HackerRank•May 20, 2025

Forming a Magic Square

Hazrat Ali

HackerRank

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

Solution
#include <bits/stdc++.h>

using namespace std;

string ltrim(const string &);
string rtrim(const string &);
vector<string> split(const string &);

/*
 * Complete the 'formingMagicSquare' function below.
 *
 * The function is expected to return an INTEGER.
 * The function accepts 2D_INTEGER_ARRAY s as parameter.
 */

const int SQUARES[8][3][3] = {
    {{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}}
};


int formingMagicSquare(vector<vector<int>>& s) {
    int global_cost = INT_MAX, local_cost = 0;
 
    for (int i = 0; i < 8; i++) {
       
        local_cost = 0;
        for (int j = 0; j < 3; j++) {
            for (int k = 0; k < 3; k++) {
               
                local_cost += abs(s[j][k] - SQUARES[i][j][k]);
            }
        }
        global_cost = min(local_cost, global_cost);
    }
    return global_cost;
}

int main()
{
    ofstream fout(getenv("OUTPUT_PATH"));

    vector<vector<int>> s(3);

    for (int i = 0; i < 3; i++) {
        s[i].resize(3);

        string s_row_temp_temp;
        getline(cin, s_row_temp_temp);

        vector<string> s_row_temp = split(rtrim(s_row_temp_temp));

        for (int j = 0; j < 3; j++) {
            int s_row_item = stoi(s_row_temp[j]);

            s[i][j] = s_row_item;
        }
    }

    int result = formingMagicSquare(s);

    fout << result << "\n";

    fout.close();

    return 0;
}

string ltrim(const string &str) {
    string s(str);

    s.erase(
        s.begin(),
        find_if(s.begin(), s.end(), not1(ptr_fun<int, int>(isspace)))
    );

    return s;
}

string rtrim(const string &str) {
    string s(str);

    s.erase(
        find_if(s.rbegin(), s.rend(), not1(ptr_fun<int, int>(isspace))).base(),
        s.end()
    );

    return s;
}

vector<string> split(const string &str) {
    vector<string> tokens;

    string::size_type start = 0;
    string::size_type end = 0;

    while ((end = str.find(" ", start)) != string::npos) {
        tokens.push_back(str.substr(start, end - start));

        start = end + 1;
    }

    tokens.push_back(str.substr(start));

    return tokens;
}



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