### Implement Quick Sort in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm implements the Quick Sort, an efficient, comparison-based, divide and conquer sorting algorithm. It picks an element as a pivot and partitions the given array around the picked pivot.

```APIDOC
Algorithm: QuickSort
  Purpose: Sorts an array of elements using the Quick Sort algorithm.
  Method: Comparison sort, divide and conquer.
  Input:
    - array: An array of comparable elements.
  Output: The sorted array.
  Complexity: Average O(n log n), Worst O(n^2).
```

--------------------------------

### Implement Heap Sort in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm implements the Heap Sort, a comparison-based sorting algorithm that uses a binary heap data structure. It builds a max-heap (or min-heap) from the input data and repeatedly extracts the maximum (or minimum) element.

```APIDOC
Algorithm: HeapSort
  Purpose: Sorts an array of elements using the Heap Sort algorithm.
  Method: Comparison sort, uses a binary heap.
  Input:
    - array: An array of comparable elements.
  Output: The sorted array.
  Complexity: O(n log n) in worst, average, and best case.
```

--------------------------------

### Calculate Total of Arithmetic Progression Elements in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm calculates the sum of all elements in an arithmetic progression. It provides implementations using a simple loop and a more optimized approach leveraging triangular numbers.

```APIDOC
Algorithm: ArithmeticProgression
  Purpose: Calculates the sum of elements in an arithmetic progression.
  Methods:
    - Loop (Iterative): Sums elements one by one.
    - Triangular Numbers (Formula): Uses the formula n/2 * (first + last).
  Input:
    - sequence: An arithmetic progression (e.g., start, common difference, number of terms).
  Output: The total sum of elements.
```

--------------------------------

### Calculate i-th Fibonacci Element in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This section covers various methods to compute the i-th element of a Fibonacci sequence. Implementations include iterative (loop), recursive, matrix multiplication, and Binet's formula approaches, each with different performance characteristics.

```APIDOC
Algorithm: FibonacciSequence
  Purpose: Computes the i-th element of the Fibonacci sequence.
  Methods:
    - Loop (Iterative): O(n) time, O(1) space.
    - Recursion: O(2^n) time (naive), O(n) with memoization. O(n) space for call stack.
    - Matrix Multiplication: O(log n) time, O(1) space.
    - Binet's Formula: O(1) time (using floating point arithmetic, potential precision issues).
  Input:
    - i: The index of the element to find (non-negative integer).
  Output: The i-th Fibonacci number.
```

--------------------------------

### Implement Counting Sort for Integers in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm implements the Counting Sort, a non-comparison based sorting algorithm effective for sorting integers within a specific range. It counts the frequency of each element and uses that information to place elements in their sorted position.

```APIDOC
Algorithm: CountingSort
  Purpose: Sorts an array of non-negative integers.
  Method: Non-comparison sort, counting frequencies.
  Input:
    - array: An array of non-negative integers.
    - max_value: The maximum value in the array.
  Output: The sorted array.
  Limitations: Works efficiently only for integers within a limited range.
  Complexity: O(n + k) where n is number of elements, k is range of input.
```

--------------------------------

### Count Subsequence Occurrences using Dynamic Programming in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm counts the number of times a specific subsequence occurs within a larger sequence. It typically employs dynamic programming to efficiently track and sum up occurrences.

```APIDOC
Algorithm: SubsequenceCounter
  Purpose: Counts the number of times a subsequence appears in a given sequence.
  Method: Dynamic Programming
  Input:
    - mainSequence: The sequence to search within.
    - subSequence: The subsequence to count.
  Output: The total count of occurrences.
  Complexity: O(mn) where m is length of mainSequence, n is length of subSequence.
```

--------------------------------

### Implement Bubble Sort in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm implements the Bubble Sort, a simple comparison-based sorting algorithm. It repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order.

```APIDOC
Algorithm: BubbleSort
  Purpose: Sorts an array of elements using the Bubble Sort algorithm.
  Method: Comparison sort.
  Input:
    - array: An array of comparable elements.
  Output: The sorted array.
  Complexity: O(n^2) in worst and average case, O(n) in best case.
```

--------------------------------

### Find Longest Increasing Subsequence using Dynamic Programming in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm determines the longest increasing subsequence within a given sequence using dynamic programming. It can be solved in O(n log n) or O(n^2) time depending on the specific implementation.

```APIDOC
Algorithm: LongestIncreasingSubsequence
  Purpose: Finds the longest increasing subsequence (LIS) within a given sequence.
  Method: Dynamic Programming
  Input:
    - sequence: A sequence of comparable elements (e.g., int[], List<Integer>)
  Output: The longest increasing subsequence.
  Complexity: O(n^2) or O(n log n) depending on implementation.
```

