結果

問題 No.510 二次漸化式
ユーザー aru aruaru aru
提出日時 2020-12-27 11:57:23
言語 Go
(1.22.1)
結果
AC  
実行時間 178 ms / 3,000 ms
コード長 7,668 bytes
コンパイル時間 11,040 ms
コンパイル使用メモリ 233,156 KB
実行使用メモリ 49,792 KB
最終ジャッジ日時 2024-10-01 08:08:21
合計ジャッジ時間 16,144 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 1 ms
6,812 KB
testcase_01 AC 2 ms
5,248 KB
testcase_02 AC 57 ms
5,248 KB
testcase_03 AC 57 ms
5,248 KB
testcase_04 AC 56 ms
5,248 KB
testcase_05 AC 53 ms
5,248 KB
testcase_06 AC 84 ms
7,424 KB
testcase_07 AC 85 ms
7,424 KB
testcase_08 AC 85 ms
7,424 KB
testcase_09 AC 85 ms
7,424 KB
testcase_10 AC 24 ms
5,248 KB
testcase_11 AC 24 ms
5,248 KB
testcase_12 AC 24 ms
5,248 KB
testcase_13 AC 24 ms
5,248 KB
testcase_14 AC 26 ms
5,248 KB
testcase_15 AC 25 ms
5,248 KB
testcase_16 AC 117 ms
49,792 KB
testcase_17 AC 118 ms
49,792 KB
testcase_18 AC 117 ms
49,792 KB
testcase_19 AC 118 ms
49,792 KB
testcase_20 AC 119 ms
49,792 KB
testcase_21 AC 119 ms
49,792 KB
testcase_22 AC 117 ms
49,792 KB
testcase_23 AC 174 ms
49,792 KB
testcase_24 AC 175 ms
49,792 KB
testcase_25 AC 172 ms
49,792 KB
testcase_26 AC 171 ms
49,792 KB
testcase_27 AC 171 ms
49,792 KB
testcase_28 AC 173 ms
49,792 KB
testcase_29 AC 170 ms
49,792 KB
testcase_30 AC 170 ms
49,792 KB
testcase_31 AC 178 ms
49,024 KB
testcase_32 AC 178 ms
49,024 KB
testcase_33 AC 178 ms
49,792 KB
testcase_34 AC 151 ms
48,256 KB
testcase_35 AC 123 ms
48,256 KB
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 # 

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)
var wr = bufio.NewWriter(os.Stdout)

func out(x ...interface{}) {
	fmt.Fprintln(wr, x...)
}

func getI() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func getF() float64 {
	sc.Scan()
	i, e := strconv.ParseFloat(sc.Text(), 64)
	if e != nil {
		panic(e)
	}
	return i
}

func getInts(N int) []int {
	ret := make([]int, N)
	for i := 0; i < N; i++ {
		ret[i] = getI()
	}
	return ret
}

func getS() string {
	sc.Scan()
	return sc.Text()
}

// min, max, asub, absなど基本関数
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
}

// min for n entry
func nmin(a ...int) int {
	ret := a[0]
	for _, e := range a {
		ret = min(ret, e)
	}
	return ret
}

// max for n entry
func nmax(a ...int) int {
	ret := a[0]
	for _, e := range a {
		ret = max(ret, e)
	}
	return ret
}

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
}

func mulMod(A, B [4][4]int) [4][4]int {
	H := 4
	W := 4
	K := 4
	var C [4][4]int

	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
}

const mod = int(1e9 + 7)

func main() {
	defer wr.Flush()
	sc.Split(bufio.ScanWords)
	sc.Buffer([]byte{}, 1000000)
	// this template is new version.
	// use getI(), getS(), getInts(), getF()
	n := getI()
	q := getI()

	x := make([]int, n+1)
	y := make([]int, n+1)

	e := func() S {
		return S{[4][4]int{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}}
	}
	merger := func(a, b S) S {
		return S{mulMod(b.a, a.a)}
	}
	mapper := func(f F, x S) S {
		return x
	}
	comp := func(f, g F) F {
		return f
	}
	id := func() F {
		return F{0}
	}

