Forming a Magic Square

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 .

 php

<?php

// Complete the formingMagicSquare function below.

function getCost($matrix, $squaremag) {

$cost = 0;

for($i =0; $i < 3; $i++) {

for($j = 0; $j < 3; $j++) {

$cost += abs($matrix[$i][$j] - $squaremag[$i][$j]);

}

}

return $cost;

}

function formingMagicSquare($s) {

$mgicsquare1 = [

[8,3,4],

[1,5,9],

[6,7,2]

];

$mgicsquare2 = [

[6,1,8],

[7,5,3],

[2,9,4]

];

$mgicsquare3 = [

[2,7,6],

[9,5,1],

[4,3,8]

];

$mgicsquare4 = [

[4,9,2],

[3,5,7],

[8,1,6]

];

$mgicsquare5 = [

[4,3,8],

[9,5,1],

[2,7,6]

];

$mgicsquare6 = [

[2,9,4],

[7,5,3],

[6,1,8]

];

$mgicsquare7 = [

[6,7,2],

[1,5,9],

[8,3,4]

];

$mgicsquare8 = [

[8,1,6],

[3,5,7],

[4,9,2]

];

$mincost = getCost($s, $mgicsquare1);

$mincost =

$mincost > getCost($s, $mgicsquare2) ?

getCost($s, $mgicsquare2) : $mincost;

$mincost =

$mincost > getCost($s, $mgicsquare3) ?

getCost($s, $mgicsquare3) : $mincost;

$mincost =

$mincost > getCost($s, $mgicsquare4) ?

getCost($s, $mgicsquare4) : $mincost;

$mincost =

$mincost > getCost($s, $mgicsquare5) ?

getCost($s, $mgicsquare5) : $mincost;

$mincost =

$mincost > getCost($s, $mgicsquare6) ?

getCost($s, $mgicsquare6) : $mincost;

$mincost =

$mincost > getCost($s, $mgicsquare7) ?

getCost($s, $mgicsquare7) : $mincost;

$mincost =

$mincost > getCost($s, $mgicsquare8) ?

getCost($s, $mgicsquare8) : $mincost;

return $mincost;

}

$fptr = fopen(getenv("OUTPUT_PATH"), "w");

$stdin = fopen("php://stdin", "r");

$s == array();

for ($i = 0; $i < 3; $i++) {

fscanf($stdin, "%[^\n]", $s_temp);

$s[] = array_map('intval', preg_split('/ /', $s_temp, -1,

PREG_SPLIT_NO_EMPTY));

}

$result = formingMagicSquare($s);

fwrite($fptr, $result . "\n");

fclose($stdin);

fclose($fptr);