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Find the Width of Columns of a Grid

Easy

Samsung

0 views

Topics:

Arrays

You are given a 0-indexed m x n integer matrix grid. The width of a column is the maximum length of its integers.

For example, if grid = [[-10], [3], [12]], the width of the only column is 3 since -10 is of length 3.

Return an integer array ans of size n where ans[i] is the width of the i^th column.

The length of an integer x with len digits is equal to len if x is non-negative, and len + 1 otherwise.

Example 1:

Input: grid = [[1],[22],[333]]
Output: [3]
Explanation: In the 0^th column, 333 is of length 3.

Example 2:

Input: grid = [[-15,1,3],[15,7,12],[5,6,-2]]
Output: [3,1,2]
Explanation: 
In the 0^th column, only -15 is of length 3.
In the 1^st column, all integers are of length 1. 
In the 2^nd column, both 12 and -2 are of length 2.

Constraints:

m == grid.length
n == grid[i].length
1 <= m, n <= 100
-10⁹ <= grid[r][c] <= 10⁹

Find the Width of Columns of a Grid

Easy

Samsung

0 views

Topics:

Arrays

You are given a 0-indexed m x n integer matrix grid. The width of a column is the maximum length of its integers.

For example, if grid = [[-10], [3], [12]], the width of the only column is 3 since -10 is of length 3.

Return an integer array ans of size n where ans[i] is the width of the i^th column.

The length of an integer x with len digits is equal to len if x is non-negative, and len + 1 otherwise.

Example 1:

Input: grid = [[1],[22],[333]]
Output: [3]
Explanation: In the 0^th column, 333 is of length 3.

Example 2:

Input: grid = [[-15,1,3],[15,7,12],[5,6,-2]]
Output: [3,1,2]
Explanation: 
In the 0^th column, only -15 is of length 3.
In the 1^st column, all integers are of length 1. 
In the 2^nd column, both 12 and -2 are of length 2.

Constraints:

m == grid.length
n == grid[i].length
1 <= m, n <= 100
-10⁹ <= grid[r][c] <= 10⁹

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

Can the grid be empty, and if so, what should I return?
What is the maximum number of rows and columns the grid can have?
Can any of the strings in the grid be null or empty?
Are all rows guaranteed to have the same number of columns?
Should I return a new array, or can I modify the input grid in place (if that were helpful, which I don't currently anticipate)?

Brute Force Solution

Approach

We want to find the maximum width for each column in a grid of numbers represented as text. The brute force method involves checking every number in each column to find the largest number of digits.

Here's how the algorithm would work step-by-step:

Look at the first column of the grid.
Go through each number written as text in that column, one by one.
Determine the number of digits (width) of each number.
Keep track of the largest number of digits we've seen so far in that column.
Repeat these steps for every column in the grid.
The final answer will be a list of the maximum widths found for each column.

Code Implementation

def find_column_widths_brute_force(grid):
    number_of_columns = len(grid[0])
    column_widths = []

    # Iterate through each column in the grid
    for column_index in range(number_of_columns):
        max_width_for_column = 0

        # Iterate through each row in the current column
        for row in grid:
            text_value = str(row[column_index])
            current_width = len(text_value)

            # Find the max width for current column
            if current_width > max_width_for_column:
                max_width_for_column = current_width

        column_widths.append(max_width_for_column)

    return column_widths

Try it yourself on LeetCode

Big(O) Analysis

Time Complexity

O(m*n) – The algorithm iterates through each column of the grid. Let 'n' be the number of columns in the grid, and 'm' be the number of rows. For each column, it iterates through each row to find the width of the number represented as text. Therefore, the time complexity is proportional to the product of the number of rows and the number of columns, resulting in a time complexity of O(m*n).

Space Complexity

O(C) – The algorithm iterates through each column of the grid, keeping track of the maximum width seen so far for each column. To store these maximum widths, an auxiliary list or array of size C is needed, where C is the number of columns in the grid. No other significant data structures or recursive calls are used that consume space dependent on the input size. Therefore, the space complexity is primarily determined by the size of this auxiliary list, leading to a space complexity of O(C).

Optimal Solution

Approach

To find the width of each column, we need to examine each element in the grid. The goal is to find the maximum width required for each column by comparing the lengths of all string representations in that column.

Here's how the algorithm would work step-by-step:

Go through each column of the grid one at a time.
For each column, look at every cell within that column.
Figure out how wide each cell is by converting the value to text and counting the letters.
Keep track of the widest cell seen so far in that column.
Once you've checked every cell in the column, remember the maximum width found for that column.
Move to the next column and repeat the process until you've checked all the columns.
The list of maximum widths you've saved will be the answer: the width of each column.

Code Implementation

def find_column_width(grid):
    number_of_columns = len(grid[0])
    column_widths = []

    # Iterate through each column of the grid
    for column_index in range(number_of_columns):
        maximum_column_width = 0

        # Iterate through each row in the current column
        for row_index in range(len(grid)): 
            cell_value = grid[row_index][column_index]
            cell_width = len(str(cell_value))

            # Keep track of the max width
            maximum_column_width = max(maximum_column_width, cell_width)

        # Store the maximum width for the current column
        column_widths.append(maximum_column_width)

    return column_widths

Try it yourself on LeetCode

Big(O) Analysis

Time Complexity

O(m*n) – The algorithm iterates through each column of the grid, where 'n' represents the number of columns. For each column, it then iterates through each row, where 'm' represents the number of rows, to find the maximum width. Converting each integer element to a string has O(1) complexity because the maximum possible length is limited by the integer range defined in the problem. Therefore, the overall time complexity is determined by the nested loops, resulting in O(m*n) where m is the number of rows, and n is the number of columns.

