沙漏的定義

在一個二位陣列中，我們將形如下面示例的數字集合成為沙漏。

a b c
  d
e f g

例如：

1 1 1 0 0 0
0 1 0 0 0 0
1 1 1 0 0 0
0 0 2 4 4 0
0 0 0 2 0 0
0 0 1 2 4 0

共擁有16組沙漏(具體見題目末尾圖)

每個沙漏的數字和稱之為沙漏和(hourglass sum)

For Example：

Function Description

Complete the function hourglassSum in the editor below. It should return an integer, the maximum hourglass sum in the array.

hourglassSum has the following parameter(s):

• arr: an array of integers

Input Format

Each of the 6 lines inputs arr[i] $arr[$

Constraints

• $-9 ≤ arr[i][j] ≤ 9$
• $0 ≤ i, j ≤ 5$

Output Format

Print the largest(maximum) hourglass sum found in arr.

Sample Input

1 1 1 0 0 0
0 1 0 0 0 0
1 1 1 0 0 0
0 0 2 4 4 0
0 0 0 2 0 0
0 0 1 2 4 0

Sample Output

19

Explanation

arr contains the following hourglasses

using System.CodeDom.Compiler;
using System.Collections.Generic;
using System.Collections;
using System.ComponentModel;
using System.Diagnostics.CodeAnalysis;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Reflection;
using System.Runtime.Serialization;
using System.Text.RegularExpressions;
using System.Text;
using System;

class Solution {

    // the hourglassSum function.
    static int hourglassSum(int[][] arr) {

        //取二維陣列中子陣列的個數
        int length = arr.Length;
        //初始化hourglassSum和sum，sum用來臨時儲存每次計算的沙漏和，hourglassSum用來儲存目前最大的和
        int sum = 0;
        int hourglassSum = 0;
        //遍歷陣列的非邊緣數字（即可以成為沙漏中心的數字）
        for (int j = 1; j < length - 1; j++){
            for (int i = 1; i < arr[j].Length - 1; i++){
                //當前沙漏數字的和
                sum = arr[i-1][j-1] + arr[i-1][j] + arr[i-1][j+1] + arr[i][j] + arr[i+1][j-1] + arr[i+1][j] + arr[i+1][j+1];
                //第一次將和直接賦值給hourglassSum，防止所有hourglassSum都小與0的情況
                if (i == 1 && j == 1){
                   hourglassSum = sum;
                }
                //當前的沙漏和與目前最大的比較，hourglassSum儲存較大的一個
                hourglassSum = sum > result ? sum : result;
            }
        }

        return hourglassSum;               
    }

    static void Main(string[] args) {
        //初始化二維陣列
        int[][] arr = new int[][] {new int[]{1, 1, 1, 0, 0, 0},
                                       new int[]{0, 1, 0, 0, 0, 0},
                                       new int[]{1, 1, 1, 0, 0, 0},
                                       new int[]{0, 0, 2, 4, 4, 0},
                                       new int[]{0, 0, 0, 2, 0, 0},
                                       new int[]{0, 0, 1, 2, 4, 0}};
        //呼叫函式
        int result = hourglassSum(arr);
        //輸出結果
        Console.WriteLine(result);
        Console.ReadKey();
    }
}

Expected Output : 19