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 programint 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 programarr = [-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?> |
Javascript
<script>// JavaScript Program to find magic index.function magicIndex(arr, start, end){ // If No Magic Index return -1; if (start > end) return -1; let midIndex = Math.floor((start + end) / 2); let midValue = arr[midIndex]; // Magic Index Found, return it. if (midIndex == midValue) return midIndex; // Search on Left side let 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 program let arr = [ -10, -5, 2, 2, 2, 3, 4, 7, 9, 12, 13 ]; let n = arr.length; let index = magicIndex(arr, 0, n - 1); if (index == -1) document.write("No Magic Index"); else document.write("Magic Index is : " + index);// This code is contributed by Surbhi Tyagi.</script> |
Output:
Magic Index is : 2
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.
In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.
