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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.
1def maxCount(m, n, ops):
2 for op in ops:
3 m = min(m, op[0])
4 n = min(n, op[1])
5 return m * n
6
7# Example usage:
8print(maxCount(3, 3, [[2, 2], [3, 3]]))In this Python solution, we iterate over each operation to find the minimum a and b values, which define the smallest submatrix that is affected by all operations. We return the product of these minimum values as the number of maximum integers.
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.
#include <algorithm>
using namespace std;
int maxCount(int m, int n, vector<vector<int>>& ops) {
vector<vector<int>> matrix(m, vector<int>(n, 0));
int count = 0;
int maxVal = 0;
for (const auto& op : 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++ solution uses a vector of vectors to create an m x n matrix. It increments the necessary elements based on each operation. Finally, it counts how many times the maximum value appears in the matrix.