给定数组中的定点（值等于索引） - 1 使用二进制搜索索引

Question

是否可以修改此代码，使索引值从 1 开始，而不是 0？ 因此，如果数组是 0 1 3 4，程序将返回 3。

class Main 
    { 
        static int binarySearch(int arr[], int low, int high) 
        { 
            if(high >= low) 
            {    
                /* low + (high - low)/2; */
                int mid = (low + high)/2;   
                if(mid == arr[mid]) 
                    return mid; 
                if(mid > arr[mid]) 
                    return binarySearch(arr, (mid + 1), high); 
                else
                    return binarySearch(arr, low, (mid -1)); 
            } 
            
            /* Return -1 if there is  
               no Fixed Point */
            return -1; 
        } 
            
        //main function 
        public static void main(String args[]) 
        { 
            int arr[] = {-10, -1, 0, 3 , 10, 11, 30, 50, 100}; 
            int n = arr.length; 
            System.out.println("Fixed Point is " 
                       + binarySearch(arr,0, n-1));         
        }  
    } 

Answer 1

只需在调用binarySearch时将0更改为1，将n-1更改为n并在arr的0索引处添加一个随机数，即执行以下操作：

int arr[] = {99999999/*note this random large number*/, -10, -1, 0, 4/*note this 4*/ , 10, 11, 30, 50, 100}; 

和

binarySearch(arr, 1, n);

带证明的完整示例：

public class SOTest 
    { 
        static int binarySearch(int arr[], int low, int high) 
        { 
            if(high >= low) 
            {    
                /* low + (high - low)/2; */
                int mid = (low + high)/2;   
                if(mid == arr[mid]) 
                    return mid; 
                if(mid > arr[mid]) 
                    return binarySearch(arr, (mid + 1), high); 
                else
                    return binarySearch(arr, low, (mid -1)); 
            } 
            
            /* Return -1 if there is  
               no Fixed Point */
            return -1; 
        } 
            
        //main function 
        public static void main(String args[]) 
        { 
            int arr[] = {99999999/*some very positive value*/, -10, -1, 0, 4/*note this 4*/, 10, 11, 30, 50, 100}; 
            int n = arr.length; 
            System.out.println("Fixed Point is " 
                       + binarySearch(arr, 1, n));         
        }  
    } 

输出：

Fixed Point is 4

Answer 2

您可以将二分搜索替换为 (mid+1)。

class Main 
    { 
        static int binarySearch(int arr[], int low, int high) 
        { 
            if(high >= low) 
            {    
                /* low + (high - low)/2; */
                int mid = low+(high-low)/2;   
                if((mid+1) == arr[mid]) 
                    return mid+1; 
                if((mid+1) > arr[mid]) 
                    return binarySearch(arr, (mid + 1), high); 
                else
                    return binarySearch(arr, low, (mid -1)); 
            } 
            
            /* Return -1 if there is  
               no Fixed Point */
            return -1; 
        } 
            
        //main function 
        public static void main(String args[]) 
        { 
            int arr[] = {0,1,3,4}; 
            int n = arr.length; 
            System.out.println("Fixed Point is " 
                       + binarySearch(arr,0, n-1));         
        }  
    } 

输入：

arr = {0,1,3,4}

输出：

固定点是 3