	D := make([]S, n+1)
	for i := 0; i <= n; i++ {
		D[i].a[0][0] = 1
		D[i].a[1][3] = 1
		D[i].a[2][3] = 1
		D[i].a[3][3] = 1
	}
	seg := newLazySegtree(D, e, merger, mapper, comp, id)

	for k := 0; k < q; k++ {
		op := getS()
		switch op {
		case "x":
			i, e := getI(), getI()
			x[i] = e
			var v [4][4]int
			v[0][0] = 1
			v[1][3] = 1
			v[2][3] = 1
			v[3][3] = 1
			v[0][2] = x[i] % mod
			v[1][1] = y[i] % mod
			v[2][1] = 2 * y[i] % mod
			v[2][2] = y[i] * y[i] % mod
			seg.Set(i, S{v})
		case "y":
			i, e := getI(), getI()
			y[i] = e
			var v [4][4]int
			v[0][0] = 1
			v[1][3] = 1
			v[2][3] = 1
			v[3][3] = 1
			v[0][2] = x[i] % mod
			v[1][1] = y[i] % mod
			v[2][1] = 2 * y[i] % mod
			v[2][2] = y[i] * y[i] % mod
			seg.Set(i, S{v})
		case "a":
			i := getI()
			ret := seg.Prod(0, i).a
			tot := 0
			for l := 0; l < 4; l++ {
				tot += ret[0][l]
				tot %= mod
			}
			out(tot)
		}
	}

	// out(seg)
	// for i := 0; i < 5; i++ {
	// 	seg.Set(i, Data(rand.Intn(50)))
	// 	//seg.Set(i, Data(i+1))
	// }
	// seg.Update()
	// out(seg)
	// ret := seg.Query(0, 4)
	// out("Query", ret)
	// seg.UpdateAt(3, 1)
	// out(seg)
	// ret = seg.Query(1, 4)
	// out("Query", ret)
	// out("Get", seg.Get(4))

}

type S struct {
	a [4][4]int
}
type F struct {
	a int
}
type E func() S
type Merger func(a, b S) S
type Mapper func(f F, x S) S
type Comp func(f, g F) F
type Id func() F
type Compare func(v S) bool
type LazySegtree struct {
	n      int
	size   int
	log    int
	d      []S
	lz     []F
	e      E
	merger Merger
	mapper Mapper
	comp   Comp
	id     Id
}

