CPMagical CP Library

Problem solution · Go

Codeforces 1605E — Array Equalizer

Codeforces 1605E — Array Equalizer: a Go solution using sorting and greedy selection. Learn the idea, check the complexity, and read the full code, with credit to EndlessCheng Codeforces Go.

Technique
Sorting and greedy selection
Source
EndlessCheng Codeforces Go
Length
74 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

Sorting and greedy selection

For Codeforces 1605E — Array Equalizer, the implementation first exposes a useful order, then scans that order while making locally justified choices.

  1. Choose the key that reveals the greedy or grouping structure.
  2. Sort the relevant records by that key.
  3. Scan in order, maintaining the invariant that makes each local choice safe.

Code notes

  • 74 lines of Go from the credited upstream file 1605E.go.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected.

Complexity

Sorting is typically the dominant term unless the subsequent scan uses a more expensive nested operation.

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 1605E — Array Equalizer · GoGo
Use this to learn the idea, then write your own version.
package main import (	"bufio"	. "fmt"	"io"	"slices"	"sort") // https://github.com/EndlessChengfunc cf1605E(in io.Reader, _w io.Writer) {	out := bufio.NewWriter(_w)	defer out.Flush()	var n, x, q int	Fscan(in, &n)	a := make([]int, n+1)	for i := 1; i <= n; i++ {		Fscan(in, &a[i])	}	for i := 1; i <= n; i++ {		Fscan(in, &x)		a[i] = x - a[i]	}	a[1]++ 	b := make([]int, n+1)	b[1] = 1	for i := 1; i <= n; i++ {		for j := i * 2; j <= n; j += i {			a[j] -= a[i]			b[j] -= b[i]		}	} 	var c, e []int	s := 0	for i := 1; i <= n; i++ {		if b[i] == 0 {			if a[i] < 0 {				s += -a[i]			} else {				s += a[i]			}		} else if b[i] > 0 {			c = append(c, a[i])		} else {			e = append(e, a[i])		}	} 	k, t := len(c), len(e)	slices.Sort(c)	sc := make([]int, k+1)	for i, v := range c {		sc[i+1] = sc[i] + v	}	slices.Sort(e)	se := make([]int, t+1)	for i, v := range e {		se[i+1] = se[i] + v	} 	Fscan(in, &q)	for range q {		Fscan(in, &x)		i := sort.Search(k, func(i int) bool { return c[i] > -x })		j := sort.Search(t, func(i int) bool { return e[i] > x })		Fprintln(out, s+sc[k]-2*sc[i]+x*(k-2*i)+se[t]-2*se[j]-x*(t-2*j))	}} //func main() { cf1605E(bufio.NewReader(os.Stdin), os.Stdout) }

Keep practising

Did this explanation save you time? I'm a Grade 11 student building this free library to make difficult algorithms easier to understand.

Buy me a coffee ↗