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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: 

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.

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 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 .

Limbajul de programare folosit: python3

Cod:

import sys

data = list(map(int, sys.stdin.read().strip().split()))
arr = data[:9]
# all 8 3x3 magic squares
mags = [
    [8,1,6,3,5,7,4,9,2],
    [6,1,8,7,5,3,2,9,4],
    [4,9,2,3,5,7,8,1,6],
    [2,9,4,7,5,3,6,1,8],
    [8,3,4,1,5,9,6,7,2],
    [4,3,8,9,5,1,2,7,6],
    [6,7,2,1,5,9,8,3,4],
    [2,7,6,9,5,1,4,3,8],
]
ans = min(sum(abs(a-b) for a,b in zip(arr,mag)) for mag in mags)
print(ans)

Scor obtinut: 1.0

Submission ID: 464552817

Link challenge: https://www.hackerrank.com/challenges/magic-square-forming/problem

Forming a Magic Square