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Archive for December, 2024
In a graph, find the largest complete subgraph
December 23, 2024
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Problem
In a graph, you want to find the largest complete subgraph. A complete subgraph is a graph in which every node is connected to every other node.
Real-life example: in a party it’s a group of friends where everybody knows each other.
Solution
It’s a well-known graph problem that can be solved with the Bron-Kerbosch algorithm. You can find more info here, where you can also find a Python implementation.
How to solve a two-variable equation with Sympy
December 13, 2024
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Problem
You have a two-variable equation and you want to solve it with Python / Sympy.
Solution
Let’s see this example:
7x + 9y = 8
9x - 8y = 69What is the value of ‘x’ and ‘y’?
We could solve it manually too, of course, but let’s say we have hundreds of these. So let’s solve it with Python using the Sympy library.
>>> import sympy as sp
>>>
>>> x = sp.symbols('x')
>>> y = sp.symbols('y')
>>>
>>> eq1 = sp.Eq(7 * x + 9 * y, 8)
>>> eq2 = sp.Eq(9 * x - 8 * y, 69)
>>>
>>> system = [eq1, eq2]
>>>
>>> sol_set = sp.linsolve(system, x, y)
>>> sol_set
{(5, -3)}
>>>
>>> 7 * 5 + 9 * (-3)
8
>>> 9 * 5 - 8 * (-3)
69
Python Adventures 