--------------------------------

### Implement American Flag Sort in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm implements the American Flag Sort, an in-place distribution sort that is efficient for sorting arrays of integers or other comparable elements. It works by partitioning the array into buckets based on digit values.

```APIDOC
Algorithm: AmericanFlagSort
  Purpose: Sorts an array of elements using the American Flag Sort algorithm.
  Method: Distribution sort, in-place.
  Input:
    - array: An array of comparable elements.
  Output: The sorted array.
  Complexity: Average O(nk) where k is number of passes, Worst O(n^2).
```

--------------------------------

### Find Longest Common Subsequence using Dynamic Programming in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm finds the longest common subsequence between two sequences using a dynamic programming approach. It typically involves building a matrix to store the lengths of common subsequences for all prefixes of the input sequences.

```APIDOC
Algorithm: LongestCommonSubsequence
  Purpose: Computes the longest common subsequence (LCS) of two sequences.
  Method: Dynamic Programming
  Input:
    - sequence1: A sequence of elements (e.g., String, List)
    - sequence2: A sequence of elements (e.g., String, List)
  Output: The longest common subsequence.
  Complexity: O(mn) where m and n are the lengths of the sequences.
```

--------------------------------

### Implement Insertion Sort in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm implements the Insertion Sort, a simple sorting algorithm that builds the final sorted array (or list) one item at a time. It is much less efficient on large lists than more advanced algorithms.

```APIDOC
Algorithm: InsertionSort
  Purpose: Sorts an array of elements using the Insertion Sort algorithm.
  Method: Comparison sort, in-place.
  Input:
    - array: An array of comparable elements.
  Output: The sorted array.
  Complexity: O(n^2) in worst and average case, O(n) in best case.
```

--------------------------------

### Implement Merge Sort in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm implements the Merge Sort, an efficient, comparison-based, divide and conquer sorting algorithm. It divides the unsorted list into n sublists, each containing one element, and then repeatedly merges sublists to produce new sorted sublists until there is only one sublist remaining.

```APIDOC
Algorithm: MergeSort
  Purpose: Sorts an array of elements using the Merge Sort algorithm.
  Method: Comparison sort, divide and conquer.
  Input:
    - array: An array of comparable elements.
  Output: The sorted array.
  Complexity: O(n log n) in worst, average, and best case.
```

--------------------------------

### Implement Radix Sort for Integers in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm implements the Radix Sort, a non-comparison based integer sorting algorithm. It sorts numbers by processing individual digits, from the least significant digit to the most significant digit, using a stable sorting algorithm like Counting Sort.

```APIDOC
Algorithm: RadixSort
  Purpose: Sorts an array of non-negative integers.
  Method: Non-comparison sort, digit-by-digit.
  Input:
    - array: An array of non-negative integers.
  Output: The sorted array.
  Limitations: Works efficiently only for integers.
  Complexity: O(nk) where n is number of elements, k
```

--------------------------------

### Find Largest Sum of Contiguous Subarray using Kadane's Algorithm in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm finds the contiguous subarray within a one-dimensional array of numbers which has the largest sum. Kadane's algorithm provides an efficient O(n) solution.

```APIDOC
Algorithm: Kadane's Algorithm
  Purpose: Finds the maximum sum of a contiguous subarray.
  Method: Dynamic Programming (Greedy approach)
  Input:
    - array: An array of numbers (e.g., int[]).
  Output: The maximum sum.
  Complexity: O(n) time, O(1) space.
```

--------------------------------

### Find Longest Palindromic Subsequence using Dynamic Programming in Java

Source: https://github.com/phishman3579/java-algorithms-implementation/blob/master/README.md

This algorithm determines the longest palindromic subsequence of a given sequence. It typically uses dynamic programming, often by relating it to the longest common subsequence problem between the string and its reverse.

```APIDOC
Algorithm: LongestPalindromicSubsequence
  Purpose: Finds the longest palindromic subsequence (LPS) within a given sequence.
  Method: Dynamic Programming
  Input:
    - sequence: A sequence of characters (e.g., String).
  Output: The longest palindromic subsequence.
  Complexity: O(n^2) where n is the length of the sequence.
```

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