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Problem solution · Go

Codeforces 1455E — Four Points

Codeforces 1455E — Four Points: 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
122 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 1455E — Four Points, 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

  • 122 lines of Go from the credited upstream file 1455E.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 1455E — Four Points · GoGo
Use this to learn the idea, then write your own version.
package main import (	"bufio"	. "fmt"	"io") // github.com/EndlessCheng/codeforces-gofunc CF1455E(_r io.Reader, _w io.Writer) {	in := bufio.NewReader(_r)	out := bufio.NewWriter(_w)	defer out.Flush()	const inf int64 = 1e18	perm4 := [][]int{		{0, 1, 2, 3}, {0, 1, 3, 2}, {0, 2, 1, 3}, {0, 2, 3, 1}, {0, 3, 1, 2}, {0, 3, 2, 1},		{1, 0, 2, 3}, {1, 0, 3, 2}, {1, 2, 0, 3}, {1, 2, 3, 0}, {1, 3, 0, 2}, {1, 3, 2, 0},		{2, 0, 1, 3}, {2, 0, 3, 1}, {2, 1, 0, 3}, {2, 1, 3, 0}, {2, 3, 0, 1}, {2, 3, 1, 0},		{3, 0, 1, 2}, {3, 0, 2, 1}, {3, 1, 0, 2}, {3, 1, 2, 0}, {3, 2, 0, 1}, {3, 2, 1, 0},	} 	var T int	var x, y [4]int	for Fscan(in, &T); T > 0; T-- {		for i := 0; i < 4; i++ {			Fscan(in, &x[i], &y[i])		}		ans := inf		for _, p := range perm4 {			type neighbor struct {				to, rid   int				cap, cost int64			}			g := [8][]neighbor{}			addEdge := func(from, to int, cap, cost int64) {				g[from] = append(g[from], neighbor{to, len(g[to]), cap, cost})				g[to] = append(g[to], neighbor{from, len(g[from]) - 1, 0, -cost})			}			for i := 0; i < 4; i++ {				for j := 4; j < 6; j++ {					addEdge(i, j, inf, 1)					addEdge(j, i, inf, 1)				}			}			st, end := 6, 7			for i, w := range []int{				x[p[2]] - x[p[0]],				x[p[1]] - x[p[3]],				y[p[0]] - y[p[1]],				y[p[3]] - y[p[2]],				x[p[0]] + y[p[2]] - x[p[1]] - y[p[0]],				x[p[3]] + y[p[1]] - x[p[2]] - y[p[3]],			} {				if w > 0 {					addEdge(st, i, int64(w), 0)				} else {					addEdge(i, end, int64(-w), 0)				}			} 			dist := [8]int64{}			type pair struct{ v, i int }			fa := [8]pair{}			spfa := func() bool {				for i := 0; i < 8; i++ {					dist[i] = inf				}				dist[st] = 0				inQ := [8]bool{}				inQ[st] = true				q := []int{st}				for len(q) > 0 {					v := q[0]					q = q[1:]					inQ[v] = false					for i, e := range g[v] {						if e.cap == 0 {							continue						}						w := e.to						if newD := dist[v] + e.cost; newD < dist[w] {							dist[w] = newD							fa[w] = pair{v, i}							if !inQ[w] {								q = append(q, w)								inQ[w] = true							}						}					}				}				return dist[end] < inf			}			var maxFlow, minCost int64			for spfa() {				minF := inf				for v := end; v != st; {					p := fa[v]					if c := g[p.v][p.i].cap; c < minF {						minF = c					}					v = p.v				}				for v := end; v != st; {					p := fa[v]					e := &g[p.v][p.i]					e.cap -= minF					g[v][e.rid].cap += minF					v = p.v				}				maxFlow += minF				minCost += dist[end] * minF			}			if minCost < ans {				ans = minCost			}		}		Fprintln(out, ans)	}} //func main() { CF1455E(os.Stdin, os.Stdout) }

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