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Problem solution · Go

Codeforces 1895F — Fancy Arrays

Codeforces 1895F — Fancy Arrays: a Go solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to EndlessCheng Codeforces Go.

Technique
Direct simulation
Source
EndlessCheng Codeforces Go
Length
153 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Direct simulation

For Codeforces 1895F — Fancy Arrays, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 153 lines of Go from the credited upstream file 1895F.go.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from EndlessCheng Codeforces Go by Σndless (EndlessCheng) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeCodeforces 1895F — Fancy Arrays · GoGo
Use this to learn the idea, then write your own version.
package main import (	. "fmt"	"io"	"slices") // https://github.com/EndlessChengconst mod95 = 1_000_000_007 func pow95(x, n int) int {	res := 1	for ; n > 0; n /= 2 {		if n%2 > 0 {			res = res * x % mod95		}		x = x * x % mod95	}	return res} func berlekampMassey95(a []int) (coef []int) {	var preC []int	preI, preD := -1, 0	for i, v := range a {		d := v		for j, c := range coef {			d = (d - c*a[i-1-j]) % mod95		}		if d == 0 {			continue		} 		if preI < 0 {			coef = make([]int, i+1)			preI, preD = i, d			continue		} 		bias := i - preI		oldLen := len(coef)		newLen := bias + len(preC)		var tmp []int		if newLen > oldLen {			tmp = slices.Clone(coef)			coef = slices.Grow(coef, newLen-oldLen)[:newLen]		} 		delta := d * pow95(preD, mod95-2) % mod95		coef[bias-1] = (coef[bias-1] + delta) % mod95		for j, c := range preC {			coef[bias+j] = (coef[bias+j] - delta*c) % mod95		} 		if newLen > oldLen {			preC = tmp			preI, preD = i, d		}	} 	return} func kitamasa95(coef, a []int, n int) (ans int) {	defer func() { ans = (ans%mod95 + mod95) % mod95 }()	if n < len(a) {		return a[n]	} 	k := len(coef)	if k == 0 {		return	}	if k == 1 {		return a[0] * pow95(coef[0], n)	} 	compose := func(a, b []int) []int {		c := make([]int, k)		for _, v := range a {			for j, w := range b {				c[j] = (c[j] + v*w) % mod95			}			bk1 := b[k-1]			for j := k - 1; j > 0; j-- {				b[j] = (b[j-1] + bk1*coef[j]) % mod95			}			b[0] = bk1 * coef[0] % mod95		}		return c	} 	resC := make([]int, k)	resC[0] = 1	c := make([]int, k)	c[1] = 1	for ; n > 0; n /= 2 {		if n%2 > 0 {			resC = compose(c, resC)		}		c = compose(c, slices.Clone(c))	} 	for i, c := range resC {		ans = (ans + c*a[i]) % mod95	}	return} func cf1895F(in io.Reader, out io.Writer) {	var T, n, x, k int	for Fscan(in, &T); T > 0; T-- {		Fscan(in, &n, &x, &k)		if n == 1 {			Fprintln(out, k)			continue		} 		ans := (x + k) * pow95(k*2+1, n-1)		if x == 0 {			Fprintln(out, ans%mod95)			continue		} 		f := make([]int, x)		for i := range f {			f[i] = 1		}		sum := make([]int, x+1) 		a := make([]int, x*2)		for i := range a {			for j, v := range f {				sum[j+1] = sum[j] + v			}			for j := range f {				f[j] = (sum[min(j+k+1, x)] - sum[max(j-k, 0)]) % mod95				a[i] += f[j]			}			a[i] %= mod95		} 		coef := berlekampMassey95(a)		slices.Reverse(coef)		ans -= kitamasa95(coef, a, n-2) 		Fprintln(out, (ans%mod95+mod95)%mod95)	}} //func main() { cf1895F(bufio.NewReader(os.Stdin), os.Stdout) }

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