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‎README.md

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4. [Cartesian Product: 4 different types of products](docs/products/README.md)
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5. [Ranking of permutations & combinations: 7 different types of rankings](docs/ranking/README.md)
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6. [Number system algorithms: 3 different types for combinatorics](docs/numbersystem/README.md)
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[Home](../../README.md)
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    |    
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[Permutation Generators](../permutations/README.md)
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    |    
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[Combination Generators](../combinations/README.md)
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    |    
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[Set/Subset Generators](../sets/sets.md)
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    |    
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[Cartesian Product Generators](../products/README.md)
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[Math Functions](../calculator/README.md)
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[Ranking Algorithms](../ranking/README.md)
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[Number System Algorithms](../numbersystem/README.md)

‎docs/calculator/README.md

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[Home](../../README.md)
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    |    
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[Permutation Generators](../permutations/README.md)
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[Combination Generators](../combinations/README.md)
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[Set/Subset Generators](../sets/sets.md)
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[Cartesian Product Generators](../products/README.md)
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[Math Functions](../calculator/README.md)
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    |    
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[Ranking Algorithms](../ranking/README.md)
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[Home](../../README.md)
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</br>[Permutation Generators](../permutations/README.md)
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</br>[Combination Generators](../combinations/README.md)
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</br>[Set/Subset Generators](../sets/sets.md)
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</br>[Cartesian Product Generators](../products/README.md)
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</br>[Math Functions](../calculator/README.md)
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</br>[Ranking Algorithms](../ranking/README.md)
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</br>[Number System Algorithms](../numbersystem/README.md)
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# Math Functions in Calculator
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BigInteger result = calc.rencontresNumber(4, 1);
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System.out.println(result); // Output: 8
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```
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[Home](../../README.md)
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    |    
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[Permutation Generators](../permutations/README.md)
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[Combination Generators](../combinations/README.md)
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[Set/Subset Generators](../sets/sets.md)
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[Cartesian Product Generators](../products/README.md)
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[Math Functions](../calculator/README.md)
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[Ranking Algorithms](../ranking/README.md)
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[Home](../../README.md)
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</br>[Permutation Generators](../permutations/README.md)
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</br>[Combination Generators](../combinations/README.md)
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</br>[Set/Subset Generators](../sets/sets.md)
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</br>[Cartesian Product Generators](../products/README.md)
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</br>[Math Functions](../calculator/README.md)
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</br>[Ranking Algorithms](../ranking/README.md)
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</br>[Number System Algorithms](../numbersystem/README.md)

‎docs/combinations/README.md

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[Home](../../README.md)
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    |    
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[Permutation Generators](../permutations/README.md)
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    |    
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[Combination Generators](../combinations/README.md)
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    |    
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[Set/Subset Generators](../sets/sets.md)
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[Cartesian Product Generators](../products/README.md)
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[Math Functions](../calculator/README.md)
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    |    
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[Ranking Algorithms](../ranking/README.md)
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[Home](../../README.md)
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</br>[Permutation Generators](../permutations/README.md)
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</br>[Combination Generators](../combinations/README.md)
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</br>[Set/Subset Generators](../sets/sets.md)
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</br>[Cartesian Product Generators](../products/README.md)
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</br>[Math Functions](../calculator/README.md)
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</br>[Ranking Algorithms](../ranking/README.md)
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</br>[Number System Algorithms](../numbersystem/README.md)
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# Combination Generators
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.fromSequence(iterable)
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.stream().toList();
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```
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[Home](../../README.md)
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    |    
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[Permutation Generators](../permutations/README.md)
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[Combination Generators](../combinations/README.md)
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[Set/Subset Generators](../sets/sets.md)
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[Cartesian Product Generators](../products/README.md)
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[Math Functions](../calculator/README.md)
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[Ranking Algorithms](../ranking/README.md)
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[Home](../../README.md)
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</br>[Permutation Generators](../permutations/README.md)
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</br>[Combination Generators](../combinations/README.md)
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</br>[Set/Subset Generators](../sets/sets.md)
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</br>[Cartesian Product Generators](../products/README.md)
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</br>[Math Functions](../calculator/README.md)
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</br>[Ranking Algorithms](../ranking/README.md)
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</br>[Number System Algorithms](../numbersystem/README.md)

