Range Addition II

The idea is to find the minimum operation size for both row and column because that’s where the maximum number will be after performing all operations:

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from typing import List

class Solution:
    def maxCount(self, m: int, n: int, ops: List[List[int]]) -> int:
        # Initialize the minimum operation size with the given m and n
        min_op_row = m
        min_op_col = n

        # Traverse through all the operations
        for op in ops:
            # Update the minimum operation size if the current operation is smaller
            min_op_row = min(min_op_row, op[0])
            min_op_col = min(min_op_col, op[1])

        # The total maximum number will be the area of the rectangle
        # determined by the minimum operation size
        total_max_num = min_op_row * min_op_col

        return total_max_num

The above solution is based on the fact that all operations increment an equal-sized rectangle from the top-left corner of the matrix. The maximum value will be in the area where every operation overlaps. This area is represented by a rectangle from the top-left with dimensions equal to the smallest rectangle incremented by any operation. So we just need to find this smallest rectangle.

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class Solution:
    def maxCount(self, m: int, n: int, ops: List[List[int]]) -> int:
        min_row = m
        min_col = n
        for i in range(len(ops)):
            min_row=min(min_row, ops[i][0])
            min_col=min(min_col, ops[i][1])
        return min_row*min_col

Problem Classification

The problem is based on data manipulation and involves the concept of matrix operations. It falls under the category of numerical computing.

  1. ‘What’ components:

    • Matrix M: An m x n matrix initialized with all 0’s.
    • Operations ops: An array of operations where each operation is an array of two elements [ai, bi]. Each operation represents a modification of the matrix M - all elements M [y] for all 0 <= x < ai and 0 <= y < bi should be incremented by one.
    • Maximum integers in the matrix: After all operations have been performed on the matrix, the problem asks for the count of maximum integers in the matrix.

  2. Problem Classification:

    • Numerical computing: This problem involves computations on a numerical matrix, with each operation modifying the matrix elements.
    • Data manipulation: The problem involves modifying and interpreting data (a matrix and a list of operations in this case).
    • Array Processing: The problem involves processing the operations array and performing them on the matrix M.

The problem is a combination of understanding matrix manipulation, data interpretation, and array processing. Its solution requires an understanding of how to perform operations on matrices and how to extract information from the modified matrix.

Language Agnostic Coding Drills

  1. Distinct Concepts:

    • Variable declaration: The code begins by declaring variables min_row and min_col.
    • Looping through a list: The code then loops through each operation in ops.
    • Accessing elements in a list: Inside the loop, it accesses elements in the operations list using an index.
    • Conditional check and assignment: In the loop, a condition checks if the current operation’s row or column is less than min_row or min_col. If it is, min_row or min_col is updated to that value.
    • Multiplication and return statement: After the loop, the code multiplies min_row and min_col and returns the result.

  2. Coding Concepts or Drills:

    • Basic Python syntax: (Difficulty Level - 1) Understanding the basic syntax is the starting point. This includes knowing how to declare variables, loop through a list, and access elements in a list.
    • Conditional statements: (Difficulty Level - 2) Writing conditions to compare values and using them to update variables is a common pattern in programming. This is a bit more challenging as it requires logical thinking to determine the appropriate condition.
    • Working with nested lists: (Difficulty Level - 3) The operations are given as a list of lists, which requires understanding how to access elements in a nested list.
    • Returning the result: (Difficulty Level - 4) Knowing what value to return and when to return it is crucial to solve the problem.

  3. Problem-solving Approach:

    • Understand the problem: Recognize that the operations always start at the top left corner of the matrix (0,0) and that every operation increments the values in a sub-matrix. The sub-matrix is defined by the rows and columns in the operation, so the overlapping area of all sub-matrices will have the maximum value.
    • Initialize variables: Start with min_row and min_col as the full size of the matrix. The reasoning behind this is to find the smallest sub-matrix affected by the operations.
    • Loop through the operations: For each operation, check if the operation’s row or column is smaller than the current min_row or min_col. If it is, update min_row and min_col. This is because we are looking for the smallest common sub-matrix affected by all operations.
    • Return the result: At the end, return the area of the smallest common sub-matrix, which is min_row * min_col. This represents the count of the maximum integers in the matrix after performing all the operations.

Targeted Drills in Python

  1. Python Coding Drills:

    • Basic Python syntax:

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      # Declaring a variable
my_var = 10

# Looping through a list
my_list = [1, 2, 3, 4, 5]
for i in my_list:
    print(i)

# Accessing elements in a list
print(my_list[1])  # Outputs: 2

    • Conditional statements:

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      a = 10
b = 20
# Conditional check and assignment
if b > a:
    a = b
print(a)  # Outputs: 20

    • Working with nested lists:

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      # Nested list
my_list = [[1, 2], [3, 4], [5, 6]]
for sublist in my_list:
    for i in sublist:
        print(i)  # Outputs each number in the sublists

    • Returning the result:

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      def calculate_area(length, width):
    return length * width

print(calculate_area(4, 5))  # Outputs: 20

  2. Problem-Specific Concepts:

    This problem doesn’t have any unique problem-specific concepts outside of the general programming concepts identified. The key to this problem is understanding how operations on the matrix are performed and how they affect the matrix. This is an important concept because it allows us to determine the smallest sub-matrix affected by all operations, and to calculate the number of maximum integers in the matrix.

  3. Integration of Concepts:

    All the drills above can be integrated together in a step-by-step manner to build the final solution to the problem.

    • Begin with variable declaration and initialization. Initialize min_row and min_col as the full size of the matrix.
    • Next, loop through the list of operations. This will involve the looping through a list drill.
    • Within this loop, for each operation, check if the operation’s row or column is smaller than the current min_row or min_col. If it is, update min_row and min_col. This involves using conditional checks and assignments.
    • After the loop, return the result of min_row * min_col, which involves returning the result.

    Following these steps will lead to the final solution, with each step contributing to solving the problem.