二分查找

原理：针对有序的数组，判断其中间值和key值的大小之差，然后进行二分

适用范围：有序的数组

复杂度：时间复杂度 O(log2n)

核心代码：

int middle = (top - tail) / 2+tail;
if (key < nums[middle]) {
	top = middle - 1;
}

if (key > nums[middle]) {
	tail = middle + 1;
}

else   return middle;
			

示例代码：

import java.util.Arrays;
import java.util.Scanner;

public class RankTest {
	public static void main(String[] args) {
		int[] nums = new int[10];
		for (int i = 0; i < nums.length; i++) {
			nums[i] = i + 10;
		}
		System.out.println(Arrays.toString(nums));
		System.out.println("N在第"+(rank(nums, 18)+1)+"位");

	}

	public static int rank(int[] nums, int key) {

		int top = nums.length-1;
		int tail = 0;

		while (tail <= top) {
			int middle = (top - tail) / 2+tail;
			if (key < nums[middle]) {
				top = middle - 1;
			}
			if (key > nums[middle]) {
				tail = middle + 1;
			}

			if (key == nums[middle]) {
				return middle;
			}
		}
		return -1;
	}
}