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Problem solution · Go

Codeforces 908D — New Year and Arbitrary Arrangement

Codeforces 908D — New Year and Arbitrary Arrangement: a Go solution using dynamic programming. Learn the idea, check the complexity, and read the full code, with credit to EndlessCheng Codeforces Go.

Technique
Dynamic programming
Source
EndlessCheng Codeforces Go
Length
41 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

Dynamic programming

For Codeforces 908D — New Year and Arbitrary Arrangement, the implementation records answers for smaller states and reuses them to build the requested result without repeating work.

  1. Define precisely what one DP state represents.
  2. Establish the base cases before transitions are evaluated.
  3. Process states in dependency order and combine only already-known values.

Code notes

  • 41 lines of Go from the credited upstream file 908D.go.
  • The implementation visibly relies on sequence storage, cached states.
  • No explicit loop blocks detected.

Complexity

Multiply the number of reachable states by the work performed for each transition, then include the stored state table in memory usage.

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 908D — New Year and Arbitrary Arrangement · GoGo
Use this to learn the idea, then write your own version.
package main import (	. "fmt"	"io") // github.com/EndlessCheng/codeforces-gofunc CF908D(in io.Reader, out io.Writer) {	const mod int64 = 1e9 + 7	pow := func(x, n int64) int64 {		res := int64(1)		for ; n > 0; n >>= 1 {			if n&1 > 0 {				res = res * x % mod			}			x = x * x % mod		}		return res	} 	var k, a, b int64	Fscan(in, &k, &a, &b)	pa := a * pow(a+b, mod-2) % mod	pb := b * pow(a+b, mod-2) % mod	ab := a * pow(b, mod-2) % mod	dp := make([]int64, k)	for i := k; i > 0; i-- {		for j := k - 1; j >= 0; j-- {			if i+j >= k {				dp[j] = (i + j + ab) % mod			} else {				dp[j] = (pa*dp[j] + pb*dp[i+j]) % mod			}		}	}	Fprint(out, dp[0])} //func main() { CF908D(os.Stdin, os.Stdout) }

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