func newLazySegtree(v []S, e E, merger Merger, mapper Mapper, comp Comp, id Id) *LazySegtree {
	lseg := new(LazySegtree)
	lseg.n = len(v)
	lseg.log = lseg.ceilPow2(lseg.n)
	lseg.size = 1 << uint(lseg.log)
	lseg.d = make([]S, 2*lseg.size)
	lseg.e = e
	lseg.lz = make([]F, lseg.size)
	lseg.merger = merger
	lseg.mapper = mapper
	lseg.comp = comp
	lseg.id = id
	for i, _ := range lseg.d {
		lseg.d[i] = lseg.e()
	}
	for i, _ := range lseg.lz {
		lseg.lz[i] = lseg.id()
	}
	for i := 0; i < lseg.n; i++ {
		lseg.d[lseg.size+i] = v[i]
	}
	for i := lseg.size - 1; i >= 1; i-- {
		lseg.Update(i)
	}
	return lseg
}
func (lseg *LazySegtree) Update(k int) {
	lseg.d[k] = lseg.merger(lseg.d[2*k], lseg.d[2*k+1])
}
func (lseg *LazySegtree) AllApply(k int, f F) {
	lseg.d[k] = lseg.mapper(f, lseg.d[k])
	if k < lseg.size {
		lseg.lz[k] = lseg.comp(f, lseg.lz[k])
	}
}
func (lseg *LazySegtree) Push(k int) {
	lseg.AllApply(2*k, lseg.lz[k])
	lseg.AllApply(2*k+1, lseg.lz[k])
	lseg.lz[k] = lseg.id()
}
func (lseg *LazySegtree) Set(p int, x S) {
	p += lseg.size
	for i := lseg.log; i <= 1; i-- {
		lseg.Push(p >> uint(i))
	}
	lseg.d[p] = x
	for i := 1; i <= lseg.log; i++ {
		lseg.Update(p >> uint(i))
	}
}
func (lseg *LazySegtree) Get(p int) S {
	p += lseg.size
	for i := lseg.log; i >= 1; i-- {
		lseg.Push(p >> uint(i))
	}
	return lseg.d[p]
}
func (lseg *LazySegtree) Prod(l, r int) S {
	if l == r {
		return lseg.e()
	}
	l += lseg.size
	r += lseg.size
	for i := lseg.log; i >= 1; i-- {
		if (l>>uint(i))<<uint(i) != l {
			lseg.Push(l >> uint(i))
		}
		if (r>>uint(i))<<uint(i) != r {
			lseg.Push(r >> uint(i))
		}
	}
	sml, smr := lseg.e(), lseg.e()
	for l < r {
		if (l & 1) == 1 {
			sml = lseg.merger(sml, lseg.d[l])
			l++
		}
		if (r & 1) == 1 {
			r--
			smr = lseg.merger(lseg.d[r], smr)
		}
		l >>= 1
		r >>= 1
	}
	return lseg.merger(sml, smr)
}
func (lseg *LazySegtree) AllProd() S {
	return lseg.d[1]
}
func (lseg *LazySegtree) Apply(p int, f F) {
	p += lseg.size
	for i := lseg.log; i >= 1; i-- {
		lseg.Push(p >> uint(i))
	}
	lseg.d[p] = lseg.mapper(f, lseg.d[p])
	for i := 1; i <= lseg.log; i++ {
		lseg.Update(p >> uint(i))
	}
}
func (lseg *LazySegtree) RangeApply(l int, r int, f F) {
	if l == r {
		return
	}
	l += lseg.size
	r += lseg.size
	for i := lseg.log; i >= 1; i-- {
		if (l>>uint(i))<<uint(i) != l {
			lseg.Push(l >> uint(i))
		}
		if (r>>uint(i))<<uint(i) != r {
			lseg.Push((r - 1) >> uint(i))
		}
	}
	l2, r2 := l, r
	for l < r {
		if l&1 == 1 {
			lseg.AllApply(l, f)
			l++
		}
		if r&1 == 1 {
			r--
			lseg.AllApply(r, f)
		}
		l >>= 1
		r >>= 1
	}
	l, r = l2, r2
	for i := 1; i <= lseg.log; i++ {
		if (l>>uint(i))<<uint(i) != l {
			lseg.Update(l >> uint(i))
		}
		if (r>>uint(i))<<uint(i) != r {
			lseg.Update((r - 1) >> uint(i))
		}
	}
}
func (lseg *LazySegtree) MaxRight(l int, cmp Compare) int {
	if l == lseg.n {
		return lseg.n
	}
	l += lseg.size
	for i := lseg.log; i >= 1; i-- {
		lseg.Push(l >> uint(i))
	}
	sm := lseg.e()
	for {
		for l%2 == 0 {
			l >>= 1
		}
		if !cmp(lseg.merger(sm, lseg.d[l])) {
			for l < lseg.size {
				lseg.Push(l)
				l = 2 * l
				if cmp(lseg.merger(sm, lseg.d[l])) {
					sm = lseg.merger(sm, lseg.d[l])
					l++
				}
			}
			return l - lseg.size
		}
		sm = lseg.merger(sm, lseg.d[l])
		l++
		if l&-l == l {
			break
		}
	}
	return lseg.n
}
func (lseg *LazySegtree) MinLeft(r int, cmp Compare) int {
	if r == 0 {
		return 0
	}
	r += lseg.size
	for i := lseg.log; i >= 1; i-- {
		lseg.Push(r - 1>>uint(i))
	}
	sm := lseg.e()
	for {
		r--
		for r > 1 && r%2 != 0 {
			r >>= 1
		}
		if !cmp(lseg.merger(lseg.d[r], sm)) {
			for r < lseg.size {
				lseg.Push(r)
				r = 2*r + 1
				if cmp(lseg.merger(lseg.d[r], sm)) {
					sm = lseg.merger(lseg.d[r], sm)
					r--
				}
			}
			return r + 1 - lseg.size
		}
		sm = lseg.merger(lseg.d[r], sm)
		if r&-r == r {
			break
		}
	}
	return 0
}
func (lseg *LazySegtree) ceilPow2(n int) int {
	x := 0
	for (1 << uint(x)) < n {
		x++
	}
	return x
}
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