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Problem solution · Go

Codeforces 87D — Beautiful Road

Codeforces 87D — Beautiful Road: a Go solution using depth-first search. Learn the idea, check the complexity, and read the full code, with credit to EndlessCheng Codeforces Go.

Technique
Depth-first search
Source
EndlessCheng Codeforces Go
Length
98 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

Depth-first search

For Codeforces 87D — Beautiful Road, the implementation follows one branch at a time, making it suitable for components, trees, backtracking, or dependency exploration.

  1. Define the state carried into one recursive or stack frame.
  2. Mark or choose the current state before exploring children.
  3. Combine child results or undo the choice when the branch finishes.

Code notes

  • 98 lines of Go from the credited upstream file 87D.go.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected, together with recursive traversal.

Complexity

Count unique states for graph traversal; for backtracking, count the branching factor and maximum depth.

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 87D — Beautiful Road · GoGo
Use this to learn the idea, then write your own version.
package main import (	"bufio"	"cmp"	. "fmt"	"io"	"slices") // https://github.com/EndlessChengfunc cf87D(in io.Reader, _w io.Writer) {	out := bufio.NewWriter(_w)	defer out.Flush()	var n int	Fscan(in, &n)	type edge struct{ v, w, wt, dep, i int }	es := make([]edge, n-1)	g := make([][]int, n)	for i := range es {		var v, w, wt int		Fscan(in, &v, &w, &wt)		v--		w--		es[i] = edge{v, w, wt, 0, i + 1}		g[v] = append(g[v], w)		g[w] = append(g[w], v)	} 	dep := make([]int, n)	var dfs func(int, int)	dfs = func(v, fa int) {		for _, w := range g[v] {			if w != fa {				dep[w] = dep[v] + 1				dfs(w, v)			}		}	}	dfs(0, -1) 	for i := range es {		e := &es[i]		if dep[e.v] > dep[e.w] {			e.v, e.w = e.w, e.v		}		e.dep = dep[e.v]	}	slices.SortFunc(es, func(a, b edge) int { return cmp.Or(a.wt-b.wt, b.dep-a.dep) }) 	fa := make([]int, n)	sz := make([]int, n)	for i := range fa {		fa[i] = i		sz[i] = 1	}	find := func(x int) int {		rt := x		for fa[rt] != rt {			rt = fa[rt]		}		for fa[x] != rt {			fa[x], x = rt, fa[x]		}		return rt	} 	mx := 0	ans := []int{}	for i := 0; i < n-1; {		st := i		wt := es[st].wt		for ; i < n-1 && es[i].wt == wt; i++ {			v, w := es[i].v, es[i].w			fv := find(v)			fa[w] = fv			sz[fv] += sz[w]		}		for ; st < i; st++ {			e := es[st]			s := sz[e.w] * (sz[find(e.v)] - sz[e.w])			if s > mx {				mx = s				ans = []int{e.i}			} else if s == mx {				ans = append(ans, e.i)			}		}	}	Fprintln(out, mx*2, len(ans))	slices.Sort(ans)	for _, v := range ans {		Fprint(out, v, " ")	}} //func main() { cf87D(bufio.NewReader(os.Stdin), os.Stdout) }

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