Finding all combination of portions of a number.

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SUMMARY

The discussion focuses on finding all combinations of portions that sum up to a specific number, exemplified by the number 5, which can be expressed in six distinct ways. Participants suggest using the concept of "partition numbers" to approach the problem, emphasizing the importance of visualizing the number as a series of ones and considering different bracket placements. The user seeks programming assistance to implement this solution, referencing a code snippet on Ideone that lacks clarity.

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  • Understanding of partition numbers in combinatorial mathematics
  • Familiarity with recursive programming techniques
  • Basic knowledge of Python or similar programming languages
  • Experience with algorithm optimization strategies
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  • Research the mathematical theory behind partition numbers
  • Learn about recursive algorithms for generating combinations
  • Explore Python libraries for combinatorial functions, such as itertools
  • Study dynamic programming techniques to optimize partition calculations
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Mathematicians, computer scientists, and programmers interested in combinatorial algorithms and those looking to implement efficient solutions for partitioning numbers.

lucasfeijo
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Is there a way to define in how many ways can I form a number by it's portions?

e.g: the number 5 has 6 ways:
1+1+1+1+1
2+1+1+1
2+3
2+2+1
3+1+1
4+1​

I was trying to program that and would appreciate any help!

Thanks.
 
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This not-commented code is really hard to understand, could you explain the solution please?

Thanks
 
Also search web for 'partition numbers'
 
The basic idea is, think of your number as 1+1+1+... and think of all the different ways to put brackets in this expression.
 

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