Difference of Number of Distinct Values on Diagonals

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22

class Solution:
    def differenceOfDistinctValues(self, g: List[List[int]]) -> List[List[int]]:
        m, n = len(g), len(g[0])
        res = [[0 for _ in range(n)] for _ in range(m)]

        def populateDiag(i, j):
            tl, br = set(), set()
            for d in range(min(m - i, n - j)):
                res[i + d][j + d] = len(tl)
                tl.add(g[i + d][j + d])

            for d in range(min(m - i, n - j) - 1, -1, -1):
                res[i + d][j + d] = abs(res[i + d][j + d] - len(br))
                br.add(g[i + d][j + d])

        for j in range(n):
            populateDiag(0, j)

        for i in range(1, m):
            populateDiag(i, 0)

        return res

Can you help me with finding the isomorphism for the LeetCode ? Please provide a concise response and if an exact mapping is not possible, specify it as an approximate mapping. If the titles of the problems are the same, select a different problem. Also, explain the reasoning behind your selection. Don’t mention anything about your training cut off date. Provide the best possible answer. Do not repeat the same point. Mention which problem is simpler. If there are multiple isomorphic problem. Arrange them from simple to more complex to your best possible knowledge. Do not add Leetcode to the problem name. The response format is:

The problem can be mapped to

10 Prerequisite LeetCode Problems

This problem can involve using sets to keep track of unique values, understanding how diagonals work in a 2D array, and simple arithmetic.

Here are 10 problems to prepare:

  1. “Find All Numbers Disappeared in an Array” (LeetCode 448): This problem helps you get used to manipulating and understanding arrays.

  2. “K-diff Pairs in an Array” (LeetCode 532): This problem involves understanding arrays and simple arithmetic.

  3. “Subarray Sum Equals K” (LeetCode 560): This problem provides practice on using array manipulation and arithmetic to achieve a result.

  4. “Two Sum II - Input array is sorted” (LeetCode 167): Another problem with array manipulation and arithmetic.

  5. “Contains Duplicate II” (LeetCode 219): This problem introduces the concept of using a set to track unique values.

  6. “Island Perimeter” (LeetCode 463): This problem is about counting specific elements in a 2D grid, which could be useful for counting distinct diagonal elements.

  7. “Toeplitz Matrix” (LeetCode 766): This problem gives practice with traversing diagonals in a 2D grid.

  8. “Transpose Matrix” (LeetCode 867): This problem can help with understanding and manipulating a 2D array.

  9. “Reshape the Matrix” (LeetCode 566): This problem provides more practice with 2D array manipulation.

  10. “Rotate Image” (LeetCode 48): Rotating an image involves an understanding of how to move items in a 2D array, including items along diagonals.

Once you are comfortable with these problems, you can tackle “Difference of Number of Distinct Values on Diagonals”.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16

class Solution:
    def differenceOfDistinctValues(self, grid: List[List[int]]) -> List[List[int]]:
        d = defaultdict(list)                      

        for i, j in product(range(len(grid)),        
                            range(len(grid[0]))):
            d[i-j].append((i,j))                        

        for diag in d:
            arr = [grid[i][j] for i,j in d[diag]]       

            for idx, (i,j) in enumerate(d[diag]):       
                grid[i][j] = abs(len(set(arr[:idx])) -  
                                 len(set(arr[idx+1:])))

        return grid

Problem Classification

The problem is in the domain of 2-dimensional data manipulation and analysis, as it involves handling and processing data in a 2D matrix or grid. It also involves mathematics as the solution requires calculating distinct values and their absolute differences.

‘What’ Components:

  • A 2D grid or matrix of size m x n is given.
  • A new matrix, answer of the same size, needs to be created.
  • For each cell (r, c) in the answer matrix, two values need to be calculated:
    • topLeft[r][c]: the number of distinct values in the top-left diagonal of the cell (r, c) in the grid.
    • bottomRight[r][c]: the number of distinct values in the bottom-right diagonal of the cell (r, c) in the grid.
  • The value of each cell in the answer matrix is the absolute difference between topLeft[r][c] and bottomRight[r][c].
  • The final output is the answer matrix.

This problem can be classified as a computation problem since it involves performing operations on the data from a 2D matrix to compute a new matrix. It also falls into the category of “data transformation” since we’re transforming input data (the original grid) into a new format (the answer matrix). It also involves elements of combinatorial counting and set manipulation because it requires counting distinct values in specific regions of the grid.

It’s an “array manipulation” problem because the operations are performed on a 2D array, a common data structure in computer programming. It’s also a type of “matrix traversal” problem because the solution requires traversing the given matrix in specific ways (along the diagonals) to gather the required information.

Identifying Problem Isomorphism

Can you help me with finding the isomorphism for this problem?

Which problem does this problem map to the corresponding isomorphic problem on Leetcode ?

How did you identify that this problem is a variation of problem?