‎docs/numbersystem/README.md

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[Home](../../README.md)
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</br>[Permutation Generators](../permutations/README.md)
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</br>[Combination Generators](../combinations/README.md)
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</br>[Set/Subset Generators](../sets/sets.md)
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</br>[Cartesian Product Generators](../products/README.md)
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</br>[Math Functions](../calculator/README.md)
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</br>[Ranking Algorithms](../ranking/README.md)
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</br>[Number System Algorithms](../numbersystem/README.md)
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# Number System Algorithms
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JNumberTools provides three number system algorithms related to combinatorics, enabling efficient encoding and decoding of permutations and combinations. These APIs support `BigInteger` for large indices, making them suitable for applications in combinatorial generation, ranking, and data compression.
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**Currently Available Algorithms**
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1. [Factorial Number System (Factoradic)](#1-factorial-number-system-factoradic)
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2. [Permutation Number System (Permutadic)](#2-permutation-number-system-permutadic)
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3. [Combinatorial Number System (Combinadic)](#3-combinatorial-number-system-combinadic)
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---
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### 1. Factorial Number System (Factoradic)
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The Factorial Number System, also known as Factoradic, represents numbers as sums of factorials, where each digit is constrained by its position. It is used to encode and decode unique permutations efficiently.
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```java
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// Convert a number to its factoradic representation
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BigInteger number = BigInteger.valueOf(859);
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int[] factoradic = JNumberTools.numberSystem().factoradic(number);
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System.out.println(Arrays.toString(factoradic)); // Output: [7, 1, 2, 0, 1]
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// Convert a factoradic representation back to a number
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BigInteger result = JNumberTools.numberSystem().fromFactoradic(new int[]{7, 1, 2, 0, 1});
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System.out.println(result); // Output: 859
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```
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### 2. Permutation Number System (Permutadic)
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The Permutation Number System, or Permutadic, is a generalization of the factoradic system for k-permutations. It encodes k-permutations using a mixed-radix system, enabling efficient generation of permutations at specific indices.
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```java
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// Convert a number to its permutadic representation for n=5, k=3
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BigInteger number = BigInteger.valueOf(100);
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int[] permutadic = JNumberTools.numberSystem().permutadic(5, 3, number);
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System.out.println(Arrays.toString(permutadic)); // Output: [4, 2, 0]
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// Convert a permutadic representation back to a number
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BigInteger result = JNumberTools.numberSystem().fromPermutadic(5, new int[]{4, 2, 0});
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System.out.println(result); // Output: 100
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```
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### 3. Combinatorial Number System (Combinadic)
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The Combinatorial Number System, or Combinadic, encodes combinations by representing their indices as sums of binomial coefficients. It is used to efficiently generate and rank combinations.
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```java
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// Convert a number to its combinadic representation for n=5, k=3
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BigInteger number = BigInteger.valueOf(35);
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int[] combinadic = JNumberTools.numberSystem().combinadic(5, 3, number);
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System.out.println(Arrays.toString(combinadic)); // Output: [4, 3, 1]
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// Convert a combinadic representation back to a number
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BigInteger result = JNumberTools.numberSystem().fromCombinadic(new int[]{4, 3, 1});
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System.out.println(result); // Output: 35
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```
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[Home](../../README.md)
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</br>[Permutation Generators](../permutations/README.md)
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</br>[Combination Generators](../combinations/README.md)
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</br>[Set/Subset Generators](../sets/sets.md)
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</br>[Cartesian Product Generators](../products/README.md)
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</br>[Math Functions](../calculator/README.md)
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</br>[Ranking Algorithms](../ranking/README.md)
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</br>[Number System Algorithms](../numbersystem/README.md)

‎docs/permutations/README.md

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[Home](../../README.md)
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[Permutation Generators](../permutations/README.md)
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[Combination Generators](../combinations/README.md)
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[Set/Subset Generators](../sets/sets.md)
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[Cartesian Product Generators](../products/README.md)
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[Math Functions](../calculator/README.md)
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[Ranking Algorithms](../ranking/README.md)
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[Home](../../README.md)
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</br>[Permutation Generators](../permutations/README.md)
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</br>[Combination Generators](../combinations/README.md)
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</br>[Set/Subset Generators](../sets/sets.md)
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</br>[Cartesian Product Generators](../products/README.md)
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</br>[Math Functions](../calculator/README.md)
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</br>[Ranking Algorithms](../ranking/README.md)
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</br>[Number System Algorithms](../numbersystem/README.md)
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# Permutation Generators
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.stream().toList();
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```
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[Permutation Generators](../permutations/README.md)
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[Combination Generators](../combinations/README.md)
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[Set/Subset Generators](../sets/sets.md)
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[Cartesian Product Generators](../products/README.md)
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[Math Functions](../calculator/README.md)
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[Ranking Algorithms](../ranking/README.md)
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[Home](../../README.md)
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</br>[Permutation Generators](../permutations/README.md)
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</br>[Combination Generators](../combinations/README.md)
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</br>[Set/Subset Generators](../sets/sets.md)
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</br>[Cartesian Product Generators](../products/README.md)
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</br>[Math Functions](../calculator/README.md)
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</br>[Ranking Algorithms](../ranking/README.md)
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</br>[Number System Algorithms](../numbersystem/README.md)

