710013. Maximum difference between pair in a matrix
Maximum difference between pair in a matrix
Summary
Given an m x n matrix, find the maximum difference between the sum of two elements, where one element is from each row. The problem requires us to maximize the difference by selecting the smallest and largest elements from different rows.
Detailed Explanation
To solve this problem, we need to iterate through each row in the matrix and keep track of the minimum and maximum values encountered so far. We will also maintain two variables to store the minimum and maximum differences seen till now. The maximum difference is updated whenever a larger difference is found between the current minimum and maximum values.
Here's a step-by-step breakdown of the solution:
- Initialize
min_valandmax_valto represent the smallest and largest elements in the first row, respectively. - Iterate through each row in the matrix (m times):
- Update
min_valif the current element is smaller thanmin_val. - Update
max_valif the current element is larger thanmax_val.
- Update
- Calculate the maximum difference (
diff) between the sum ofmin_valand the sum ofmax_val. This represents the maximum difference that can be achieved by selecting one element from each row. - Return the calculated
diff.
Time Complexity: O(m * n), where m is the number of rows and n is the number of columns in the matrix.
Space Complexity: O(1), as we only use a constant amount of space to store the minimum and maximum values.
Optimized Solutions
Java
public int maxDifference(int[][] matrix) {
int m = matrix.length;
int n = matrix[0].length;
int min_val = Integer.MAX_VALUE, max_val = Integer.MIN_VALUE;
int diff = 0;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (matrix[i][j] < min_val) {
min_val = matrix[i][j];
}
if (matrix[i][j] > max_val) {
max_val = matrix[i][j];
}
}
}
diff = max_val - min_val;
return diff;
}