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Algorithm Documentation

Implementation in Java

// Java program for implementation of Bubble Sort
import java.util.*;

class BubbleSort {
    void bubbleSort(int arr[]) {
        int n = arr.length;
        for (int i = 0; i < n - 1; i++)
            for (int j = 0; j < n - i - 1; j++)
                if (arr[j] > arr[j + 1]) {
                    // swap arr[j+1] and arr[j]
                    int temp = arr[j];
                    arr[j] = arr[j + 1];
                    arr[j + 1] = temp;
                }
    }

    /* Prints the array */
    void printArray(int arr[]) {
        int n = arr.length;
        for (int i = 0; i < n; ++i)
            System.out.print(arr[i] + " ");
        System.out.println();
    }

    // Driver method to test above
    public static void main(String args[]) {
        BubbleSort ob = new BubbleSort();
        int arr[] = { 5, 1, 4, 2, 8 };
        ob.bubbleSort(arr);
        System.out.println("Sorted array");
        ob.printArray(arr);
    }
}
// Java program for implementation of Selection Sort
class SelectionSort {
    void sort(int arr[]) {
        int n = arr.length;
        for (int i = 0; i < n-1; i++) {
            int min_idx = i;
            for (int j = i+1; j < n; j++)
                if (arr[j] < arr[min_idx])
                    min_idx = j;
            
            int temp = arr[min_idx];
            arr[min_idx] = arr[i];
            arr[i] = temp;
        }
    }
}
// Java program for implementation of Insertion Sort
class InsertionSort {
    void sort(int arr[]) {
        int n = arr.length;
        for (int i = 1; i < n; ++i) {
            int key = arr[i];
            int j = i - 1;
            
            while (j >= 0 && arr[j] > key) {
                arr[j + 1] = arr[j];
                j = j - 1;
            }
            arr[j + 1] = key;
        }
    }
}
// Java program for implementation of Merge Sort
class MergeSort {
    void merge(int arr[], int l, int m, int r) {
        int n1 = m - l + 1;
        int n2 = r - m;
        
        int L[] = new int[n1];
        int R[] = new int[n2];
        
        for (int i = 0; i < n1; ++i)
            L[i] = arr[l + i];
        for (int j = 0; j < n2; ++j)
            R[j] = arr[m + 1 + j];
        
        int i = 0, j = 0, k = l;
        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) {
                arr[k] = L[i];
                i++;
            } else {
                arr[k] = R[j];
                j++;
            }
            k++;
        }
        
        while (i < n1) {
            arr[k] = L[i];
            i++;
            k++;
        }
        
        while (j < n2) {
            arr[k] = R[j];
            j++;
            k++;
        }
    }
    
    void sort(int arr[], int l, int r) {
        if (l < r) {
            int m = l + (r - l) / 2;
            sort(arr, l, m);
            sort(arr, m + 1, r);
            merge(arr, l, m, r);
        }
    }
}
// Java program for implementation of Quick Sort
class QuickSort {
    int partition(int arr[], int low, int high) {
        int pivot = arr[high];
        int i = (low - 1);
        
        for (int j = low; j < high; j++) {
            if (arr[j] <= pivot) {
                i++;
                int temp = arr[i];
                arr[i] = arr[j];
                arr[j] = temp;
            }
        }
        
        int temp = arr[i + 1];
        arr[i + 1] = arr[high];
        arr[high] = temp;
        
        return i + 1;
    }
    
    void sort(int arr[], int low, int high) {
        if (low < high) {
            int pi = partition(arr, low, high);
            sort(arr, low, pi - 1);
            sort(arr, pi + 1, high);
        }
    }
}

Time Complexity

Bubble Sort: O(nĀ²)
Selection Sort: O(nĀ²)
Insertion Sort: O(nĀ²)
Merge Sort: O(n log n)
Quick Sort: O(n log n) average

Space Complexity

Bubble Sort: O(1)
Selection Sort: O(1)
Insertion Sort: O(1)
Merge Sort: O(n)
Quick Sort: O(log n) average