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 . Example $s = [[5, 3, 4], [1, 5, 8], [6, 4, 2]] The matrix looks like this: 534158642 We can convert it to the following magic square: 834159672 This took three replacements at a cost of . Function Description Complete the formingMagicSquare function in the editor below. formingMagicSquare has the following parameter(s): int s[3][3]: a array of integers Returns int: the minimal total cost of converting the input square to a magic square Input Format Each of the lines contains three space-separated integers of row . Constraints Sample Input 0 4 9 23 5 78 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 24 5 76 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
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 .
Example
$s = [[5, 3, 4], [1, 5, 8], [6, 4, 2]]
The matrix looks like this:
We can convert it to the following magic square:
This took three replacements at a cost of .
Function Description
Complete the formingMagicSquare function in the editor below.
formingMagicSquare has the following parameter(s):
- int s[3][3]: a array of integers
Returns
- int: the minimal total cost of converting the input square to a magic square
Input Format
Each of the lines contains three space-separated integers of row .
Constraints
Sample Input 0
Sample Output 0
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
Sample Output 1
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
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