結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー aru aruaru aru
提出日時 2020-09-08 22:29:12
言語 Go
(1.23.4)
結果
AC  
実行時間 27 ms / 5,000 ms
コード長 2,799 bytes
コンパイル時間 13,632 ms
コンパイル使用メモリ 226,544 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-11-30 10:22:22
合計ジャッジ時間 13,225 ms
ジャッジサーバーID
(参考情報)
judge1 / judge4
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 37
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

package main
import (
"bufio"
"fmt"
"os"
"sort"
"strconv"
)
func out(x ...interface{}) {
fmt.Println(x...)
}
var sc = bufio.NewScanner(os.Stdin)
func getInt() int {
sc.Scan()
i, e := strconv.Atoi(sc.Text())
if e != nil {
panic(e)
}
return i
}
func getInts(N int) []int {
ret := make([]int, N)
for i := 0; i < N; i++ {
ret[i] = getInt()
}
return ret
}
func getString() string {
sc.Scan()
return sc.Text()
}
// min, max, asub, abs
func max(a, b int) int {
if a > b {
return a
}
return b
}
func min(a, b int) int {
if a < b {
return a
}
return b
}
func asub(a, b int) int {
if a > b {
return a - b
}
return b - a
}
func abs(a int) int {
if a >= 0 {
return a
}
return -a
}
func lowerBound(a []int, x int) int {
idx := sort.Search(len(a), func(i int) bool {
return a[i] >= x
})
return idx
}
func upperBound(a []int, x int) int {
idx := sort.Search(len(a), func(i int) bool {
return a[i] > x
})
return idx
}
const mod = int(1e9 + 7)
func solve1(N, K int, a []int) {
K = min(1000000, K)
sum := 0
for i := 0; i < N; i++ {
sum += a[i]
}
f := sum
s := sum
for i := N; i < K; i++ {
f = sum
s += sum
s %= mod
// out(f, s)
x := a[i%N]
a[i%N] = sum
sum += sum - x
sum %= mod
if sum < 0 {
sum += mod
}
}
out(f, s)
}
func mulMod(A, B [][]int) [][]int {
H := len(A)
W := len(B[0])
K := len(A[0])
C := make([][]int, W)
for i := 0; i < W; i++ {
C[i] = make([]int, W)
}
for i := 0; i < H; i++ {
for j := 0; j < W; j++ {
for k := 0; k < K; k++ {
C[i][j] += A[i][k] * B[k][j]
C[i][j] %= mod
}
}
}
return C
}
func powModMatrix(A [][]int, p int) [][]int {
N := len(A)
ret := make([][]int, N)
for i := 0; i < N; i++ {
ret[i] = make([]int, N)
ret[i][i] = 1
}
for p > 0 {
if p&1 == 1 {
ret = mulMod(ret, A)
}
A = mulMod(A, A)
p >>= 1
}
return ret
}
func solve2(N, K int, x []int) {
a := make([][]int, N)
for i := 0; i < N; i++ {
a[i] = make([]int, N)
}
for i := 0; i < N; i++ {
a[0][i] = 1
}
for i := 1; i < N; i++ {
a[i][i-1] = 1
}
a = powModMatrix(a, K-N)
f := 0
for i := 0; i < N; i++ {
f += x[N-1-i] * a[0][i]
f %= mod
}
a = make([][]int, N+1)
for i := 0; i < N+1; i++ {
a[i] = make([]int, N+1)
}
a[0][0] = 2
a[0][N] = -1
for i := 1; i < N+1; i++ {
a[i][i-1] = 1
}
// for i := 0; i < N+1; i++ {
// out(a[i])
// }
a = powModMatrix(a, K-N)
y := make([]int, N+1)
y[0] = 0
for i := 1; i < N+1; i++ {
y[i] = y[i-1] + x[i-1]
}
// out(y)
s := 0
for i := 0; i < N+1; i++ {
s += y[N-i] * a[0][i]
s %= mod
if s < 0 {
s += mod
}
}
out(f, s)
}
func main() {
sc.Split(bufio.ScanWords)
N, K := getInt(), getInt()
a := getInts(N)
if K > 1000000 {
solve2(N, K, a)
} else {
solve1(N, K, a)
}
}
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