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Problem solution · Go

Codeforces 85E — Guard Towers

Codeforces 85E — Guard Towers: 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
56 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 85E — Guard Towers, 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

  • 56 lines of Go from the credited upstream file 85E.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 85E — Guard Towers · GoGo
Use this to learn the idea, then write your own version.
package main import (	"bufio"	. "fmt"	"io"	"sort") // https://space.bilibili.com/206214type pair85 struct{ x, y int } func f85(v, c, lim int, a []pair85, cs []int) bool {	cs[v] = c	for w, p := range a {		if abs85(a[v].x-p.x)+abs85(a[v].y-p.y) > lim && (cs[w] == c || cs[w] == 0 && !f85(w, -c, lim, a, cs)) {			return false		}	}	return true} func CF85E(_r io.Reader, out io.Writer) {	in := bufio.NewReader(_r)	const mod = 1_000_000_007	var n, ansCC int	Fscan(in, &n)	a := make([]pair85, n)	for i := range a {		Fscan(in, &a[i].x, &a[i].y)	}	ans := sort.Search(1e4+1, func(lim int) bool {		cs := make([]int, n)		cc := 0 // 想象用两个圆去覆盖这 n 个点，某些点在两圆交集中，这些点去哪个集合都可以		for i, c := range cs {			if c == 0 {				cc++				if !f85(i, 1, lim, a, cs) {					return false				}			}		}		ansCC = cc		return true	})	p2 := 1	for ; ansCC > 0; ansCC-- {		p2 = p2 * 2 % mod	}	Fprintln(out, ans)	Fprintln(out, p2)} //func main() { CF85E(os.Stdin, os.Stdout) }func abs85(x int) int { if x < 0 { return -x }; return x }

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