[2019.02.20] Forming a Magic Square

Problem

We define a magic square to be an  matrix of distinct positive integers from  to  where the sum of any row, column, or diagonal of length  is always equal to the same number: the magic constant.

You will be given a  matrix  of integers in the inclusive range . We can convert any digit  to any other digit in the range  at cost of . Given , convert it into a magic square at minimal cost. Print this cost on a new line.

Note: The resulting magic square must contain distinct integers in the inclusive range .

For example, we start with the following matrix :

5 3 4
1 5 8
6 4 2

We can convert it to the following magic square:

8 3 4
1 5 9
6 7 2

This took three replacements at a cost of .

Function Description

Complete the formingMagicSquare function in the editor below. It should return an integer that represents the minimal total cost of converting the input square to a magic square.

formingMagicSquare has the following parameter(s):

• s: a  array of integers

Input Format

Each of the lines contains three space-separated integers of row .

Constraints

Output Format

Print an integer denoting the minimum cost of turning matrix  into a magic square.

Sample Input 0

4 9 2
3 5 7
8 1 5

Sample Output 0

1

Explanation 0

If we change the bottom right value, , from  to  at a cost of ,  becomes a magic square at the minimum possible cost.

Sample Input 1

4 8 2
4 5 7
6 1 6

Sample Output 1

4

Explanation 1

Using 0-based indexing, if we make

• -> at a cost of 
• -> at a cost of 
• -> at a cost of ,

then the total cost will be .

How I solved the problem

# 조금 어려워서 찾아보니

# 위에서는 3 x 3 으로 제한해놨기 때문에 총 8개의 가능성이 있음!
# 각각의 경우의 수와 받은 변수 사이에 차이를 구한 다음 min 값을 찾아야함

import java.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;
 
public class Solution {
 
    // Complete the formingMagicSquare function below.
    static int formingMagicSquare(int[][] s) {
        // 3 x 3 magic square
        //possible magicsquare is 8
        int[][] magic0 = {{8,1,6}, {3,5,7}, {4,9,2}};
        int[][] magic1 = {{6,1,8}, {7,5,3}, {2,9,4}};
        int[][] magic2 = {{4,9,2}, {3,5,7}, {8,1,6}};
        int[][] magic3 = {{2,9,4}, {7,5,3}, {6,1,8}};
        int[][] magic4 = {{8,3,4}, {1,5,9}, {6,7,2}};
        int[][] magic5 = {{4,3,8}, {9,5,1}, {2,7,6}};
        int[][] magic6 = {{6,7,2}, {1,5,9}, {8,3,4}};
        int[][] magic7 = {{2,7,6}, {9,5,1}, {4,3,8}};
 
        int[] sum = new int[8];
 
        //compare given parameter and possible magicsquare
        for (int i = 0; i < 3; i++) {
            for (int j = 0; j < 3; j++) {
                sum[0] += Math.abs(s[i][j] - magic0[i][j]);
                sum[1] += Math.abs(s[i][j] - magic1[i][j]);
                sum[2] += Math.abs(s[i][j] - magic2[i][j]);
                sum[3] += Math.abs(s[i][j] - magic3[i][j]);
                sum[4] += Math.abs(s[i][j] - magic4[i][j]);
                sum[5] += Math.abs(s[i][j] - magic5[i][j]);
                sum[6] += Math.abs(s[i][j] - magic6[i][j]);
                sum[7] += Math.abs(s[i][j] - magic7[i][j]);
            }
        }
 
        int min = sum[0];
 
        for (int i = 0; i < sum.length; i++) {
            if (min > sum[i]) {
                min = sum[i];
            }
        }
 
        return min;
    }
 
    private static final Scanner scanner = new Scanner(System.in);
 
    public static void main(String[] args) throws IOException {
        BufferedWriter bufferedWriter = new BufferedWriter(new FileWriter(System.getenv("OUTPUT_PATH")));
 
        int[][] s = new int[3][3];
 
        for (int i = 0; i < 3; i++) {
            String[] sRowItems = scanner.nextLine().split(" ");
            scanner.skip("(\r\n|[\n\r\u2028\u2029\u0085])?");
 
            for (int j = 0; j < 3; j++) {
                int sItem = Integer.parseInt(sRowItems[j]);
                s[i][j] = sItem;
            }
        }
 
        int result = formingMagicSquare(s);
 
        bufferedWriter.write(String.valueOf(result));
        bufferedWriter.newLine();
 
        bufferedWriter.close();
 
        scanner.close();
    }
}
 

[출처 : https://www.hackerrank.com ]