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Problem solution · Go

Codeforces 1508C — Complete the MST

Codeforces 1508C — Complete the MST: 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
134 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 1508C — Complete the MST, 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

  • 134 lines of Go from the credited upstream file 1508C.go.
  • The implementation visibly relies on sequence storage.
  • 1 loop block 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 1508C — Complete the MST · GoGo
Use this to learn the idea, then write your own version.
package main import (	"bufio"	. "fmt"	"io"	"sort") // https://space.bilibili.com/206214func prim(g [][]int) (mst int) {	n := len(g)	minW := make([]int, n)	for i := range minW {		minW[i] = 2e9	}	minW[0] = 0	used := make([]bool, n)	for {		v := -1		for i, u := range used {			if !u && (v < 0 || minW[i] < minW[v]) {				v = i			}		}		if v < 0 {			break		}		used[v] = true		mst += minW[v]		for w, wt := range g[v] {			if wt < minW[w] {				minW[w] = wt			}		}	}	return} func CF1508C(_r io.Reader, out io.Writer) {	in := bufio.NewReader(_r)	var n, m, xor int	Fscan(in, &n, &m)	type edge struct{ v, w, wt int }	es := make([]edge, m)	for i := range es {		var v, w, wt int		Fscan(in, &v, &w, &wt)		xor ^= wt		es[i] = edge{v - 1, w - 1, wt}	} 	// 反图可能是生成树	if m >= (n-2)*(n-1)/2 {		g := make([][]int, n)		for i := range g {			g[i] = make([]int, n)		}		for _, e := range es {			g[e.v][e.w] = e.wt			g[e.w][e.v] = e.wt		}		ans := int(1e18)		for i, r := range g {			for j, wt := range r[:i] {				if wt == 0 { // 枚举是 xor 的边					g[i][j] = xor					g[j][i] = xor					ans = min(ans, prim(g))					g[i][j] = 0					g[j][i] = 0				}			}		}		Fprint(out, ans)		return	} 	// 反图一定不是生成树，用一条不在生成树上的边放 xor	// 所以只需要求反图连通块，再用 Kruskal 补上原图的边	fa := make([]int, n)	for i := range fa {		fa[i] = i	}	var find func(int) int	find = func(x int) int {		if fa[x] != x {			fa[x] = find(fa[x])		}		return fa[x]	}	g := make([][]int, n)	for _, e := range es {		g[e.v] = append(g[e.v], e.w)		g[e.w] = append(g[e.w], e.v)	}	maxV := 0	for v, ws := range g {		if len(ws) < len(g[maxV]) {			maxV = v		}	}	mergeInv := func(v int) {		has := map[int]bool{v: true}		for _, w := range g[v] {			has[w] = true		}		for i := range g {			if !has[i] {				fa[find(i)] = find(v)			}		}	}	mergeInv(maxV)	for v := range g {		if find(v) != find(maxV) {			mergeInv(v)		}	} 	sort.Slice(es, func(i, j int) bool { return es[i].wt < es[j].wt })	ans := 0	for _, e := range es {		v, w := find(e.v), find(e.w)		if v != w {			fa[v] = w			ans += e.wt		}	}	Fprint(out, ans)} //func main() { CF1508C(os.Stdin, os.Stdout) }

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