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To solve this problem efficiently, observe that each operation affects a submatrix starting from the top-left corner. Thus, the final result of the operations is determined by the smallest intersected submatrix affected by all operations. Find the minimum value of "a" and "b" from all operations in ops. This will give you the dimensions of the area where the maximum integers will exist after applying all operations.
The key insight is that the size of the submatrix affected by all operations determines the count of maximum numbers in the final matrix.
Time Complexity: O(k), where k is the number of operations.
Space Complexity: O(1), as we are using only a few extra variables.
1public class Solution {
2 public int MaxCount(int m, int n, int[][] ops) {
3 foreach (var op in ops) {
4 m = Math.Min(m, op[0]);
5 n = Math.Min(n, op[1]);
6 }
7 return m * n;
8 }
9}The C# solution iterates through the operations and keeps track of the minimum bounds for rows and columns that are affected. The final product of these minimums gives us the number of maximum values in the matrix.
This approach simulates the operations directly on the matrix. For each operation, we iterate through the specified submatrix and increment the values. Finally, we determine the number of times the maximum value occurs in the matrix. Although this method is less efficient due to its higher computational cost, it reinforces understanding of the problem.
Time Complexity: O(m * n * k), where m and n are the dimensions of the matrix, and k is the number of operations.
Space Complexity: O(m * n), for the matrix.
public int MaxCount(int m, int n, int[][] ops) {
int[,] matrix = new int[m, n];
int maxVal = 0;
int count = 0;
foreach (var op in ops) {
for (int i = 0; i < op[0]; i++) {
for (int j = 0; j < op[1]; j++) {
matrix[i, j]++;
if (matrix[i, j] > maxVal) {
maxVal = matrix[i, j];
count = 1;
} else if (matrix[i, j] == maxVal) {
count++;
}
}
}
}
return count;
}
}This C# implementation manages an m x n matrix where increments occur as per each operation. It finally calculates the count of the maximum values in the matrix.