# Magic Index

Posted: 24 Feb, 2021
Difficulty: Moderate

## PROBLEM STATEMENT

#### You are given a sorted array A consisting of N integers. Your task is to find the magic index in the given array.

##### Note :
``````A magic index in an array A[0 ... N - 1] is defined to be an index i such that A[i] = i.

The elements in the array can be negative.

The elements in the array can be repeated multiple times.

There can be more than one magic index in an array.
``````
##### Input Format :
``````The first line of the input contains an integer T denoting the number of test cases.

The first line of each test case contains one integer N, as described in the problem statement.

The second line of each test case contains N space-separated integers, representing the elements of the array.
``````
##### Output Format :
``````For each test case print in a new line, one integer representing the magic index of the given array or -1 if there does not exist any magic index for the given array.

In case there is more than one magic index, print any of them.
``````
##### Note :
``````You will print the magic indices, then the runner will check whether it is a magic number or not. If your output magic numbers are correct, the runner will print "Correct", else "Incorrect".
``````
##### Note :
``````You do not need to print anything, it has already been taken care of. Just implement the given function.
``````
##### Constraints :
``````1 <= T <= 10
1 <= N <= 10^5
-10^9 <= A[i] <= 10^9

Time Limit: 1sec
`````` Approach 1
• In this brute force approach, we will check each element one by one and try to find if there is any magic index in the given array or not.
• In this approach, we will initialize our answer variable (say, ans) with ans = -1.
• Then we will iterate in the array one by one (say, loop variable i) from the beginning and check if there is any magic index in our array or not.
• If we find any index in the array such that A[i] = i, then we will assign this current index i to our answer variable ans(i.e. ans = i ) and break this loop as we have found a magic index and our task is complete.
• Finally we will print this ans variable as the answer.,