Given a number N, place numbers from the range [1, N2] in an NxN matrix such that sum in every row is equal.
Examples:
Input: N = 3
Output: 1 5 9
2 6 7
3 4 8
Sum in 1st row: 15
Sum in 2nd row: 15
Sum in 2nd row: 15
Input: N = 5
Output: 1 7 13 19 25
2 8 14 20 21
3 9 15 16 22
4 10 11 17 23
5 6 12 18 24
A Greedy Approach has been used to fill the matrix, where the insertion of elements in the matrix is done row-wise. The required matrix can be obtained using below steps:
- Fill the matrix initially with numbers in the range [1, N2] using matrix traversal.
- Traverse the matrix and change every position in a new matrix considering it as answer matrix by answer[i][j] = mat[j][(i+j)%n].
Below is the implementation of the above approach:
// Java program to distribute n^2 numbers to n people public class Numbers { public static int[][] solve(int[][] arr, int n) { // 2D array for storing the final result int[][] ans = new int[n][n]; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { // using modulo to go to the firs // column after the last column ans[i][j] = arr[j][(i + j) % n]; } } return ans; } public static void show(int[][] arr, int n) { int[][] res = solve(arr, n); for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { System.out.print(res[i][j] + " "); } System.out.println(); } } // making a 2D array containing numbers public static int[][] makeArray(int n) { int[][] arr = new int[n][n]; int c = 1; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) arr[i][j] = c++; } return arr; } // Driver Code public static void main(String[] args) { int n = 5; int[][] arr = makeArray(n); show(arr, n); } } |
1 7 13 19 25 2 8 14 20 21 3 9 15 16 22 4 10 11 17 23 5 6 12 18 24
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