java 之二分法

在Java中，除了常见的排序算法，还有几种基于二分法（Binary Search）的排序方法。这里介绍三种常见的排序方法，它们利用二分法来优化插入过程或进行查找。

1. 插入排序（Binary Insertion Sort）

这是传统插入排序的一种优化版本，使用二分查找来找到插入位置。

import java.util.Arrays;

public class BinaryInsertionSort {
    public static void main(String[] args) {
        int[] array = {64, 34, 25, 12, 22, 11, 90};
        binaryInsertionSort(array);
        System.out.println(Arrays.toString(array));
    }

    public static void binaryInsertionSort(int[] arr) {
        for (int i = 1; i < arr.length; i++) {
            int key = arr[i];
            int left = 0;
            int right = i - 1;

            // Binary search for the correct position
            while (left <= right) {
                int mid = left + (right - left) / 2;
                if (key < arr[mid]) {
                    right = mid - 1;
                } else {
                    left = mid + 1;
                }
            }

            // Shift elements to make space for key
            for (int j = i - 1; j >= left; j--) {
                arr[j + 1] = arr[j];
            }
            arr[left] = key;
        }
    }
}

2. 归并排序（Merge Sort）

归并排序是一种基于分治法的排序算法，虽然它不直接使用二分法，但其递归的过程本质上类似于二分操作。

import java.util.Arrays;

public class MergeSort {
    public static void main(String[] args) {
        int[] array = {64, 34, 25, 12, 22, 11, 90};
        mergeSort(array, 0, array.length - 1);
        System.out.println(Arrays.toString(array));
    }

    public static void mergeSort(int[] arr, int left, int right) {
        if (left < right) {
            int mid = (left + right) / 2;
            mergeSort(arr, left, mid);
            mergeSort(arr, mid + 1, right);
            merge(arr, left, mid, right);
        }
    }

    public static void merge(int[] arr, int left, int mid, int right) {
        int n1 = mid - left + 1;
        int n2 = right - mid;

        int[] L = new int[n1];
        int[] R = new int[n2];

        System.arraycopy(arr, left, L, 0, n1);
        System.arraycopy(arr, mid + 1, R, 0, n2);

        int i = 0, j = 0;
        int k = left;
        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) {
                arr[k++] = L[i++];
            } else {
                arr[k++] = R[j++];
            }
        }
        while (i < n1) {
            arr[k++] = L[i++];
        }
        while (j < n2) {
            arr[k++] = R[j++];
        }
    }
}

3. 快速排序（Quick Sort）

快速排序使用分治法，通过选取一个"基准"元素，将数组划分为两个子数组，然后递归排序这些子数组。

import java.util.Arrays;

public class QuickSort {
    public static void main(String[] args) {
        int[] array = {64, 34, 25, 12, 22, 11, 90};
        quickSort(array, 0, array.length - 1);
        System.out.println(Arrays.toString(array));
    }

    public static void quickSort(int[] arr, int low, int high) {
        if (low < high) {
            int pi = partition(arr, low, high);
            quickSort(arr, low, pi - 1);
            quickSort(arr, pi + 1, high);
        }
    }

    public static 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;
    }
}

这些算法结合了不同的排序策略，利用二分法优化了插入操作或分治策略。