Problem Description
You are given an m x n matrix M initialized with all 0's and an array of operations ops, where ops[i] = [a_i, b_i] means M[x][y] should be incremented by one for all 0 <= x < a_i and 0 <= y < b_i. Count and return the number of maximum integers in the matrix after performing all the operations.
Key Insights
- Each operation affects a rectangular submatrix starting from the top-left corner (0, 0) to (a_i - 1, b_i - 1).
- The maximum integer in the matrix will be located within the area defined by the smallest a_i and b_i values across all operations.
- If no operations are performed, every element remains 0, hence the maximum integer is 0 and the count is m * n.
Space and Time Complexity
Time Complexity: O(k), where k is the number of operations. Space Complexity: O(1), as we only need a few variables to track the minimum dimensions.
Solution
To solve this problem, we can track the smallest dimensions of the rectangle affected by all operations. We find the minimum a and b values from the operations to determine the size of the region where the maximum integer is located. The result is simply the area of this rectangle, which is min_a * min_b.