Bogo Sort 🤪

BogoSort is a super inefficient sorting algorithm based on the "generate and test" paradigm. This function successively generates permutations of its input until it finds one that is sorted.

The probability that any given randomly generated sort is correct is (1 / n!), and the average case time complexity is O(n!), where n is the number of elements in the array.

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⚠️ Warning

Using BogoSort in real-world applications is strongly discouraged. It’s purely for educational or entertainment purposes.

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🧠 How It Works

1. Shuffle: Randomly shuffle the array.
2. Check: Verify if the array is sorted.
3. Repeat: If not sorted, repeat the process.

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🖥️ Workflow Example

Initial Array: [3, 1, 2]

1. Shuffle → [2, 3, 1] (not sorted)
2. Shuffle → [1, 3, 2] (not sorted)
3. Shuffle → [1, 2, 3] (sorted!)

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📊 Visualization

graph TD
    A[Unsorted Array] --> B[Shuffle]
    B --> C{Is Sorted?}
    C -->|No| B
    C -->|Yes| D[Sorted Array]

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⚖️ Comparison with Other Algorithms

Algorithm	Time Complexity	Practical Use
BogoSort	O(n!)	Never
QuickSort	O(n log n)	Commonly used
BubbleSort	O(n²)	Rarely used

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⚙️ Implementation

Java

BogoSort.java

public class BogoSort {
    public static void bogoSort(ArrayList<Integer> array) {
        while (!isSorted(array)) {
            Collections.shuffle(array);
        }
    }

    private static boolean isSorted(ArrayList<Integer> list) {
        for (int i = 0; i < list.size() - 1; i++) {
            if (list.get(i) > list.get(i + 1)) {
                return false;
            }
        }
        return true;
    }
}

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🚨 Important Notes

• ⏳ Time Complexity: O(n!) (extremely inefficient).
• 🛑 Practical Use: Never use in production—this is a theoretical implementation.
• ✅ Edge Cases:
• For empty lists or single-element lists, the sort completes immediately.
• 🔍 Sort Check: The isSorted() helper method checks for ascending order.
• 🎲 Randomization: Uses Java's built-in Collections.shuffle() for shuffling.

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🤔 Why Does This Exist?

BogoSort is primarily used as a joke algorithm or for educational purposes to demonstrate the worst-case scenario in sorting algorithms. It’s a fun way to explain the concept of randomized algorithms and time complexity.

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🎉 Fun Fact

If you used BogoSort to sort a deck of 52 playing cards, it could take longer than the age of the universe to finish!