NewMat(m, 1)
+	v[0][0] = 1
+	v = res.Mul(v)
+
+	var ans int
+	for i := 0; i < m; i++ {
+		ans = add(ans, v[i][0])
+	}
+
+	return ans
+}

src/codeforces/set1/set19/set197/set1970/e2/solution_test.go

@@ -0,0 +1,19 @@
+package main
+
+import "testing"
+
+func runSample(t *testing.T, n int, s []int, l []int, expect int) {
+	res := solve(n, s, l)
+
+	if res != expect {
+		t.Fatalf("Sample expect %d, but got %d", expect, res)
+	}
+}
+
+func TestSample1(t *testing.T) {
+	n := 2
+	s := []int{1, 0, 1}
+	l := []int{0, 1, 1}
+	expect := 18
+	runSample(t, n, s, l, expect)
+}