ABC450-D Minimize Range

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("3 10");
            WillReturn.Add("3 21 9");
            //4
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("5 6");
            WillReturn.Add("4 100 5 10 450");
            //2
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

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

    static void Main()
    {
        List<string> InputList = GetInputList();
        long[] wkArr = GetSplitArr(InputList[0]);
        long N = wkArr[0];
        long Hou = wkArr[1];

        long[] AArr = GetSplitArr(InputList[1]);
        for (long I = 0; I <= AArr.GetUpperBound(0); I++) {
            AArr[I] %= Hou;
        }

        Array.Sort(AArr);

        var InsDeque = new Deque<long>();
        foreach (long EachA in AArr) {
            InsDeque.PushBack(EachA);
        }

        var AnswerList = new List<long>();
        for (long I = 1; I <= N; I++) {
            long Min = InsDeque[0];
            long Max = InsDeque[InsDeque.Count - 1];
            AnswerList.Add(Max - Min);

            long FirstVal = InsDeque.PopFront();
            InsDeque.PushBack(FirstVal + Hou);
        }
        Console.WriteLine(AnswerList.Min());
    }
}

#region Deque
internal class Deque<T>
{
    T[] buf;
    int offset, count, capacity;

    internal int Count { get { return count; } }

    internal Deque(int cap) { buf = new T[capacity = cap]; }

    internal Deque() { buf = new T[capacity = 16]; }

    internal T this[int index]
    {
        get { return buf[GetIndex(index)]; }
        set { buf[GetIndex(index)] = value; }
    }

    private int GetIndex(int index)
    {
        if (index >= capacity)
            throw new IndexOutOfRangeException("out of range");
        int ret = index + offset;
        if (ret >= capacity)
            ret -= capacity;
        return ret;
    }

    internal void PushFront(T item)
    {
        if (count == capacity) Extend();
        if (--offset < 0) offset += buf.Length;
        buf[offset] = item;
        count++;
    }

    internal T PopFront()
    {
        if (count == 0)
            throw new InvalidOperationException("collection is empty");
        count--;
        T ret = buf[offset++];
        if (offset >= capacity) offset -= capacity;
        return ret;
    }

    internal void PushBack(T item)
    {
        if (count == capacity) Extend();
        int id = count + offset;
        count++;
        if (id >= capacity) id -= capacity;
        buf[id] = item;
    }

    internal T PopBack()
    {
        if (count == 0)
            throw new InvalidOperationException("collection is empty");
        return buf[GetIndex(--count)];
    }

    internal void Insert(int index, T item)
    {
        if (index > count) throw new IndexOutOfRangeException();
        this.PushFront(item);
        for (int i = 0; i < index; i++)
            this[i] = this[i + 1];
        this[index] = item;
    }

    internal T RemoveAt(int index)
    {
        if (index < 0 || index >= count) throw new IndexOutOfRangeException();
        T ret = this[index];
        for (int i = index; i > 0; i--)
            this[i] = this[i - 1];
        this.PopFront();
        return ret;
    }

    private void Extend()
    {
        T[] newBuffer = new T[capacity << 1];
        if (offset > capacity - count) {
            int len = buf.Length - offset;
            Array.Copy(buf, offset, newBuffer, 0, len);
            Array.Copy(buf, 0, newBuffer, len, count - len);
        }
        else Array.Copy(buf, offset, newBuffer, 0, count);
        buf = newBuffer;
        offset = 0;
        capacity <<= 1;
    }

    internal T[] Items//デバッグ時に中身を調べるためのプロパティ
    {
        get
        {
            T[] a = new T[count];
            for (int i = 0; i < count; i++)
                a[i] = this[i];
            return a;
        }
    }
}
#endregion

解説

まず、各値の mod K は不変量と分かります。

また、相対的な位置関係だけの問題なので
自分以外にKを足すと考えれば、
自分からKを引くことも可能だと分かります。

後は、最小値を全探索すれば良いと分かるので
mod Kの昇順で、Dequeに設定してから、
以下をN回行えば、解がわかります。

●Dequeの末尾 - Dequeの先頭を解候補とする
●Dequeの先頭にKを足して、Dequeの末尾に移動