Find a Fixed Point (Value equal to index) in a given array | Duplicates Allowed
Given an array of n 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[] = {-10, -5, 2, 2, 2, 3, 4, 7, 9, 12, 13}
Output: 2 // arr[2] == 2
Input: arr[] = {-10, -5, 3, 4, 7, 9}
Output: -1 // No Fixed Point
We have a solution to find fixed point in an array of distinct elements. In this post, solution for array with duplicate values is discussed.
Consider the arr[] = {-10, -5, 2, 2, 2, 3, 4, 7, 9, 12, 13}, arr[mid] = 3
If elements are not distinct, then we see arr[mid] < mid, we cannot conclude which side the fixed is on. It could be on left side or on the right side.
We know for sure that since arr[5] = 3, arr[4] couldn't be magic index because arr[4] must be less than or equal to arr[5] (the array is Sorted).
So, the general pattern of our search would be:
- Left Side: start = start, end = min(arr[midIndex], midIndex-1)
- Right Side: start = max(arr[midIndex], midIndex+1), end = end
Below is the code for above Algorithm.
C++
// CPP Program to find magic index. #include <bits/stdc++.h> using namespace std; int magicIndex(int* arr, int start, int end) { // If No Magic Index return -1; if (start > end) return -1; int midIndex = (start + end) / 2; int midValue = arr[midIndex]; // Magic Index Found, return it. if (midIndex == midValue) return midIndex; // Search on Left side int left = magicIndex(arr, start, min(midValue, midIndex - 1)); // If Found on left side, return. if (left >= 0) return left; // Return ans from right side. return magicIndex(arr, max(midValue, midIndex + 1), end); } // Driver program int main() { int arr[] = { -10, -5, 2, 2, 2, 3, 4, 7, 9, 12, 13 }; int n = sizeof(arr) / sizeof(arr[0]); int index = magicIndex(arr, 0, n - 1); if (index == -1) cout << "No Magic Index"; else cout << "Magic Index is : " << index; return 0; } |
Java
// Java Program to find magic index. class GFG { static int magicIndex(int arr[], int start, int end) { // If No Magic Index return -1; if (start > end) return -1; int midIndex = (start + end) / 2; int midValue = arr[midIndex]; // Magic Index Found, return it. if (midIndex == midValue) return midIndex; // Search on Left side int left = magicIndex(arr, start, Math.min(midValue, midIndex - 1)); // If Found on left side, return. if (left >= 0) return left; // Return ans from right side. return magicIndex(arr, Math.max(midValue, midIndex + 1),end); } // Driver code public static void main (String[] args) { int arr[] = { -10, -5, 2, 2, 2, 3, 4, 7, 9, 12, 13 }; int n = arr.length; int index = magicIndex(arr, 0, n - 1); if (index == -1) System.out.print("No Magic Index"); else System.out.print("Magic Index is : "+index); } } // This code is contributed by Anant Agarwal. |
Python 3
# Python 3 Program to find # magic index. def magicIndex(arr, start, end): # If No Magic Index return -1 if (start > end): return -1 midIndex = int((start + end) / 2) midValue = arr[midIndex] # Magic Index Found, return it. if (midIndex == midValue): return midIndex # Search on Left side left = magicIndex(arr, start, min(midValue, midIndex - 1)) # If Found on left side, return. if (left >= 0): return left # Return ans from right side. return magicIndex(arr, max(midValue, midIndex + 1), end) # Driver program arr = [-10, -5, 2, 2, 2, 3, 4, 7, 9, 12, 13] n = len(arr) index = magicIndex(arr, 0, n - 1) if (index == -1): print("No Magic Index") else: print("Magic Index is :", index) # This code is contributed by Smitha Dinesh Semwal |
C#
// C# Program to find magic index. using System; class GFG { static int magicIndex(int []arr, int start, int end) { // If No Magic Index return -1; if (start > end) return -1; int midIndex = (start + end) / 2; int midValue = arr[midIndex]; // Magic Index Found, return it. if (midIndex == midValue) return midIndex; // Search on Left side int left = magicIndex(arr, start, Math.Min(midValue, midIndex - 1)); // If Found on left side, return. if (left >= 0) return left; // Return ans from right side. return magicIndex(arr, Math.Max(midValue, midIndex + 1),end); } // Driver code public static void Main () { int []arr = { -10, -5, 2, 2, 2, 3, 4, 7, 9, 12, 13 }; int n = arr.Length; int index = magicIndex(arr, 0, n - 1); if (index == -1) Console.WriteLine("No Magic Index"); else Console.WriteLine("Magic Index is : " + index); } } // This code is contributed by vt_m. |
PHP
<?php // PHP Program to find magic index. function magicIndex($arr, $start, $end) { // If No Magic Index return -1; if ($start > $end) return -1; $midIndex = floor(($start + $end) / 2); $midValue = $arr[$midIndex]; // Magic Index Found, return it. if ($midIndex == $midValue) return $midIndex; // Search on Left side $left = magicIndex($arr, $start, min($midValue, $midIndex - 1)); // If Found on left side, return. if ($left >= 0) return $left; // Return ans from right side. return magicIndex($arr, max($midValue, $midIndex + 1), $end); } // Driver Code $arr = array(-10, -5, 2, 2, 2, 3, 4, 7, 9, 12, 13); $n = sizeof($arr); $index = magicIndex($arr, 0, $n - 1); if ($index == -1) echo "No Magic Index"; else echo "Magic Index is : " , $index; // This code is contributed by nitin mittal ?> |
Output:
Magic Index is : 2
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