Find a Fixed Point (Value equal to index) in a given array

1.7

Given an array of n distinct integers sorted in ascending order, write a function that returns a Fixed Point in the array, if there is any Fixed Point present in array, else returns -1. Fixed Point in an array is an index i such that arr[i] is equal to i. Note that integers in array can be negative.

Examples:

  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

Method 1 (Linear Search)
Linearly search for an index i such that arr[i] == i. Return the first such index found. Thanks to pm for suggesting this solution.

C/C++

// C/C++ program to check fixed point 
// in an array using linear search
#include<stdio.h>

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


output:

Fixed Point is 3

Time Complexity: O(n)



Method 2 (Binary Search)
First check whether middle element is Fixed Point or not. If it is, then return it; otherwise check whether index of middle element is greater than value at the index. If index is greater, then Fixed Point(s) lies on the right side of the middle point (obviously only if there is a Fixed Point). Else the Fixed Point(s) lies on left side.

C/C++

// C/C++ program to check fixed point 
// in an array using binary search
#include<stdio.h>

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 


Output:

Fixed Point is 3

Algorithmic Paradigm: Divide & Conquer
Time Complexity: O(Logn)

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