[알고리즘] 26. 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 .

답 : 

import sys

square = []

for i in range(3):

square.append(list(map(int, input().strip().split(' '))))

# 8가지로 정해져있음

magic_squares = [[[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]]]

# 최댓값을 집어넣음

minimum_cost = sys.maxsize

for magic_square in magic_squares:

cost = 0

for i in range(3):

for j in range(3):

cost += abs(magic_square[i][j] - square[i][j])

minimum_cost = min(minimum_cost, cost)

print(minimum_cost)

기존의 매직넘버들과 비교해서 cost를 비교하는 것..! 

저런 리스트가 있는줄도 몰랐다...