710023. Compute Before Matrix
Compute Before Matrix
Summary
Given a matrix, compute all prefix sums along each row and column. The problem involves manipulating a 2D array to store cumulative sums for both rows and columns.
Detailed Explanation
To solve this problem, we can use a simple algorithm that iterates through the matrix and calculates the prefix sum for each row and column. We start by initializing an empty 2D array prefix_sum with the same dimensions as the input matrix. Then, we iterate through each element of the original matrix, adding it to the corresponding row and column in prefix_sum.
Here's a step-by-step breakdown:
- Initialize
prefix_sumwith zeros. - Iterate through each element
(i, j)in the original matrix:- Add the current element to the
i-throw ofprefix_sum. - Add the current element to the
j-thcolumn ofprefix_sum.
- Add the current element to the
- Return
prefix_sum.
The time complexity for this algorithm is O(m * n), where m and n are the number of rows and columns in the matrix, respectively. The space complexity is also O(m * n) because we need to store the prefix sums.
Optimized Solutions
Java
public int[][] computeBeforeMatrix(int[][] matrix) {
int m = matrix.length;
int n = matrix[0].length;
int[][] prefix_sum = new int[m][n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
prefix_sum[i][j] += matrix[i][j];
if (i > 0) {
prefix_sum[i][j] += prefix_sum[i - 1][j];
}
if (j > 0) {
prefix_sum[i][j] += prefix_sum[i][j - 1];
}
}
}
return prefix_sum;
}