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Problem solution · Go

Codeforces 372D — Choosing Subtree is Fun

Codeforces 372D — Choosing Subtree is Fun: 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
275 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 372D — Choosing Subtree is Fun, 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

  • 275 lines of Go from the credited upstream file 372D.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 372D — Choosing Subtree is Fun · GoGo
Use this to learn the idea, then write your own version.
package main import (	"cmp"	. "fmt"	"io"	"math/bits"	"time") // https://github.com/EndlessChengtype nodeM72[K comparable, V any] struct {	son      [2]*nodeM72[K, V]	priority uint	key      K	value    V	subSize  int} func (o *nodeM72[K, V]) size() int {	if o != nil {		return o.subSize	}	return 0} func (o *nodeM72[K, V]) maintain() {	o.subSize = 1 + o.son[0].size() + o.son[1].size()} func (o *nodeM72[K, V]) rotate(d int) *nodeM72[K, V] {	x := o.son[d^1]	o.son[d^1] = x.son[d]	x.son[d] = o	o.maintain()	x.maintain()	return x} type treapM72[K comparable, V any] struct {	rd         uint	root       *nodeM72[K, V]	comparator func(a, b K) int} func (t *treapM72[K, V]) fastRand() uint {	t.rd ^= t.rd << 13	t.rd ^= t.rd >> 17	t.rd ^= t.rd << 5	return t.rd} func (t *treapM72[K, V]) size() int   { return t.root.size() }func (t *treapM72[K, V]) empty() bool { return t.size() == 0 } func (t *treapM72[K, V]) _put(o *nodeM72[K, V], key K, value V) *nodeM72[K, V] {	if o == nil {		o = &nodeM72[K, V]{priority: t.fastRand(), key: key, value: value}	} else {		c := t.comparator(key, o.key)		if c == 0 {			o.value = value		} else {			d := 0			if c > 0 {				d = 1			}			o.son[d] = t._put(o.son[d], key, value)			if o.son[d].priority > o.priority {				o = o.rotate(d ^ 1)			}		}	}	o.maintain()	return o} func (t *treapM72[K, V]) put(key K, value V) { t.root = t._put(t.root, key, value) } func (t *treapM72[K, V]) _delete(o *nodeM72[K, V], key K) *nodeM72[K, V] {	if o == nil {		return nil	}	if c := t.comparator(key, o.key); c != 0 {		d := 0		if c > 0 {			d = 1		}		o.son[d] = t._delete(o.son[d], key)	} else {		if o.son[1] == nil {			return o.son[0]		}		if o.son[0] == nil {			return o.son[1]		}		d := 0		if o.son[0].priority > o.son[1].priority {			d = 1		}		o = o.rotate(d)		o.son[d] = t._delete(o.son[d], key)	}	o.maintain()	return o} func (t *treapM72[K, V]) delete(key K) { t.root = t._delete(t.root, key) } func (t *treapM72[K, V]) min() *nodeM72[K, V] { return t.kth(0) }func (t *treapM72[K, V]) max() *nodeM72[K, V] { return t.kth(t.size() - 1) } func (t *treapM72[K, V]) lowerBoundIndex(key K) (kth int) {	for o := t.root; o != nil; {		c := t.comparator(key, o.key)		if c < 0 {			o = o.son[0]		} else if c > 0 {			kth += o.son[0].size() + 1			o = o.son[1]		} else { // 相等			kth += o.son[0].size()			break		}	}	return} func (t *treapM72[K, V]) upperBoundIndex(key K) (kth int) {	for o := t.root; o != nil; {		c := t.comparator(key, o.key)		if c < 0 {			o = o.son[0]		} else if c > 0 {			kth += o.son[0].size() + 1			o = o.son[1]		} else {			kth += o.son[0].size() + 1			break		}	}	return} func (t *treapM72[K, V]) kth(k int) (o *nodeM72[K, V]) {	if k < 0 || k >= t.root.size() {		return	}	for o = t.root; o != nil; {		leftSize := o.son[0].size()		if k < leftSize {			o = o.son[0]		} else {			k -= leftSize + 1			if k < 0 {				break			}			o = o.son[1]		}	}	return} func (t *treapM72[K, V]) prev(key K) *nodeM72[K, V] { return t.kth(t.lowerBoundIndex(key) - 1) }func (t *treapM72[K, V]) next(key K) *nodeM72[K, V] { return t.kth(t.upperBoundIndex(key)) } func (t *treapM72[K, V]) find(key K) *nodeM72[K, V] {	o := t.kth(t.lowerBoundIndex(key))	if o == nil || o.key != key {		return nil	}	return o} func newMap72[K cmp.Ordered, V any]() *treapM72[K, V] {	return &treapM72[K, V]{		rd:         uint(time.Now().UnixNano())/2 + 1,		comparator: cmp.Compare[K],	}} func cf372D(in io.Reader, out io.Writer) {	var n, k, dfn int	Fscan(in, &n, &k)	g := make([][]int, n)	for range n - 1 {		var v, w int		Fscan(in, &v, &w)		v--		w--		g[v] = append(g[v], w)		g[w] = append(g[w], v)	} 	const mx = 17	pa := make([][mx]int, n)	dep := make([]int, n)	vToDFN := make([]int, n)	var build func(int, int)	build = func(v, p int) {		vToDFN[v] = dfn		dfn++		pa[v][0] = p		for _, w := range g[v] {			if w != p {				dep[w] = dep[v] + 1				build(w, v)			}		}	}	build(0, -1)	for i := range mx - 1 {		for v := range pa {			if p := pa[v][i]; p != -1 {				pa[v][i+1] = pa[p][i]			} else {				pa[v][i+1] = -1			}		}	}	uptoDep := func(v, d int) int {		for k := uint(dep[v] - d); k > 0; k &= k - 1 {			v = pa[v][bits.TrailingZeros(k)]		}		return v	}	getLCA := func(v, w int) int {		if dep[v] > dep[w] {			v, w = w, v		}		w = uptoDep(w, dep[v])		if w == v {			return v		}		for i := mx - 1; i >= 0; i-- {			if pv, pw := pa[v][i], pa[w][i]; pv != pw {				v, w = pv, pw			}		}		return pa[v][0]	}	getDis := func(v, w int) int { return dep[v] + dep[w] - dep[getLCA(v, w)]*2 } 	t := newMap72[int, int]()	getInc := func(v, dfnV int) int {		o := t.prev(dfnV)		if o == nil {			o = t.max()		}		p := o.value		o = t.next(dfnV)		if o == nil {			o = t.min()		}		q := o.value		return getDis(p, v) + getDis(v, q) - getDis(p, q)	} 	var ans, s, l int	for r, dfnR := range vToDFN {		t.put(dfnR, r)		s += getInc(r, dfnR)		for s > k*2-2 {			dfnL := vToDFN[l]			s -= getInc(l, dfnL)			t.delete(dfnL)			l++		}		ans = max(ans, r-l+1)	}	Fprint(out, ans)} //func main() { cf372D(bufio.NewReader(os.Stdin), os.Stdout) }

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