879287. Generate a matrix with each row and column of given sum
Generate a matrix with each row and column of given sum
Summary
Given a positive integer n and two integers row_sum and col_sum, generate an n x n matrix such that each row's sum is equal to row_sum and each column's sum is equal to col_sum. This problem involves arrays, matrices, and greedy algorithms.
Detailed Explanation
The given problem can be solved by using a greedy approach. We start by initializing the first row of the matrix with values from 1 to row_sum, in such a way that it covers all possible sums up to row_sum.
Then for each subsequent row, we calculate the remaining sum required to reach row_sum and fill the cells accordingly.
For columns, we use a similar approach. We start by initializing the first column with values from 1 to col_sum, in such a way that it covers all possible sums up to col_sum.
Then for each subsequent column, we calculate the remaining sum required to reach col_sum and fill the cells accordingly.
Here is a step-by-step breakdown of the solution:
- Initialize an
n x nmatrix with zeros. - For the first row, generate numbers from 1 to
row_sum. - For each subsequent row, calculate the remaining sum required to reach
row_sum. Fill the cells accordingly. - Repeat steps 2-3 for columns instead of rows.
- Return the generated matrix.
Time complexity: O(n^2) Space complexity: O(n^2)
Optimized Solutions
Java
public class Main {
public static void main(String[] args) {
int n = 4;
int rowSum = 10;
int colSum = 5;
int[][] matrix = new int[n][n];
// Initialize first row and column
for (int i = 0; i < n; i++) {
matrix[0][i] = i + 1;
matrix[i][0] = i + 1;
}
// Calculate remaining sums for rows
int remainingRowSum = rowSum - (n * (n + 1) / 2);
for (int i = 1; i < n; i++) {
for (int j = 1; j < n; j++) {
if (remainingRowSum > colSum) {
matrix[i][j] = remainingRowSum - (i + j - 1);
remainingRowSum -= matrix[i][j];
} else {
matrix[i][j] = colSum;
remainingRowSum = 0;
}
}
}
// Calculate remaining sums for columns
int remainingColSum = colSum - (n * (n + 1) / 2);
for (int i = 1; i < n; i++) {
for (int j = 1; j < n; j++) {
if (remainingColSum > rowSum) {
matrix[i][j] = remainingColSum - (i + j - 1);
remainingColSum -= matrix[i][j];
} else {
matrix[i][j] = rowSum;
remainingColSum = 0;
}
}
}
// Print the generated matrix
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
System.out.print(matrix[i][j] + " ");
}
System.out.println();
}
}
}