关于变量公式在循环体外的错误

 1 import java.util.Scanner;
 2 public class TestArray {
 3 
 4     public static void main(String[] args){
 5         int [] array = new int[]{13,24,35,56,77,89,90};
 6         Scanner input = new Scanner(System.in);
 7         int i = input.nextInt();
 8         int start = 0;
 9         int end = array.length-1;
10         int middle ;//此处middle，只申明变量，不赋值
11         int index = -1;
12         while(start<end){
13             middle= (start+end)/2;//暂不清楚为什么只能在循环体内写入此公式，而不能在循环体外。
14             if(i==array[middle]){
15                 index = middle+1;
16                 break;
17             }
18             if(i > array[middle]){
19                 start = middle+1;
20             }
21             if(i < array[middle]){
22                 end = middle-1;
23             }
24         }
25 
26         if(index == -1){
27             System.out.println("没找到");
28         }else{
29             System.out.println("在第"+index+"位");
30         }
31     }
32 }