ABC194-C Squared Error

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");
            WillReturn.Add("2 8 4");
            //56
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("5");
            WillReturn.Add("-5 8 9 -4 -3");
            //950
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();

        long[] AArr = InputList[1].Split(' ').Select(pX => long.Parse(pX)).ToArray();
        int N = AArr.Length;

        long SumVal = AArr.Sum();
        long Answer = 0;
        foreach (long EachLong in AArr) {
            Answer += EachLong * EachLong * (N - 1);
            SumVal -= EachLong;
            Answer += -2 * EachLong * SumVal;
        }
        Console.WriteLine(Answer);
    }
}

解説

例えば、数列が
A B C D
の場合

(A-B)^2 + (A-C)^2 + (A-D)^2 + (B-C)^2 + (B-D)-2 + (C-D)^2

= A^2 -2AB + B^2 +
  A^2 -2AC + C^2 +
  A^2 -2AD + D^2 +
  B^2 -2BC + C^2 +
  B^2 -2BD + D^2 +
  C^2 -2CD + D^2

= 3 * (A^2 + B^2 + C^2 + D^2)
 -2A(B+C+D)
 -2B(C+D)
 -2CD

になることをふまえてます。