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Answer to Question #182821 in Python for vijay

Area of Rectangle

Given an MxN matrix filled with

X's and O's, find the largest rectangle containing only X's and return its area. If there are no Xs in the entire matrix print 0.Input

The first line of input will be containing two space-separated integers, denoting M and N.

The next M lines will contain N space-separated integers, denoting the elements of the matrix.

The output should be a single line containing the area of the maximum rectangle.

Explanation

For example, if the given M, N and elements of matrix are as the following

The matrix from indices (1, 2) to (2, 4) has the maximum rectangle with

X. So the output should be the area of the maximum rectangle with X, which is 6.

Sample Input 1

Sample Output 1

Sample Input 2

Sample Output 2

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Dear Ramesh the code works well in python 3.9

This code is not working in python 3.9 can yu update a right answer for it

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Python Matrices and NumPy Arrays

A matrix is a two-dimensional data structure where numbers are arranged into rows and columns. For example:

This matrix is a 3x4 (pronounced "three by four") matrix because it has 3 rows and 4 columns.

• Python Matrix

Python doesn't have a built-in type for matrices. However, we can treat a list of a list as a matrix. For example:

We can treat this list of a list as a matrix having 2 rows and 3 columns.

Be sure to learn about Python lists before proceed this article.

Let's see how to work with a nested list.

When we run the program, the output will be:

Here are few more examples related to Python matrices using nested lists.

• Add two matrices
• Transpose a Matrix
• Multiply two matrices

Using nested lists as a matrix works for simple computational tasks, however, there is a better way of working with matrices in Python using NumPy package.

• NumPy Array

NumPy is a package for scientific computing which has support for a powerful N-dimensional array object. Before you can use NumPy, you need to install it. For more info,

• Visit: How to install NumPy?
• If you are on Windows, download and install anaconda distribution of Python. It comes with NumPy and other several packages related to data science and machine learning.

Once NumPy is installed, you can import and use it.

NumPy provides multidimensional array of numbers (which is actually an object). Let's take an example:

As you can see, NumPy's array class is called ndarray .

How to create a NumPy array?

There are several ways to create NumPy arrays.

1. Array of integers, floats and complex Numbers

When you run the program, the output will be:

2. Array of zeros and ones

Here, we have specified dtype to 32 bits (4 bytes). Hence, this array can take values from -2 -31 to 2 -31 -1 .

3. Using arange() and shape()

Learn more about other ways of creating a NumPy array .

Matrix Operations

Above, we gave you 3 examples: addition of two matrices, multiplication of two matrices and transpose of a matrix. We used nested lists before to write those programs. Let's see how we can do the same task using NumPy array.

Addition of Two Matrices

We use + operator to add corresponding elements of two NumPy matrices.

Multiplication of Two Matrices

To multiply two matrices, we use dot() method. Learn more about how numpy.dot works.

Note: * is used for array multiplication (multiplication of corresponding elements of two arrays) not matrix multiplication.

Transpose of a Matrix

We use numpy.transpose to compute transpose of a matrix.

As you can see, NumPy made our task much easier.

Access matrix elements, rows and columns

Access matrix elements

Similar like lists, we can access matrix elements using index. Let's start with a one-dimensional NumPy array.

Now, let's see how we can access elements of a two-dimensional array (which is basically a matrix).

Access rows of a Matrix

Access columns of a Matrix

If you don't know how this above code works, read slicing of a matrix section of this article.

Slicing of a Matrix

Slicing of a one-dimensional NumPy array is similar to a list. If you don't know how slicing for a list works, visit Understanding Python's slice notation .

Let's take an example:

Now, let's see how we can slice a matrix.

As you can see, using NumPy (instead of nested lists) makes it a lot easier to work with matrices, and we haven't even scratched the basics. We suggest you to explore NumPy package in detail especially if you trying to use Python for data science/analytics.

NumPy Resources you might find helpful:

• NumPy Tutorial
• NumPy Reference

Table of Contents

• What is a matrix?
• Numbers(integers, float, complex etc.) Array
• Zeros and Ones Array
• Array Using arange() and shape()
• Multiplication
• Access elements
• Access rows
• Access columns
• Slicing of Matrix
• Useful Resources

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5 Best Ways to Calculate the Area of a Polygon in Python

💡 Problem Formulation: Calculating the area of a polygon can be a common task in various fields like computer graphics, game development, and geographic information systems. Given the coordinates of the vertices of a polygon, the desired output is the calculated area of that polygon.

Method 1: Shoelace Formula

The Shoelace formula, also known as Gauss’s area formula, is a mathematical algorithm that can compute the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. This method is efficient and accurate for any non-self-intersecting polygon, whether it’s concave or convex.

Here’s an example:

Output: Polygon Area: 45.5

This code snippet defines a function shoelace_formula() that takes a list of vertices, where each vertex is a tuple of x and y coordinates. It calculates the area based on the Shoelace formula by iterating over the vertices and summing up the cross products of the coordinates, and then dividing the absolute value by 2.