‎docs/products/README.md

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[Home](../../README.md)    |    [Permutation Generators](../permutations/README.md)    |    
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[Combination Generators](../combinations/README.md)    |    [Set/subset Generators](../sets/sets.md)    |    [Cartesian Product Generators](../products/README.md)
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[Home](../../README.md)
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</br>[Permutation Generators](../permutations/README.md)
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</br>[Combination Generators](../combinations/README.md)
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</br>[Set/Subset Generators](../sets/sets.md)
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</br>[Cartesian Product Generators](../products/README.md)
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</br>[Math Functions](../calculator/README.md)
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</br>[Ranking Algorithms](../ranking/README.md)
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</br>[Number System Algorithms](../numbersystem/README.md)
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.lexOrderMth(1_000_000_000_000_000_000L, 0)
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[Home](../../README.md)
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</br>[Permutation Generators](../permutations/README.md)
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</br>[Combination Generators](../combinations/README.md)
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</br>[Set/Subset Generators](../sets/sets.md)
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</br>[Cartesian Product Generators](../products/README.md)
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</br>[Math Functions](../calculator/README.md)
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</br>[Ranking Algorithms](../ranking/README.md)
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</br>[Number System Algorithms](../numbersystem/README.md)

‎docs/ranking/README.md

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[Home](../../README.md)
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</br>[Permutation Generators](../permutations/README.md)
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</br>[Combination Generators](../combinations/README.md)
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</br>[Set/Subset Generators](../sets/sets.md)
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</br>[Cartesian Product Generators](../products/README.md)
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</br>[Math Functions](../calculator/README.md)
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</br>[Ranking Algorithms](../ranking/README.md)
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</br>[Number System Algorithms](../numbersystem/README.md)
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# Ranking Algorithms
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JNumberTools provides the following 7 ranking algorithms for permutations and combinations. These APIs calculate the lexicographical rank of a given permutation or combination, supporting `BigInteger` for large indices, enabling efficient ranking even in massive combinatorial spaces.
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**Currently Available Algorithms**
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1. [Ranking of Unique Permutation](#1-ranking-of-unique-permutation)
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2. [Ranking of k-Permutation](#2-ranking-of-k-permutation)
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3. [Ranking of Repetitive Permutation](#3-ranking-of-repetitive-permutation)
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4. [Ranking of Unique Combination](#4-ranking-of-unique-combination)
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5. [Ranking of Repetitive Combination](#5-ranking-of-repetitive-combination)
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6. [Ranking of Multiset Permutation](#6-ranking-of-multiset-permutation)
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7. [Ranking of Multiset Combination](#7-ranking-of-multiset-combination)
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---
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### 1. Ranking of Unique Permutation
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Calculates the rank of a unique permutation starting from 0th. For example, there are a total of 4!=24 permutations of [0,1,2,3], where the first permutation [0,1,2,3] has rank 0 and the last permutation [3,2,1,0] has the rank of 23.
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```java
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BigInteger rank = JNumberTools.rankOf().uniquePermutation(3, 2, 1, 0);
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```
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### 2. Ranking of k-Permutation
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Calculates the rank of a k-permutation. For example, if we select 5 elements out of 8 [0,1,2,3,4,5,6,7], there are a total of <sup>8</sup>P<sub>5</sub> permutations, out of which the 1000<sup>th</sup> permutation is [8,4,6,2,0].
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```java
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// Will return 1000
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BigInteger rank = JNumberTools.rankOf().kPermutation(8, 4, 6, 2, 0);
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```
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### 3. Ranking of Repetitive Permutation
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Calculates the rank of a repetitive permutation.
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```java
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// 1,0,0,1 is the 9th repeated permutation of two digits 0 and 1
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int elementCount = 2;
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BigInteger result = JNumberTools.rankOf()
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.repeatedPermutation(elementCount, new Integer[]{1, 0, 0, 1});
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```
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### 4. Ranking of Unique Combination
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Calculates the rank of a given combination. For example, if we generate combinations of 4 elements out of 8 in lex order, the 35th combination will be [1,2,3,4]. Given the input 8 and [1,2,3,4], the API returns 35, the rank of the combination.
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```java
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```
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### 5. Ranking of Repetitive Combination
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This feature is currently in development and will be available in a future release.
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### 6. Ranking of Multiset Permutation
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This feature is currently in development and will be available in a future release.
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### 7. Ranking of Multiset Combination
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This feature is currently in development and will be available in a future release.
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[Home](../../README.md)
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</br>[Permutation Generators](../permutations/README.md)
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</br>[Combination Generators](../combinations/README.md)
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</br>[Set/Subset Generators](../sets/sets.md)
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</br>[Cartesian Product Generators](../products/README.md)
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</br>[Math Functions](../calculator/README.md)
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</br>[Ranking Algorithms](../ranking/README.md)
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</br>[Number System Algorithms](../numbersystem/README.md)

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