Language Agnostic Coding Drills

  1. Identification of coding concepts:

    • Basic Data Structures: The code makes use of Python lists and a dictionary. Understanding these data structures and how to manipulate them is a fundamental concept in Python.

    • Function Definition: The code is contained within a function definition, a crucial concept in programming that allows the encapsulation and reuse of code.

    • Nested Loops: The code uses a nested loop to iterate over each cell in the matrix, another fundamental programming concept.

    • 2D Matrix Traversal: The problem involves traversing a 2D matrix in a specific way, namely along the diagonals.

    • DefaultDict and List Appending: The code employs defaultdict to create a dictionary with default list values, and appends values to these lists.

    • Product function from itertools module: This function is used to generate cartesian product of input iterables which is a slightly advanced Python concept.

    • Set Operations: The code uses sets to find the distinct values in each diagonal of the matrix.

  2. Coding concepts in order of increasing difficulty:

    • Basic Data Structures: Understanding lists and dictionaries is fundamental to almost any kind of programming task.

    • Function Definition: Once comfortable with basic data structures, learning to encapsulate code into functions is a logical next step.

    • Nested Loops: Nested loops are a slightly more complex concept as they require understanding how to work with multi-dimensional data and how to control the flow of the program.

    • 2D Matrix Traversal: This concept requires a good understanding of nested loops and how to use them to access and manipulate multi-dimensional data.

    • DefaultDict and List Appending: These are slightly more advanced concepts that require an understanding of Python’s standard library and how to use it to simplify code.

    • Product function from itertools module: Understanding how to use functions from Python’s standard library to simplify code is a more advanced concept, requiring a good understanding of Python’s built-in functions and data structures.

    • Set Operations: This is the most advanced concept, as it requires understanding of the mathematical concept of sets, and how to use Python’s set data structure and its associated methods.

  3. Problem-solving approach:

    • First, the problem requires identifying all diagonals in the grid. This is achieved using a defaultdict with the key being the difference between the row and column indices, which identifies each diagonal uniquely.

    • Each diagonal is then traversed, and for each cell, the number of distinct values in the top-left and bottom-right parts of the diagonal is computed. This is done by slicing the diagonal into two parts and converting each part into a set (to find distinct values), and then calculating the absolute difference between the sizes of these two sets.

    • The result is stored in the original grid at the corresponding cell. After processing all cells, the modified grid is returned as the result.

Each of the identified coding concepts or drills contribute to the final solution by allowing the manipulation and traversal of the 2D grid, the identification and traversal of diagonals, the calculation of the number of distinct values, and the storage of the final result.

Targeted Drills in Python

  1. Python drills for each concept:

    • Basic Data Structures:

      1
2
3
4
5

      my_list = [1, 2, 3, 4]
print(my_list)

my_dict = {'apple': 1, 'banana': 2}
print(my_dict)

    • Function Definition:

      1
2
3
4

      def hello_world():
    print("Hello, world!")

hello_world()

    • Nested Loops:

      1
2
3

      for i in range(3):
    for j in range(3):
        print(f"i: {i}, j: {j}")

    • 2D Matrix Traversal:

      1
2
3
4

      matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
for i in range(len(matrix)):
    for j in range(len(matrix[0])):
        print(matrix[i][j])

    • DefaultDict and List Appending:

      1
2
3
4
5
6

      from collections import defaultdict
d = defaultdict(list)
d['a'].append(1)
d['a'].append(2)
d['b'].append(3)
print(d)

    • Product function from itertools module:

      1
2
3

      from itertools import product
for i, j in product(range(3), range(3)):
    print(f"i: {i}, j: {j}")

    • Set Operations:

      1
2
3
4

      set1 = {1, 2, 3}
set2 = {2, 3, 4}
print(set1.union(set2))
print(set1.intersection(set2))

  2. Drills for specific needs of the problem:

    • Identifying diagonals in a 2D grid:

      1
2
3
4
5
6

      grid = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
d = defaultdict(list)
for i in range(len(grid)):
    for j in range(len(grid[0])):
        d[i-j].append((i, j))
print(d)

    • Calculating the number of distinct values in a list:

      1
2
3

      my_list = [1, 2, 2, 3, 3, 3]
num_distinct = len(set(my_list))
print(num_distinct)

  3. How to merge these drills for the final solution:

    • Start by creating a defaultdict where each key-value pair represents a diagonal in the 2D grid.

    • Iterate over each cell in the grid, add the cell’s coordinates to the list corresponding to its diagonal in the defaultdict.

    • For each cell, calculate the number of distinct values in the top-left and bottom-right parts of its diagonal. This can be done by slicing the list of cells in the diagonal and converting each part into a set.

    • Calculate the absolute difference between the sizes of these two sets and store the result in the original grid at the corresponding cell.

    • After processing all cells, return the modified grid as the result.

Each drill trains a separate skill that is used in the final solution, and practicing these drills will help you understand how each part of the solution works and how they fit together.