Space Complexity

O(n) – The algorithm iterates through the grid, row by row. The primary space usage comes from storing the maximum width found for each column. Because there will be a number of columns equivalent to the number of cells in each row in the grid, the size of this maximum width array increases linearly with the width of the grid. Therefore, if 'n' is the number of columns in the grid, the auxiliary space used is O(n).

Edge Cases

Case	How to Handle
Null or empty grid	Return an empty array if the input grid is null or has zero rows, as there are no columns to process.
Grid with zero columns (empty strings in each row)	Return an empty array since no column widths can be computed.
Grid with one row	Iterate over the single row's string lengths directly to determine the column widths.
Grid with rows of different lengths	The problem states all rows have the same number of columns, so we assume consistent row length and proceed using the first row's length.
Very long strings within the grid (potential memory/performance bottleneck)	The algorithm's time complexity depends on the number of cells (rows * columns) and the length of strings in each cell, so consider string interning or alternative data structures for extremely long strings.
Grid with a large number of rows and columns (scalability)	Ensure the solution has a time complexity of O(rows * cols * k), where k is the maximum string length, as a naive approach might lead to performance issues with extremely large grids.
Grid containing non-ASCII characters that affect string length calculation	Ensure the string length calculation correctly handles multi-byte characters according to the problem requirements (e.g., using Unicode-aware length calculation if needed).
Integer overflow when calculating string lengths	String lengths should be cast to long integer types to prevent integer overflows when lengths are large.

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

Can the grid be empty, and if so, what should I return?
What is the maximum number of rows and columns the grid can have?
Can any of the strings in the grid be null or empty?
Are all rows guaranteed to have the same number of columns?
Should I return a new array, or can I modify the input grid in place (if that were helpful, which I don't currently anticipate)?

Brute Force Solution

Approach

We want to find the maximum width for each column in a grid of numbers represented as text. The brute force method involves checking every number in each column to find the largest number of digits.

Here's how the algorithm would work step-by-step:

Look at the first column of the grid.
Go through each number written as text in that column, one by one.
Determine the number of digits (width) of each number.
Keep track of the largest number of digits we've seen so far in that column.
Repeat these steps for every column in the grid.
The final answer will be a list of the maximum widths found for each column.

Code Implementation

def find_column_widths_brute_force(grid):
    number_of_columns = len(grid[0])
    column_widths = []

    # Iterate through each column in the grid
    for column_index in range(number_of_columns):
        max_width_for_column = 0

        # Iterate through each row in the current column
        for row in grid:
            text_value = str(row[column_index])
            current_width = len(text_value)

            # Find the max width for current column
            if current_width > max_width_for_column:
                max_width_for_column = current_width

        column_widths.append(max_width_for_column)

    return column_widths

Try it yourself on LeetCode

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

Here's how the algorithm would work step-by-step:

Go through each column of the grid one at a time.
For each column, look at every cell within that column.
Figure out how wide each cell is by converting the value to text and counting the letters.
Keep track of the widest cell seen so far in that column.
Once you've checked every cell in the column, remember the maximum width found for that column.
Move to the next column and repeat the process until you've checked all the columns.
The list of maximum widths you've saved will be the answer: the width of each column.

Code Implementation

def find_column_width(grid):
    number_of_columns = len(grid[0])
    column_widths = []

    # Iterate through each column of the grid
    for column_index in range(number_of_columns):
        maximum_column_width = 0

        # Iterate through each row in the current column
        for row_index in range(len(grid)): 
            cell_value = grid[row_index][column_index]
            cell_width = len(str(cell_value))

            # Keep track of the max width
            maximum_column_width = max(maximum_column_width, cell_width)

        # Store the maximum width for the current column
        column_widths.append(maximum_column_width)

    return column_widths

Try it yourself on LeetCode

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Null or empty grid	Return an empty array if the input grid is null or has zero rows, as there are no columns to process.
Grid with zero columns (empty strings in each row)	Return an empty array since no column widths can be computed.
Grid with one row	Iterate over the single row's string lengths directly to determine the column widths.
Grid with rows of different lengths	The problem states all rows have the same number of columns, so we assume consistent row length and proceed using the first row's length.
Very long strings within the grid (potential memory/performance bottleneck)	The algorithm's time complexity depends on the number of cells (rows * columns) and the length of strings in each cell, so consider string interning or alternative data structures for extremely long strings.
Grid with a large number of rows and columns (scalability)	Ensure the solution has a time complexity of O(rows * cols * k), where k is the maximum string length, as a naive approach might lead to performance issues with extremely large grids.
Grid containing non-ASCII characters that affect string length calculation	Ensure the string length calculation correctly handles multi-byte characters according to the problem requirements (e.g., using Unicode-aware length calculation if needed).
Integer overflow when calculating string lengths	String lengths should be cast to long integer types to prevent integer overflows when lengths are large.