第19回PAST J 3人組

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");
            WillReturn.Add("1 3 4 6 2 9");
            //1
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("2");
            WillReturn.Add("0 0 0 0 0 100000000");
            //100000000
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("5");
            WillReturn.Add("614 490 420 945 613 585 760 38 926 725 667 685 449 455 873");
            //35
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static int[] mAArr;
    static int UB;

    static void Main()
    {
        List<string> InputList = GetInputList();
        mAArr = InputList[1].Split(' ').Select(pX => int.Parse(pX)).ToArray();
        UB = mAArr.GetUpperBound(0);

        var Stk = new Stack<JyoutaiDef>();
        JyoutaiDef WillPush;
        WillPush.SelectedIndList = new List<int>();
        Stk.Push(WillPush);

        int Answer = int.MaxValue;
        while (Stk.Count > 0) {
            JyoutaiDef Popped = Stk.Pop();

            if (Popped.SelectedIndList.Count == mAArr.Length) {
                int CurrAnswer = DeriveAnswer(Popped.SelectedIndList);
                Answer = Math.Min(Answer, CurrAnswer);
                continue;
            }

            // 未使用番号の最小値を使う
            int UseMin = 0;
            for (int I = 0; I <= UB; I++) {
                if (Popped.SelectedIndList.Contains(I)) {
                    UseMin++;
                }
                else {
                    break;
                }
            }

            for (int I = UseMin + 1; I <= UB; I++) {
                if (Popped.SelectedIndList.Contains(I)) continue;
                for (int J = I + 1; J <= UB; J++) {
                    if (Popped.SelectedIndList.Contains(J)) continue;
                    WillPush.SelectedIndList = new List<int>(Popped.SelectedIndList);
                    WillPush.SelectedIndList.Add(UseMin);
                    WillPush.SelectedIndList.Add(I);
                    WillPush.SelectedIndList.Add(J);
                    Stk.Push(WillPush);
                }
            }
        }
        Console.WriteLine(Answer);
    }

    // 解候補を返す
    static int DeriveAnswer(List<int> pIndList)
    {
        var SumList = new List<int>();
        for (int I = 0; I <= UB; I += 3) {
            int CurrSum = 0;
            CurrSum += mAArr[pIndList[I + 0]];
            CurrSum += mAArr[pIndList[I + 1]];
            CurrSum += mAArr[pIndList[I + 2]];
            SumList.Add(CurrSum);
        }
        return SumList.Max() - SumList.Min();
    }

    struct JyoutaiDef
    {
        internal List<int> SelectedIndList;
    }
}

解説

15C3 = 455
12C3 = 220
 9C3 =  84
 6C3 =  20
で455*220*84*20 = 168168000
なので組み合わせをDFSで列挙してます。
計算量削減で、未使用番号の最小値を必ず使うようにしてます。