Forming a Magic Square

We define a magic square to be an n x m matrix of distinct positive integers from 1 to where the sum of any row, column, or diagonal of length n is always equal to the same number: the magic constant.

You will be given a 3 x 3 matrix of integers in the inclusive range [1, 9]. We can convert any digit a to any other digit b in the range [1, 9] at cost of |a - b|. Given s, 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 [1, 9].

For example, we start with the following matrix s:

1
2
3

5 3 4
1 5 8
6 4 2

We can convert it to the following magic square:

1
2
3

8 3 4
1 5 9
6 7 2

This took three replacements at a cost of |5 - 8| + |8 - 9| + |4 - 7| = 7.

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 3 x 3 array of integers

Input Format

Each of the lines contains three space-separated integers of row s[i].

Constraints

Output Format

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

Sample Input 0

1
2
3

4 9 2
3 5 7
8 1 5

Sample Output 0

1

1

Explanation 0

If we change the bottom right value, s[2][2], from 5 to 6 at a cost of |6 - 5| = 1, s becomes a magic square at the minimum possible cost.

Sample Input 1

1
2
3

4 8 2
4 5 7
6 1 6

Sample Output 1

1

4

Explanation 1

Using 0-based indexing, if we make

• s[0][1] -> 9 at a cost of |9 - 8| = 1
• s[1][0] -> 3 at a cost of |3 - 4| = 1
• s[2][0] -> 8 at a cost of |8 - 6| = 2

then the total cost will be 1 + 1 + 2 = 4.

Solution

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function formingMagicSquare(s) {
    const magicSquare = [
        [2, 7, 6, 9, 5, 1, 4, 3, 8],
        [2, 9, 4, 7, 5, 3, 6, 1, 8],
        [4, 3, 8, 9, 5, 1, 2, 7, 6],
        [4, 9, 2, 3, 5, 7, 8, 1, 6],
        [6, 1, 8, 7, 5, 3, 2, 9, 4],
        [6, 7, 2, 1, 5, 9, 8, 3, 4],
        [8, 1, 6, 3, 5, 7, 4, 9, 2],
        [8, 3, 4, 1, 5, 9, 6, 7, 2]    
    ];

    const inputData = s.reduce((target, array) => { 
        target.push(...array);
        return target;
    }, []);

    return Math.min(...magicSquare.reduce((target, ms) => { 
        target.push(ms.reduce((innerTarget, number, innerIndex) => { 
            innerTarget += Math.abs(inputData[innerIndex] - number);

            return innerTarget;
        }, 0));

        return target;
    }, []));
}