二叉搜索条件

Binary search condition

本文关键字：条件搜索更新时间：2023-10-16

我总是对二叉搜索算法的状况感到困惑，它在编程竞赛中花费了我很多时间。我的问题是何时使用这些条件中的每一个？
1. while (low < high)
2. while (high - low > 1)
3. while (low <= high)
low = 解决方案集中的最小值。
high = 解决方案集中的最大值。

while (low < high)在搜索范围[low, high)时使用。更新high 时，请使用 high = mid 。更新low时，请使用 low = mid + 1 。
while (high - low > 1)在搜索范围(low, high)时使用。更新high时，请使用 high = mid 。更新low 时，请使用 low = mid 。
while (low <= high) 在搜索范围[low, high]时使用。更新high时，请使用 high = mid - 1 。更新low 时，请使用 low = mid + 1 。

代码如下：

public class BinarySearch {
    public static void main(String[] args) {
        Integer[] nums = { 4, 9, 12, 18, 20, 26, 28, 29, 55 };
        for (int i = 0; i < nums.length; ++i) {
            System.out.println(binarySearch1(nums, nums[i]));
            System.out.println(binarySearch2(nums, nums[i]));
            System.out.println(binarySearch3(nums, nums[i]));
        }
    }
    public static <T extends Comparable<T>> int binarySearch1(T[] array, T value) {
        final int NOT_FOUND = -1;
        int low = 0;
        int high = array.length;
        while (low < high) {
            int mid = low + (high - low) / 2;
            int comparison = array[mid].compareTo(value);
            if (comparison == 0) {
                return mid;
            } else if (comparison > 0) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return NOT_FOUND;
    }
    public static <T extends Comparable<T>> int binarySearch2(T[] array, T value) {
        final int NOT_FOUND = -1;
        int low = -1;
        int high = array.length;
        while (high - low > 1) {
            int mid = low + (high - low) / 2;
            int comparison = array[mid].compareTo(value);
            if (comparison == 0) {
                return mid;
            } else if (comparison > 0) {
                high = mid;
            } else {
                low = mid;
            }
        }
        return NOT_FOUND;
    }
    public static <T extends Comparable<T>> int binarySearch3(T[] array, T value) {
        final int NOT_FOUND = -1;
        int low = 0;
        int high = array.length - 1;
        while (low <= high) {
            int mid = low + (high - low) / 2;
            int comparison = array[mid].compareTo(value);
            if (comparison == 0) {
                return mid;
            } else if (comparison > 0) {
                high = mid - 1;
            } else {
                low = mid + 1;
            }
        }
        return NOT_FOUND;
    }
}