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Problem solution · Go

Codeforces 1082G — Petya and Graph

Codeforces 1082G — Petya and Graph: a Go solution using breadth-first search. Learn the idea, check the complexity, and read the full code, with credit to EndlessCheng Codeforces Go.

Technique
Breadth-first search
Source
EndlessCheng Codeforces Go
Length
91 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

Breadth-first search

For Codeforces 1082G — Petya and Graph, the implementation explores reachable states in layers, which is the standard shape for unweighted shortest paths and minimum-step transitions.

  1. Model each valid configuration as a state and each legal move as an edge.
  2. Seed the queue with the starting state and mark it immediately.
  3. Expand each state once, recording distance or reachability for unseen neighbours.

Code notes

  • 91 lines of Go from the credited upstream file 1082G.go.
  • The implementation visibly relies on sequence storage.
  • 1 loop block detected, together with recursive traversal.

Complexity

Verify that each state and transition is processed only a bounded number of times; that determines the traversal cost.

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 1082G — Petya and Graph · GoGo
Use this to learn the idea, then write your own version.
package main import (	"bufio"	. "fmt"	"io") // https://space.bilibili.com/206214func cf1082G(_r io.Reader, out io.Writer) {	in := bufio.NewReader(_r)	const inf int = 1e18	var n, m, cost, v, w, profit, tot int	Fscan(in, &n, &m) 	st := 0	end := n + m + 1	type nb struct{ to, rid, cap int }	g := make([][]nb, end+1)	addEdge := func(from, to, cap int) {		g[from] = append(g[from], nb{to, len(g[to]), cap})		g[to] = append(g[to], nb{from, len(g[from]) - 1, 0})	}	for i := 1; i <= n; i++ {		Fscan(in, &cost)		addEdge(m+i, end, cost)	}	for i := 1; i <= m; i++ {		Fscan(in, &v, &w, &profit)		addEdge(st, i, profit)		addEdge(i, m+v, inf)		addEdge(i, m+w, inf)		tot += profit	} 	var d []int	bfs := func() bool {		d = make([]int, len(g))		d[st] = 1		q := []int{st}		for len(q) > 0 {			v := q[0]			q = q[1:]			for _, e := range g[v] {				if w := e.to; e.cap > 0 && d[w] == 0 {					d[w] = d[v] + 1					q = append(q, w)				}			}		}		return d[end] > 0	}	var iter []int	var dfs func(int, int) int	dfs = func(v, minF int) int {		if v == end {			return minF		}		for ; iter[v] < len(g[v]); iter[v]++ {			e := &g[v][iter[v]]			w := e.to			if e.cap > 0 && d[w] > d[v] {				f := dfs(w, min(minF, e.cap))				if f > 0 {					e.cap -= f					g[w][e.rid].cap += f					return f				}			}		}		return 0	}	dinic := func() (maxFlow int) {		for bfs() {			iter = make([]int, len(g))			for {				f := dfs(st, inf)				if f > 0 {					maxFlow += f				} else {					break				}			}		}		return	}	Fprint(out, tot-dinic())} //func main() { cf1082G(os.Stdin, os.Stdout) }

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