A magic index in an array A[l.. .n-l] is defined to be an index such that A[i] = i. Given a sorted array of distinct integers, write a method to find a magic index, if one exists, in array A.

magicarray.cpp

#include <iostream>
#include <string>
#include <vector>
#include <math.h>
#include <map>
#include <fstream>
#include < ctime >
#include <algorithm>
#include <vector>
#include <iostream>
using namespace std;

int main(){
    int d[] = { -40,-20,-1,1, 2,3,5,6,8,12,13};
    vector<int> x(begin(d), end(d));

    int left= 0, right = x.size()-1;
    int mid = (left+right)/2;
    
    while( left <= right ){
        if( x[mid] < mid )
            left = mid+1;
        else if( x[mid] > mid )
            right = mid-1;
        else {
            cout << mid << endl;
            break;
        }
        mid = (left+right)/2;
    }

    cout << endl << "Done." <<endl;
    cin.get();
    return 0;
}