在给定数组中找到一个固定点（值等于索引）

给定一个按升序排列的 n 个不同整数的数组，编写一个函数，返回数组中的一个定点，如果数组中存在任何定点，否则返回 -1。数组中的不动点是一个索引 i，使得 arr[i] 等于 i。请注意，数组中的整数可以为负数。
例子：

Input: arr[] = {-10, -5, 0, 3, 7}
  Output: 3  // arr[3] == 3 

  Input: arr[] = {0, 2, 5, 8, 17}
  Output: 0  // arr[0] == 0 


  Input: arr[] = {-10, -5, 3, 4, 7, 9}
  Output: -1  // No Fixed Point

方法一(线性搜索)
线性搜索索引 i 使得 arr[i] == i。返回找到的第一个此类索引。感谢 pm 提出这个解决方案。

C++

// C++ program to check fixed point
// in an array using linear search
#include 
using namespace std;
 
int linearSearch(int arr[], int n)
{
    int i;
    for(i = 0; i < n; i++)
    {
        if(arr[i] == i)
            return i;
    }
 
    /* If no fixed point present then return -1 */
    return -1;
}
 
/* Driver code */
int main()
{
    int arr[] = {-10, -1, 0, 3, 10, 11, 30, 50, 100};
    int n = sizeof(arr)/sizeof(arr[0]);
    cout << "Fixed Point is " << linearSearch(arr, n);
    return 0;
}
 
// This is code is contributed by rathbhupendra

C

// C program to check fixed point
// in an array using linear search
#include
 
int linearSearch(int arr[], int n)
{
    int i;
    for(i = 0; i < n; i++)
    {
        if(arr[i] == i)
            return i;
    }
 
    /* If no fixed point present then return -1 */
    return -1;
}
 
/* Driver program to check above functions */
int main()
{
    int arr[] = {-10, -1, 0, 3, 10, 11, 30, 50, 100};
    int n = sizeof(arr)/sizeof(arr[0]);
    printf("Fixed Point is %d", linearSearch(arr, n));
    getchar();
    return 0;
}

Java

// Java program to check fixed point
// in an array using linear search
  
class Main
{
    static int linearSearch(int arr[], int n)
    {
        int i;
        for(i = 0; i < n; i++)
        {
            if(arr[i] == i)
                return i;
        }
       
        /* If no fixed point present
           then return -1 */
        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 "
                     + linearSearch(arr, n));
    }
}

Python

# Python program to check fixed point
# in an array using linear search
def linearSearch(arr, n):
    for i in range(n):
        if arr[i] is i:
            return i
    # If no fixed point present then return -1
    return -1
 
# Driver program to check above functions
arr = [-10, -1, 0, 3, 10, 11, 30, 50, 100]
n = len(arr)
print("Fixed Point is " + str(linearSearch(arr,n)))
 
# This code is contributed by Pratik Chhajer

C#

// C# program to check fixed point
// in an array using linear search
using System;
 
class GFG
{
    static int linearSearch(int []arr, int n)
    {
        int i;
        for(i = 0; i < n; i++)
        {
            if(arr[i] == i)
                return i;
        }
         
        /* If no fixed point present
        then return -1 */
        return -1;
    }
    // Driver code
    public static void Main()
    {
        int []arr = {-10, -1, 0, 3, 10, 11, 30, 50, 100};
        int n = arr.Length;
        Console.Write("Fixed Point is "+ linearSearch(arr, n));
    }
}
 
// This code is contributed by Sam007

Javascript

 
// JavaScript program to check fixed point
// in an array using linear search
 
    function linearSearch(arr, n)
    {
        let i;
        for(i = 0; i < n; i++)
        {
            if(arr[i] == i)
                return i;
        }
     
        /* If no fixed point present
        then return -1 */
        return -1;
    }
 
// Driver Code
    let arr = [-10, -1, 0, 3, 10, 11, 30, 50, 100];
    let n = arr.length;
    document.write("Fixed Point is "
                + linearSearch(arr, n));
 

输出：

Fixed Point is 3

时间复杂度：O(n)
方法二(二分查找)
首先检查中间元素是否为Fixed Point。如果是，则返回；否则检查中间元素的索引是否大于索引处的值。如果 index 更大，则 Fixed Point(s) 位于中间点的右侧(显然只有在有 Fixed Point 时)。否则，固定点位于左侧。

C++

// C++ program to check fixed point
// in an array using binary search
#include 
using namespace std;
 
int binarySearch(int arr[], int low, int high)
{
    if(high >= low)
    {
        int mid = (low + high)/2; /*low + (high - low)/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;
}
 
/* Driver code */
int main()
{
    int arr[10] = {-10, -1, 0, 3, 10, 11, 30, 50, 100};
    int n = sizeof(arr)/sizeof(arr[0]);
    cout<<"Fixed Point is "<< binarySearch(arr, 0, n-1);
    return 0;
}
 
// This code is contributed by rathbhupendra

C

// C program to check fixed point
// in an array using binary search
#include
 
int binarySearch(int arr[], int low, int high)
{
    if(high >= low)
    {
        int mid = (low + high)/2;  /*low + (high - low)/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;
}
 
/* Driver program to check above functions */
int main()
{
    int arr[10] = {-10, -1, 0, 3, 10, 11, 30, 50, 100};
    int n = sizeof(arr)/sizeof(arr[0]);
    printf("Fixed Point is %d", binarySearch(arr, 0, n-1));
    getchar();
    return 0;
}

Java

// Java program to check fixed point
// in an array using binary search
 
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));       
    }
}

Python

# Python program to check fixed point
# in an array using binary search
def binarySearch(arr, low, high):
    if high >= low:
        mid = (low + high)//2
     
    if mid is 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
 
 
# Driver program to check above functions */
arr = [-10, -1, 0, 3, 10, 11, 30, 50, 100]
n = len(arr)
print("Fixed Point is " + str(binarySearch(arr, 0, n-1)))
 
 
# This code is contributed by Pratik Chhajer

C＃

// C# program to check fixed point
// in an array using binary search
using System;
 
class GFG
{
    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;
    }
         
    // Driver code
    public static void Main()
    {
        int []arr = {-10, -1, 0, 3 , 10, 11, 30, 50, 100};
        int n = arr.Length;
        Console.Write("Fixed Point is "+ binarySearch(arr,0, n-1));    
    }
}
// This code is contributed by Sam007

PHP

= $low)
    {
         
         /*low + (high - low)/2;*/
        $mid = (int)(($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 Po*/
    return -1;
}
 
    // Driver Code
    $arr = array(-10, -1, 0, 3, 10,
                  11, 30, 50, 100);
    $n = count($arr);
    echo "Fixed Point is: "
        . binarySearch($arr, 0, $n - 1);
         
// This code is contributed by Anuj_67
?>

Javascript

 
// javascript program to check fixed point
// in an array using binary search 
 
 
function binarySearch( arr, low, high)
{
    
    if(high >= low)
    {
        let mid = Math.floor((low + high)/2); /*low + (high - low)/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;
}
 
    // Driver program
    let arr = [-10, -1, 0, 3, 10, 11, 30, 50, 100];
    let n = arr.length;
    document.write("Fixed Point is "+ binarySearch(arr, 0, n-1));
     
    // This code is contributed by jana_sayantan.

输出：

Fixed Point is 3

算法范式：分而治之
时间复杂度：O(Logn)

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