713972. Fill the Matrix
Medium
Fill the Matrix
Slug: fill-the-matrix--170647
Difficulty: Medium
Id: 713972
Topic Tags: Mathematical, BFS, Algorithms
Company Tags: Oracle
Summary
The "Fill the Matrix" problem involves filling a given matrix with values in such a way that each row and column sum is equal to a given target value. This problem requires a combination of mathematical and algorithmic skills.
Detailed Explanation
To solve this problem, we can use Breadth-First Search (BFS) as our approach. We will start by initializing the first row with values from 1 to n, where n is the number of columns in the matrix. Then, for each subsequent row, we will fill it by iterating over each column and calculating the value based on the sum of the current column and the target value minus the sum of all previous rows.
Here's a step-by-step breakdown:
- Initialize the first row with values from 1 to n.
- For each subsequent row:
- Iterate over each column and calculate the value for that cell as follows:
matrix[i][j] = target_sum - sum_of_previous_rows - (i * n) - where
target_sumis the target value,sum_of_previous_rowsis the sum of all previous rows, and(i * n)is the sum of all cells in the current row.
- Iterate over each column and calculate the value for that cell as follows:
- Repeat step 2 until the entire matrix is filled.
Here's an example to illustrate this:
public class Main {
public static void main(String[] args) {
int[][] matrix = new int[4][5];
int targetSum = 15;
for (int i = 0; i < matrix.length; i++) {
int sumOfPreviousRows = 0;
for (int j = 0; j < matrix[i].length; j++) {
matrix[i][j] = targetSum - sumOfPreviousRows - (i * 5);
sumOfPreviousRows += matrix[i][j];
}
}
}
}