formingMagicSquare.php

function formingMagicSquare($s) {
    if (checkMagic($s)) {
        return 0;
    }
    
    $cost = 0;
    if ($s[1][1] != 5) {
        $cost = abs(5 - $s[1][1]);
        $s[1][1] = 5;    
    }
    
    if (checkMagic($s)) {
        return $cost;
    }
    
    // check all pairs
    /** 
        (0,0), (2,2) = 10
        (0,1), (2,1) = 10
        (2,0), (0,2) = 10
        (1,0), (1,2) = 10
    **/
    $pairs = [
        [[0,0], [2,2]],
        [[0,1], [2,1]],
        [[2,0], [0,2]],
        [[1,0], [1,2]]
    ];
    
    $mincost = 0;
    $tmp = $s;
    foreach ($p in $pairs)
    {
        $t = ($s[$p[0][0],p[0][1]] + $s[$p[1][0],p[1][1]] - 10);
        if ($t == 0) {
            continue;
        }
        
        // check this leg
        $tmp[$p[0][0],p[0][1]] += $t;
        
    }

    
    return $mincost + $cost;
}

function checkMagic($s) 
{   
    // vertically
    $sum = 0;
    for ($i = 0; $i < 3; $i++) {
        for ($j = 0; $j < 3; $j++) {
            $sum += $s[$i][$j];
        }
        if ($sum != 15) {
            return false;
        }
        $sum = 0;
    }
    
    // horizontally
    $sum = 0;
    for ($j = 0; $j < 3; $j++) {
        for ($i = 0; $i < 3; $i++) {
            $sum += $s[$i][$j];
        }
        if ($sum != 15) {
            return false;
        }
        $sum = 0;
    }
    
    // diagonally
    $sum = 0;
    for ($j = 0; $j < 3; $j++) {
        $sum += $s[$j][$j];
    }
    if ($sum != 15) {
        return false;
    }
    
    $sum = 0;
    for ($j = 0; $j < 3; $j++) {
        $sum += $s[2 - $j][$j];
    }
    if ($sum != 15) {
        return false;
    }
    
    
    return true;
}

$s =  [[8, 3, 4], [1, 4, 9], [6, 7, 1]];
echo formingMagicSquare($s);