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Problem solution · Go

Codeforces 78E — Evacuation

Codeforces 78E — Evacuation: 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
151 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 78E — Evacuation, 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

  • 151 lines of Go from the credited upstream file 78E.go.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks 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 78E — Evacuation · GoGo
Use this to learn the idea, then write your own version.
package main import (	. "fmt"	"io"	"math") // https://github.com/EndlessChengfunc cf78E(in io.Reader, out io.Writer) {	var n, t int	Fscan(in, &n, &t)	a := make([]string, n)	for i := range a {		Fscan(in, &a[i])	} 	st := n * n * 2	end := st + 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})	} 	type pair struct{ x, y int }	dir4 := []pair{{-1, 0}, {1, 0}, {0, -1}, {0, 1}}	bfs0 := func(sx, sy int) [][]int {		dis := make([][]int, n)		for i := range dis {			dis[i] = make([]int, n)			for j := range dis[i] {				dis[i][j] = 1e9			}		}		dis[sx][sy] = 0		q := []pair{{sx, sy}}		for step := 1; len(q) > 0; step++ {			tmp := q			q = nil			for _, p := range tmp {				for _, d := range dir4 {					x, y := p.x+d.x, p.y+d.y					if 0 <= x && x < n && 0 <= y && y < n && a[x][y] <= '9' {						if dis[x][y] == 1e9 {							dis[x][y] = step							q = append(q, pair{x, y})						}					}				}			}		}		return dis	} 	var disZ [][]int	ds := make([][][][]int, n)	for i, r := range a {		ds[i] = make([][][]int, n)		for j, c := range r {			if c == 'Z' {				disZ = bfs0(i, j)			} else if '0' < c && c <= '9' {				addEdge(st, i*n+j, int(c-'0'))				ds[i][j] = bfs0(i, j)			}		}	} 	for i := range n {		var s string		Fscan(in, &s)		for j, c := range s {			if !('0' < c && c <= '9') {				continue			}			capsule := n*n + i*n + j			addEdge(capsule, end, int(c-'0'))			for i0, r := range ds {			o:				for j0, d := range r {					if d == nil || d[i][j] > t || d[i][j] > disZ[i][j] {						continue					}					if i0 == i && j0 == j { // 这里忘判了 WA 了一发						addEdge(i0*n+j0, capsule, 9)						continue					}					for _, dir := range dir4 {						x, y := i+dir.x, j+dir.y						if 0 <= x && x < n && 0 <= y && y < n && a[x][y] <= '9' && d[x][y] < disZ[x][y] {							addEdge(i0*n+j0, capsule, 9)							continue o						}					}				}			}		}	} 	dis := make([]int, len(g))	bfs := func() bool {		clear(dis)		dis[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 && dis[w] == 0 {					dis[w] = dis[v] + 1					q = append(q, w)				}			}		}		return dis[end] > 0	}	iter := make([]int, len(g))	var dfs func(int, int) int	dfs = func(v, totalFlow int) (curFlow int) {		if v == end {			return totalFlow		}		for ; iter[v] < len(g[v]); iter[v]++ {			e := &g[v][iter[v]]			if w := e.to; e.cap > 0 && dis[w] > dis[v] {				f := dfs(w, min(totalFlow-curFlow, e.cap))				if f == 0 {					continue				}				e.cap -= f				g[w][e.rid].cap += f				curFlow += f				if curFlow == totalFlow {					break				}			}		}		return	}	maxFlow := 0	for bfs() {		clear(iter)		maxFlow += dfs(st, math.MaxInt)	}	Fprint(out, maxFlow)} //func main() { cf78E(bufio.NewReader(os.Stdin), os.Stdout) }

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