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Problem solution · Go

Codeforces 514E — Darth Vader and Tree

Codeforces 514E — Darth Vader and Tree: 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
136 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 514E — Darth Vader and Tree, 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

  • 136 lines of Go from the credited upstream file 514E.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 514E — Darth Vader and Tree · GoGo
Use this to learn the idea, then write your own version.
package main import (	. "fmt"	"io"	"slices") // https://github.com/EndlessChengconst mod14 = 1_000_000_007 func pow14(x, n int) int {	res := 1	for ; n > 0; n /= 2 {		if n%2 > 0 {			res = res * x % mod14		}		x = x * x % mod14	}	return res} func berlekampMassey14(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]) % mod14		}		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 * pow14(preD, mod14-2) % mod14		coef[bias-1] = (coef[bias-1] + delta) % mod14		for j, c := range preC {			coef[bias+j] = (coef[bias+j] - delta*c) % mod14		} 		if newLen > oldLen {			preC = tmp			preI, preD = i, d		}	} 	return} func kitamasa14(coef, a []int, n int) (ans int) {	defer func() { ans = (ans%mod14 + mod14) % mod14 }()	if n < len(a) {		return a[n]	} 	k := len(coef)	if k == 0 {		return	}	if k == 1 {		return a[0] * pow14(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) % mod14			}			bk1 := b[k-1]			for j := k - 1; j > 0; j-- {				b[j] = (b[j-1] + bk1*coef[j]) % mod14			}			b[0] = bk1 * coef[0] % mod14		}		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]) % mod14	}	return} func cf514E(in io.Reader, out io.Writer) {	var n, x, v int	Fscan(in, &n, &x)	const mx = 100	cnt := [mx + 1]int{}	for range n {		Fscan(in, &v)		cnt[v]++	} 	f := make([]int, mx*2+2)	f[0] = 1	for i := 1; i < len(f); i++ {		f[i] = 1		for j, c := range cnt[1 : min(i, mx)+1] {			f[i] += c * f[i-1-j]		}		f[i] %= mod14	}	coef := berlekampMassey14(f)	slices.Reverse(coef)	Fprint(out, kitamasa14(coef, f, x))} //func main() { cf514E(bufio.NewReader(os.Stdin), os.Stdout) }

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