天下一プログラマーコンテスト2013 決勝 A 天下一有無

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("2 2");
            //4
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("3 2");
            //10
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static int[] GetSplitArr(string pStr)
    {
        return (pStr == "" ? new string[0] : pStr.Split(' ')).Select(pX => int.Parse(pX)).ToArray();
    }

    const int Hou = 1000000007;

    static int mYoko;
    static int mTate;

    static int AllBitOn;

    static void Main()
    {

        List<string> InputList = GetInputList();
        int[] wkArr = GetSplitArr(InputList[0]);
        int N = wkArr[0];
        int M = wkArr[1];

        mYoko = Math.Max(N, M);
        mTate = Math.Min(N, M);

        AllBitOn = (1 << mYoko) - 1;

        List<int> YokoList = DeriveYokoList();

        // 場合の数[上のBit列]なDP表
        int[] PrevDP = new int[AllBitOn + 1];
        PrevDP[0] = 1;

        for (int I = 1; I <= mTate; I++) {
            int[] CurrDP = new int[AllBitOn + 1];
            for (int J = 0; J <= AllBitOn; J++) {
                if (PrevDP[J] == 0) continue;

                string BinStr1 = Convert.ToString(J, 2);
                BinStr1 = BinStr1.PadLeft(mYoko, '0');

                foreach (int EachYoko in YokoList) {
                    string BinStr2 = Convert.ToString(EachYoko, 2);
                    BinStr2 = BinStr2.PadLeft(mYoko, '0');

                    bool IsOK = true;
                    for (int K = 0; K <= BinStr2.Length - 1; K++) {
                        if (BinStr2[K] == '0') continue;
                        int Ind1 = K - 1;
                        int Ind2 = K;
                        int Ind3 = K + 1;

                        if (0 <= Ind1 && BinStr1[Ind1] == '1') IsOK = false;
                        if (BinStr1[Ind2] == '1') IsOK = false;
                        if (Ind3 <= BinStr1.Length - 1 && BinStr1[Ind3] == '1') IsOK = false;
                        if (IsOK == false) break;
                    }
                    if (IsOK) {
                        CurrDP[EachYoko] += PrevDP[J];
                        CurrDP[EachYoko] %= Hou;
                    }
                }
            }
            PrevDP = CurrDP;
        }

        int Answer = 0;
        for (int I = 0; I <= AllBitOn; I++) {
            Answer += PrevDP[I];
            Answer %= Hou;
        }

        Answer--; // 0の分を引く
        if (Answer > 0) {
            Answer += Hou;
        }
        Answer %= Hou;
        Console.WriteLine(Answer);
    }

    // 横に配置する候補のList
    static List<int> DeriveYokoList()
    {
        var YokoList = new List<int>();
        for (int I = 0; I <= AllBitOn; I++) {
            string BinStr = Convert.ToString(I, 2);
            if (BinStr.Contains("11")) {
                continue;
            }
            YokoList.Add(I);
        }
        return YokoList;
    }
}

解説

行ごとに決めていくbitDPで、
場合の数[上のBit列]なDP表を更新してます。

計算量は、15*(2^15) なので、間に合います。