ABC208-E Digit Products

問題へのリンク

C#のソース

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("13 2");
            //5
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("100 80");
            //99
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("1000000000000000000 1000000000");
            //841103275147365677
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    struct JyoutaiDef
    {
        internal long Prod;    // 数字の積
        internal bool FreeNum; // 数字自由フラグ
        internal bool UseNonZero; // 0以外を使用したか
    }

    static void Main()
    {
        List<string> InputList = GetInputList();
        long[] wkArr = InputList[0].Split(' ').Select(pX => long.Parse(pX)).ToArray();
        string StrN = wkArr[0].ToString();
        long K = wkArr[1];

        // 場合の数[状態定義]なDP表
        var PrevDP = new Dictionary<JyoutaiDef, long>();
        JyoutaiDef FirstJyoutai;
        FirstJyoutai.Prod = 1;
        FirstJyoutai.FreeNum = false;
        FirstJyoutai.UseNonZero = false;
        PrevDP[FirstJyoutai] = 1;

        for (int I = 0; I <= StrN.Length - 1; I++) {
            var CurrDP = new Dictionary<JyoutaiDef, long>();
            foreach (var EachPair in PrevDP) {
                for (char NewChar = '0'; NewChar <= '9'; NewChar++) {
                    if (EachPair.Key.FreeNum == false && StrN[I] < NewChar) break;

                    long NewProd = EachPair.Key.Prod;
                    if (NewChar != '0' || EachPair.Key.UseNonZero) {
                        NewProd *= (NewChar - '0');
                    }
                    NewProd = Math.Min(NewProd, K + 1);

                    bool NewFreeNum = EachPair.Key.FreeNum;
                    if (StrN[I] > NewChar) NewFreeNum = true;

                    bool NewUseNonZero = EachPair.Key.UseNonZero;
                    if (NewChar != '0') {
                        NewUseNonZero = true;
                    }

                    JyoutaiDef NewJyoutai;
                    NewJyoutai.Prod = NewProd;
                    NewJyoutai.FreeNum = NewFreeNum;
                    NewJyoutai.UseNonZero = NewUseNonZero;
                    if (CurrDP.ContainsKey(NewJyoutai) == false) {
                        CurrDP[NewJyoutai] = 0;
                    }
                    CurrDP[NewJyoutai] += EachPair.Value;
                }
            }
            PrevDP = CurrDP;
        }

        long Answer = 0;
        foreach (var EachPair in PrevDP) {
            if (EachPair.Key.Prod <= K && EachPair.Key.UseNonZero)
                Answer += EachPair.Value;
        }
        Console.WriteLine(Answer);
    }
}

解説

桁DPで解いてます。