Method 2: Matplotlib Path

Using Matplotlib’s Path and PathPatch, we can find the area of a polygon by creating a path object from the vertices of the polygon and then getting the area using its containment tests. This method is straightforward for those already using Matplotlib for plotting in Python.

This code snippet uses Matplotlib’s Path and PathPatch to create a path object from the polygon’s vertices and then calculates the area of the patch. The contained points method is leveraged with an arbitrarily large negative radius to ensure the whole area is considered.

Method 3: SciPy Convex Hull

If the polygon is convex, the SciPy library provides a function to compute its Convex Hull, which we can then use to calculate the area. This method is more suited for convex polygons and relies on the external SciPy library.

This snippet utilizes the ConvexHull function from SciPy’s spatial module to create a convex hull around the provided points and then outputs the volume attribute, which, in the case of a 2-dimensional hull, represents the area.

Method 4: Shapely Library

Shapely is a BSD-licensed Python package for manipulation and analysis of planar geometric objects, which amongst many functionalities, can calculate the area of a polygon. It’s a powerful method for complex geometrical computations beyond just area calculations.

By importing Polygon from the Shapely library, we can easily create a polygon object from the list of vertices and directly access its area property to find the area of the polygon.

Bonus One-Liner Method 5: NumPy Cross Product

For those looking for a minimalistic approach, NumPy can be used to calculate the area using the Shoelace formula in a compact, one-liner function.

This function splits the x and y coordinates using NumPy arrays and calculates the cross product via the dot product and array rolling, giving us the polygon’s area in just a single line of NumPy code.

Summary/Discussion

• Method 1: Shoelace Formula. Straightforward. Works with any polygon. Pure Python without dependencies.
• Method 2: Matplotlib Path. Intuitive for Matplotlib users. Limited to Matplotlib’s capabilities.
• Method 3: SciPy Convex Hull. Utilizes scientific library. Best for convex shapes. Requires SciPy.
• Method 4: Shapely Library. Robust for complex geometric analysis. Requires external package.
• Method 5: NumPy Cross Product. Compact one-liner. Requires understanding of NumPy. Convenient for NumPy users.

Emily Rosemary Collins is a tech enthusiast with a strong background in computer science, always staying up-to-date with the latest trends and innovations. Apart from her love for technology, Emily enjoys exploring the great outdoors, participating in local community events, and dedicating her free time to painting and photography. Her interests and passion for personal growth make her an engaging conversationalist and a reliable source of knowledge in the ever-evolving world of technology.

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Program to find area of largest island in a matrix in Python

Suppose we have a binary matrix. Here 1 represents land and 0 represents water, And an island is a group of 1s that are neighboring whose perimeter is surrounded by water. We can assume that the edges of the matrix are surrounded by water. We have to find the area of the largest island in matrix.

So, if the input is like

then the output will be 6.

To solve this, we will follow these steps −

• Define a function dfs() . This will take matrix, r, c
• total := total + 1
• matrix[r, c] := 0
• dfs(matrix, r - 1, c)
• dfs(matrix, r, c - 1)
• dfs(matrix, r + 1, c)
• dfs(matrix, r, c + 1)
• From the main method, do the following −
• r_len := row count of matrix
• c_len := column count of matrix
• max_island := 0
• dfs(matrix, r, c)
• max_island := maximum of max_island, total
• return max_island

Let us see the following implementation to get better understanding −

 Live Demo

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Find regions with most common region size in a given boolean matrix

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Given a boolean 2D array , arr[][] of size N*M where a group of connected 1s forms an island. Two cells are said to be connected if they are adjacent to each other horizontally, vertically, or diagonally. The task is to find the position of the top left corner of all the regions with the most common region size. 

Input: arr[][] = {{0, 0, 1, 1, 0},                           {1, 0, 1, 1, 0},                           {0, 0, 0, 0, 0},                           {0, 0, 0, 0, 1}} Output: {1, 0}, {3, 4} Explanation: There are 3 regions, two with length 1 and the other with length 4. So the length of most common region is 1 and the positions of those regions are {1, 0}, {3, 4}. Input: arr[][] = {{0, 0, 1, 1, 0},                          {0, 0, 1, 1, 0},                          {0, 0, 0, 0, 0},                          {0, 0, 0, 0, 1}} Output: {0, 2} Explanation: There are 2 regions, one with length 1 and the other with 4. Since both the regions have same frequency, both are the most common region. Hence, print position of any one of the regions.

Approach: The idea is based on the problem of finding the number of islands in Boolean 2D-matrix . The idea is to store the size of the regions along with their top-left corner position in a hashmap . And then iterate through the hashmap to find the most common region and print the required regions. Follow the steps below to solve the problem:

• Initialize a hashmap to store the size of the regions along with their top-left corner position.
• Maintain a visited array to keep track of all visited cells.
• Traverse the given 2D array, row-wise , and if the current element is ‘1’ and is not visited, perform DFS traversal from this node. After the traversal, store the size of the region in the map.
• After completing the above steps, iterate over the map to find the most common region and then print all the positions corresponding to the key in the map.  

Below is the implementation of the above approach:

Time Complexity: O(N*M)   Auxiliary Space: O(N*M)

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