排序算法解析：从基础到高级

排序算法是计算机科学中一个至关重要的概念，无论是在数据结构、数据库管理还是机器学习领域，排序算法都扮演着不可或缺的角色。本专栏旨在为读者提供一个全面的排序算法解析，从基础到高级，帮助读者深入理解排序算法的原理、实现以及应用。

第一部分：排序算法基础

1. 排序算法简介

排序算法是将一组数据按照特定的顺序重新排列的算法。它们可以根据不同的性能指标进行分类，如时间复杂度、空间复杂度和稳定性。

2. 基本概念

排序算法可以分为比较排序和非比较排序，以及原地排序和非原地排序。每种分类都有其特定的应用场景和优势。

3. 基本排序算法

以下是一些基本排序算法的Java实现：

冒泡排序

public class BubbleSort {
    public static 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] and arr[j+1]
                    int temp = arr[j];
                    arr[j] = arr[j + 1];
                    arr[j + 1] = temp;
                }
            }
        }
    }
}

选择排序

public class SelectionSort {
    public static void selectionSort(int[] arr) {
        int n = arr.length;
        for (int i = 0; i < n - 1; i++) {
            // Find the minimum element in unsorted array
            int minIndex = i;
            for (int j = i + 1; j < n; j++) {
                if (arr[j] < arr[minIndex]) {
                    minIndex = j;
                }
            }
            // Swap the found minimum element with the first element
            int temp = arr[minIndex];
            arr[minIndex] = arr[i];
            arr[i] = temp;
        }
    }
}

插入排序

public class InsertionSort {
    public static void insertionSort(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;
        }
    }
}

第二部分：中级排序算法

1. 归并排序

public 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;
        int 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) / 2;
            sort(arr, l, m);
            sort(arr, m + 1, r);
            merge(arr, l, m, r);
        }
    }
}

2. 快速排序

public class QuickSort {
    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);
        }
    }
    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;
    }
}

3. 堆排序

public class HeapSort {
    void heapify(int[] arr, int n, int i) {
        int largest = i;
        int l = 2 * i + 1;
        int r = 2 * i + 2;
        if (l < n && arr[l] > arr[largest])
            largest = l;
        if (r < n && arr[r] > arr[largest])
            largest = r;
        if (largest != i) {
            int swap = arr[i];
            arr[i] = arr[largest];
            arr[largest] = swap;
            heapify(arr, n, largest);
        }
    }
    void sort(int[] arr) {
        int n = arr.length;
        for (int i = n / 2 - 1; i >= 0; i--)
            heapify(arr, n, i);
        for (int i = n - 1; i >= 0; i--) {
            int temp = arr[0];
            arr[0] = arr[i];
            arr[i] = temp;
            heapify(arr, i, 0);
        }
    }
}

第三部分：高级排序算法

1. 希尔排序

public class ShellSort {
    void shellSort(int[] arr) {
        int n = arr.length;
        int gap = n / 2;
        while (gap > 0) {
            for (int i = gap; i < n; i++) {
                int temp = arr[i];
                int j;
                for (j = i; j >= gap && arr[j - gap] > temp; j -= gap) {
                    arr[j] = arr[j - gap];
                }
                arr[j] = temp;
            }
            gap /= 2;
        }
    }
}

2. 计数排序

public class CountingSort {
    void countingSort(int[] arr, int max) {
        int[] output = new int[arr.length];
        int[] count = new int[max + 1];
        for (int i = 0; i < arr.length; i++)
            count[arr[i]]++;
        for (int i = 1; i <= max; i++)
            count[i] += count[i - 1];
        for (int i = arr.length - 1; i >= 0; i--) {
            output[count[arr[i]] - 1] = arr[i];
            count[arr[i]]--;
        }
        for (int i = 0; i < arr.length; i++)
            arr[i] = output[i];
    }
}

3. 桶排序

public class BucketSort {
    void bucketSort(float[] arr) {
        int n = arr.length;
        int i;
        float[] b = new float[n];
        for (i = 0; i < n; ++i) {
            b[i] = arr[i];
        }
        float min = b[0];
        float max = b[0];
        for (i = 1; i < n; ++i) {
            if (b[i] < min) {
                min = b[i];
            } else if (b[i] > max) {
                max = b[i];
            }
        }
        float range = (max - min) / n;
        int[] count = new int[n];
        for (i = 0; i < n; i++) {
            count[((int) ((b[i] - min) / range))]++;
        }
        for (i = 1; i < n; i++) {
            count[i] += count[i - 1];
        }
        float[] sortedArray = new float[n];
        for (i = n - 1; i >= 0; i--) {
            sortedArray[count[((int) ((b[i] - min) / range)) - 1] - 1] = b[i];
            count[((int) ((b[i] - min) / range))]--;
        }
        for (i = 0; i < n; i++) {
            arr[i] = sortedArray[i];
        }
    }
}

4. 基数排序

public class RadixSort {
    void radixSort(int[] arr) {
        int max = getMax(arr);
        for (int exp = 1; max / exp > 0; exp *= 10) {
            countSort(arr, exp);
        }
    }
    int getMax(int[] arr) {
        int max = arr[0];
        for (int i = 1; i < arr.length; i++) {
            if (arr[i] > max)
                max = arr[i];
        }
        return max;
    }
    void countSort(int[] arr, int exp) {
        int n = arr.length;
        int[] output = new int[n];
        int[] count = new int[10];
        for (int i = 0; i < n; i++) {
            count[(arr[i] / exp) % 10]++;
        }
        for (int i = 1; i < 10; i++) {
            count[i] += count[i - 1];
        }
        for (int i = n - 1; i >= 0; i--) {
            output[count[(arr[i] / exp) % 10] - 1] = arr[i];
            count[(arr[i] / exp) % 10]--;
        }
        for (int i = 0; i < n; i++) {
            arr[i] = output[i];
        }
    }
}